Mean Wind and Turbulence Conditions in the Boundary Layer above Forests

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ACTA UNIVERSITATIS

UPSALIENSIS UPPSALA

Digital Comprehensive Summaries of Uppsala Dissertations

from the Faculty of Science and Technology

1212

Mean Wind and Turbulence

Conditions in the Boundary Layer

above Forests

JOHAN ARNQVIST

ISSN 1651-6214 ISBN 978-91-554-9123-9

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Dissertation presented at Uppsala University to be publicly examined in Ekmansalen, EBC, Norbyvägen 14, Uppsala, Friday, 6 February 2015 at 13:00 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Søren Larsen (DTU).

Abstract

Arnqvist, J. 2015. Mean Wind and Turbulence Conditions in the Boundary Layer above Forests. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1212. 47 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9123-9.

As wind turbines have grown, new installation areas become possible. Placing wind turbines in forested landscapes introduce uncertainties to the wind resource estimation. Even though close-to-canopy processes have been studied intensively during the last thirty years, the focus has mostly been on exchange processes and the height span of the studies has been below the rotor of a modern wind turbine.

This thesis contains analysis of new measurements from a 138 m high tower in a forested landscape. The previous knowledge of near-canopy processes is extended to the region above the roughness sublayer. It is shown that above the roughness sublayer, the surface layer behaves as over low vegetation, and Monin-Obukhov similarity is shown to hold for several variables. However, in stable stratification, effects that could be linked to the boundary layer depth are shown to be present in the measurements. These include wind turning with height, the behaviour of the turbulence length scale and the curvature of the wind profile.

Two new analytical models are presented in the thesis. One is a flux-profile expression in the roughness sublayer, which allows for analytical integration of the wind gradient. The model suggests that the roughness-sublayer effect depends on stratification and that the aerodynamic roughness length changes with stability. A decrease of roughness length in stable stratification is confirmed with a new method to determine the roughness length using measurements from the 138 m tower.

The other model determines the spectral tensor in stable stratification using analytical solution to the rapid distortion equations for stratified shear flow, with homogeneous stratification and shear. By using a formulation for the integration time of the distortions of an isotropic spectrum, a model is derived which provides the cross spectra of velocity and temperature at any two given points in space.

Finally the existence of waves in the wind over forests is investigated and it is concluded that the Kelvin-Helmholtz instability can create waves which are coherent in time and exist over the entire height span of wind turbine rotors. Linear wave theory is shown to be able to explain certain features of the waves.

Keywords: Wind power, Forest, Turbulence, Waves, Spectra, Wind model, Atmospheric stability

Johan Arnqvist, Department of Earth Sciences, LUVAL, Villav. 16, Uppsala University, SE-75236 Uppsala, Sweden.

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vad som av vinden viskas, är ingen av oss, som vet, ty susande språkets mening är skogarnas hemlighet Gustav Fröding, I skogen

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List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Arnqvist J and Bergström H, 2014. Flux-proﬁle relation with roughness sublayer correction. Quarterly Journal of the Royal

Meteorological Society DOI: 10.1002/qj.2426

II Arnqvist J, Segalini A, Dellwik E and Bergström H, 2014. Wind statistics from a forested landscape. Accepted for publication in

Boundary Layer Meteorology

III Segalini A and Arnqvist J, 2014. A spectral model for stably stratiﬁed turbulence. Submitted to Journal of Fluid Mechanics

IV Arnqvist J, Nappo C and Bergström H, 2014. Canopy waves, observations and predictions from linear theory. To be submitted to

Agricultural and Forest Meteorology

In paper I and IV I had the main responsibility for doing the analysis, struc-turing the paper and writing the text. I developed the theory in paper I. In paper II I had the main responsibility for coordinating the writing process and I wrote most of the text. I contributed in post processing the measurement data used in paper II and shared responsibility for doing the analysis. In paper III I contributed to writing the text, shared the responsibility for analysing the data and the model output and shared responsibility for ﬁnding suitable expressions for the model parameters.

The following publication is not included in the thesis

Dellwik E, Arnqvist J, Bergström H, Mohr M, Söderberg S, Hahmann A N. Meso-scale modeling of a forested landscape Journal of Physics: Confer-ence Series (Online) (ISSN: 1742-6596) (DOI: http://dx.doi.org/10.1088/1742-6596/524/1/012121), vol: 524, issue: 1, 2014

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1. Introduction

Wind power is a growing industry. Increasing awareness of the risk for climate change induced by anthropogenic activities together with increasing energy demands has spawned the rise of wind industry. As the industry has grown over the last thirty years, so has the turbine size. The hub height of a typical wind turbine has grown, from being 20-30 m in 1990 to around 120 m twenty years later. The growth of the turbines has opened up to new possible sites, of which forested areas are particularly interesting for Sweden since more than half of the country is covered with forest.

Wind power is subject to two basic requirements: First, sufﬁcient wind, and second, a functioning turbine. Forest conditions can be a challenge to both those requirements. It is well known that the wind is lower in forested areas, yet at some height the wind must be equal to that over low vegetation since the driving pressure force is the same. Building high enough turbines should therefore enable high enough mean wind. The operation of wind turbines is a more complex matter which involves the turbulent nature of the wind. Turbu-lent gusts impose loads on wind turbines and they must be built to withstand a certain amount of turbulence to avoid too much downtime due to maintenance and repair. While it is intuitively clear that a rough surface such as a forest should lead to more turbulence, the reality is more complex. Temperature gra-dients in the atmosphere work to amplify or reduce turbulence, and it is less clear how forests affects temperature gradients.

1.1 Aim of this thesis

In connection to the growing demand for precise predictions on loads and yields of wind power in forested areas this thesis aims to improve the knowl-edge of wind conditions in the height span relevant to wind energy. Basically, two main questions can be identiﬁed for wind power in forested areas:

• How high must a wind turbine be over the forest to produce a sufﬁcient

amount of electricity?

• How sturdy must a wind turbine be to withstand the turbulence created

by the forest?

These two questions are the basis for the research leading up to this thesis. The authors’ work is however only covering the part of these questions related in a direct way to the wind. It is thus relevant to rephrase the questions in terms of the wind conditions.

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• How does the mean wind proﬁle behave over forests?

• How does turbulence generated by forests decay with height?

• Is the turbulence over forests any different from that over low

vegeta-tion?

The scientiﬁc papers contained in this thesis are all directly related to the above questions, and the text in this thesis discuss the results of the papers in context of the above questions.

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2. Background

2.1 The atmospheric boundary layer over forests

The atmospheric boundary layer is deﬁned by the presence of turbulence. Tur-bulent eddies communicate anything that happens at the surface, e. g. heating by the sun or a change in surface roughness, rapidly through the boundary layer. The depth of the atmospheric boundary layer is varying between ap-proximately 100 m to 2 km, with lower values during the night, when cooling of the surface work to reduce the turbulence, and higher during the day, when heating of the surface helps to mix the air.

The lowest 10% of the boundary layer is called the surface layer. Within the surface layer the air is in almost direct contact with the ground, and the turbulence is characterized by a cascade of eddy sizes, giving it predictable features, such as a logarithmic wind proﬁle and turbulence properties that are relatively constant with height. Over low vegetation, the surface layer starts at the ground, but over forests it has been observed that the ﬂow within the forest behaves differently, so the surface layer starts at a height d, the so called

displacement height, above the ground.

Within the forest turbulence intensity is very high, around 100%, implying that a typical change of wind due to a turbulent gust is of the same magnitude as the mean wind. The turbulent energy is also much more evenly spread out, with turbulent ﬂuctuations of the same size in all directions. Within the forest, the wind speed increase close to exponentially with height, which is seen both from theoretical considerations and observations.

Above the forest, close to the forest edge, there is another layer, the

rough-ness sublayer. The roughrough-ness sublayer is deﬁned by the fact that turbulent

mixing is more efﬁcient there than in the surface layer, and therefore tradi-tional relationships between turbulent transport and gradients of mean values must be adjusted. A schematic picture of the turbulence in the surface layer, the roughness sublayer, the forest layer as well as a typical scale of forest to turbine is shown in Figure 2.1

2.2 Scaling parameters

The concept of similarity says that once proper key parameters has been iden-tified, all flows can be compared to each other, no matter the scale of the flow, since all properties scale with the key parameters. In the atmospheric surface layer the key parameters are:

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Figure 2.1. A schematic picture of the ﬂow regimes in forest terrain. The tree height

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Variable name Physical interpretation Dimension

z Height m

(u_w2_{+ v}_w2₎1/2 _{Vertical momentum ﬂux} _m2_s−2

−w_t _{Vertical temperature ﬂux} _ms−1_K g/T0 Buoyancy ms−2K−1

where overbar denotes an averaged quantity so that u= u − ¯u. u, v and

w, are the ﬂuctuating velocity in longitudinal, lateral and vertical direction respectively, tis the ﬂuctuations in temperature, T0is the background

temper-ature and g is the gravitational acceleration.

The use of similarity theory in the atmospheric surface layer is well known as the Monin-Obukhov similarity theory (Wyngaard, 2010). In the surface layer, gradients of turbulent fluxes are small compared to gradients of mean values, so fluxes are typically evaluated just above the surface and then as-sumed constant with height. It is conventional to rewrite the surface fluxes to a velocity scale u_∗= (uw2+vw2)1/4, and a temperature scale T_∗= −wt/u_∗.The buoyancy parameter can be given further physical meaning by the hydrostatic equation and the gas law. It can then be expressed as a measure of the weight of a thin vertical slab of the atmosphere, and is thus useful in creating a mea-sure of how prone the atmosphere is to vertical movement.

In order to create a similarity expression for how the wind speed, U ,changes in the surface layer as a function of the height, z, we must ﬁrst construct a length scale, l, from the other key parameters so that we can relate z to and independent scale. The only way to construct a length scale is

l= −u

4

∗T0

T_∗g (2.1)

This scale was ﬁrst identiﬁed by Obukhov in 1946, and its product with the reciprocal of the non-dimensional von Kármán constant, 1/κ, is referred to as the Obukhov length, L. We can now construct the wind speed gradient from dimensional arguments

∂U ∂z =

u_∗

κzφ(z/L). (2.2)

φ(z/L) is a universal function of the ratio z/L, which is a measure of the ratio

between inertial scale of the turbulent eddies (z) to the buoyancy scale of the turbulent eddies (L).

With the correction that over forests the relevant height is not z, but rather (z − d), Equation 2.2 accurately describes the wind gradient in the surface layer over forests, which is shown in Paper II. Closer to the tree tops, in the roughness sublayer, Equation 2.2 is invalid. The similarity theory can however be widened by introducing new key parameters in addition to the set that is valid for surface layers.

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In the roughness sublayer, another length scale than z− d becomes rele-vant. The choice of this length scale has been discussed in several publications (Kaimal and Finnigan, 1994; Physick and Garratt, 1995; Harman and Finni-gan, 2007; Ridder, 2009) and it is shown in Paper I that h− d, where h is the tree height, is a relevant length scale for the roughness sublayer. If we again take the example of wind shear, it can be written, after including the roughness sublayer length scale,

∂U ∂z =

u_∗

κzΦ[(z − d)/L,(z − d)/(h − d)]. (2.3)

Above the surface layer it is foremost the Coriolis parameter, f , that be-comes important to describe the ﬂow. Including f makes is possible to con-struct new length scales from combinations of the key parameters. The sim-plest one is

lf = u_∗

| f |. (2.4)

This was recognized by Rossby and Montgomery (1935), who used it as a measure of the boundary layer height,δ.

δ = Cu∗

| f |, (2.5)

where C is a constant, initially proposed by Rossby and Montgomery (1935) to be C= 0.15, but later reports span from 0.1 (Gryning et al, 2007) to 0.7 (Zilitinkevich et al, 2007). Zilitinkevich (1972) identiﬁed another length scale from the key parameters of the boundary layer

lns= u2_∗ T0 −w_t_{f g} 1/2, (2.6) where lnsis a scale height for the night time stable boundary layer. To account

for long term stable stratiﬁcation, or background stable stratiﬁcation that is not related to diurnal change in L, Pollard et al (1973) included the Brunt Väisälä frequency, N= g∂θ θ0∂z, (2.7)

whereθ is the potential temperature, as a key parameter for the stable bound-ary layer. N can be thought of as the natural frequency for adiabatic oscilla-tions in stable stratiﬁcation. This results in yet another length scale formula-tion,

lbs= u_∗

| f N|1/2. (2.8)

The boundary layer height can be expressed as a combination of these three length scales. Zilitinkevich et al (2007) proposes

δ−2_{= (Cl}

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where C, Cnsand Cbsare empirical constants for the neutral, nocturnally stable

and long term stable boundary layer respectively.

With a measure of the boundary layer height, the similarity theory can be further developed to include the scale of z− d compared to δ. In the case of wind gradient the similarity is:

∂U ∂z =

u_∗

κzΦ[(z − d)/L,(z − d)/(h − d),(z − d)/δ]. (2.10)

where there is very little overlap between the to last arguments, so that either (z−d)/δ or (z−d)/(h−d) is insigniﬁcant depending on the height of interest. The inﬂuence of f on the wind means that it is no longer possible to assume that the wind direction is independent of height. The turning of the mean wind direction, on the northern hemisphere to the right with height (wind veer), is shown in Paper II to be a prominent feature over forests.

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3. Data and Measurement sites

3.1 Measurement sites

This thesis is mostly based on analysis of new measurements coming from two sites, Ryningsnäs in the south-east part of Sweden and Skogaryd in the south-west part of Sweden. The locations of the measurement sites can be seen in Figure 3.1, where satellite images are included in order to show the forest cover. At the western site, Skogaryd, measurement data were collected from a 38 m high tower. The measurement set-up was focused on near- and within-canopy processes. 3D wind and virtual temperature was measured at the heights 1, 6, 12, 18, 30.5 and 38 m, with a frequency of 20 Hz, by USA-1 (Metek Gmbh) sonic anemometers. In addition, the reference temperature was measured at 1 and 6 m at 1 Hz by Risø PT-100 instruments. The forest consisted mainly of even aged spruce with a mean tree height estimated by visual inspection to 25 m. The campaign ran from October 2011 to June 2012 and the obtained data was used in Paper I to determine the mean wind proﬁle and in Section 5 of this thesis to characterize the turbulence in the forest.

The eastern site, Ryningsnäs, included a 138 m high tower with meteorolog-ical instruments measuring wind, wind direction, temperature, humidity ﬂux and radiation. Additional measurements of wind up to 250 m were made with a Zephir LIDAR (LIght Detection And Ranging), as well as a short campaign of radio soundings. The tower was instrumented with sonic anemometers of the type USA-1 (Metek Gmbh), sampled at 20 Hz at 40, 59, 80, 98, 120 and 138 m. The background temperature was measured with Risø PT-100 at 40, 80, 98 and 138 m. In addition, the tower was equipped with seven Thies cup anemometers located at 25, 40, 60, 80, 97, 120 and 138 that was used as a reference and complement to the sonic anemometers in the analysis. The site was dominated by two wind turbines located in the directions 55◦ and 180◦ approximately 200 m from the measurement tower, and a big clearing ranging from 90-180◦. In the dominant west-wind sector the upwind condition is ma-ture forest close to the tower. In the large scale there is patchy forest cover for more than 200 km to the west.

As can be seen in Figure 3.1 satellite images show that the forest cover is patchy at both sites. The patchiness comes from clear cuttings which are typical in Swedish forestry and are likely to be dominant at any wind power site located in a Swedish forest. Directional analysis of measurements from several instruments were done in order to determine the most homogeneous upwind conditions, representative of forest ﬂow. In addition to studying the

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Figure 3.1. A map of sweden with the location of the two ﬁeld sites. X-marks indicate

the positions of the measurement towers. The round white mark indicate the additional tower used in Paper IV, originally erected for sound propagation research (Öhlund and Larsson, 2015)

measurements in the tower, data from airborne LIDAR-scans of the ground were analysed (Lantmäteriet, 2013) for both sites. From the LIDAR-scans, maps of ground elevation and forest height was produced. The data was av-eraged in 5x5x1 m3 cubes, and the ground height was taken as the minimum value in each cube 5x5 m column. The forest density was determined through the fraction of incoming light intensity to outgoing light intensity in each layer, using the method of Solberg et al (2006), and scaled between 0 and 1. The re-sults from the LIDAR-scan analysis can be seen in Figure 3.2. After careful analysis of both in situ measurements and LIDAR-scans the sectors 210-340◦ and 240-280◦were selected for Skogaryd and Ryningsnäs respectively.

The tree height from visual inspection was 20 m for Ryningsnäs and 25 m for Skogaryd. In Figure 3.3 the distribution of tree height from each 5x5 m column, located in the selected sector within a radius of 200 m from the respective measurement tower. is shown. For Skogaryd, the distribution has a peak at the same value as by visual inspection. For Ryningsnäs the distribution also has a clear peak, but the LIDAR-scans suggest a slightly higher value than from visual inspection.

3.2 Data preparation

To study properties of the wind, the data was prepared for analysis by ap-plying Reynolds decomposition. This was done in the same manner for both sites, with a 30-min block average. Details regarding the statistical prepara-tion can be found in paper II. A short summary is that the coordinate sys-tem was aligned with the mean wind vector at each height and that the

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ve-Figure 3.2. Measurement site Ryningsnäs (top panel) and Skogaryd (bottom panel),

with surface height as vertical coordinate, tree height as grey colour and two cross sections North-South and East-West) of laser scans. The colours show forest density in a scale from 0 to 1.

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Tree height [m]

0 5 10 15 20 25 30

Figure 3.3. Normalized distribution of the tree height in the selected sector within 200

m from the measurement tower. Ryningsnäs in light gray, and Skogaryd in dark gray

locity components were decomposed as U,u,V,v,W and w, where V = 0. To determine how the flow properties depend on stratification, the data was sorted into stability classes. The surface-layer stability measure is the non-dimensional (z − d)/L, so in the surface layer the correct way to establish stability classes would be to sort them according to (z − d)/L. But, as the Ekman layer, the forest layer, and the roughness sublayer all have different length scales that can be used to create non-dimensional measures of stabil-ity, limits for the stability classes was set on the magnitude of L only, so that data from all layers would have the same limits. In the following section, the classes Stable, 100< L < 400, Neutral, |L| > 1000, and Unstable, Near Neu-tral, −1000 < L < −100, is shown in the figures. Data from both sites has been filtered with a newly developed despiking algorithm (see Appendix A of Paper II) in order to remove erroneous data due to snow or rime ice. Two flow conditions have been used for both sites based on measurements at z≈ 40 m, one on the required stationarity and one on minimum wind speed. The sta-tionarity criterion required that the mean wind direction did not change more than 10◦between individual 30-min periods and that the wind speed from the centre 10-min average did not deviate more than 10% from the first and last. The wind speed condition of U > 3 ms−1was used to ensure that mechanical turbulence was large enough that higher order statistics would converge. The

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same height, 40 m, was used to determine u_∗and L, which is throughout this thesis considered as constants for each 30-min period.

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4. Mean wind proﬁle

From scaling arguments, it was shown in Secion 2 that the mean wind gradient over forest can be written as

∂U ∂z =

u_∗

κzΦ[(z − d)/L,(z − d)/δ,(z − d)/(h − d)]. (4.1)

Integrating Equation 4.1 with height gives the mean wind proﬁle. Several studies has been performed in order to develop an expression for Φ (Cellier and Brunet, 1992; Physick and Garratt, 1995; Mölder et al, 1999; Harman and Finnigan, 2007; Ridder, 2009). Close to the forest,(z − d)/δ is small enough to be ignored, so the standard expression is to set

Φ = φm(z − d,L)ϕ(z − d,lf), (4.2)

whereφmis the non-dimensional gradient for surface layer andϕ is a universal

function of z−d and some length scale, lf, connected to the forest or the height

of the roughness sublayer. There is no consensus about which the appropriate form of ϕ is, and one problem with all the above formulations except for the one proposed by Ridder (2009) is that they do not enable the integral of Equation 4.1 to be expressed in an analytical form. The aim of Paper I was to ﬁnd such a form ofϕ. Following Harman and Finnigan (2007) the length scale h−d was used to represent the forest and an expression for ϕ, which has an analytical form of the integrated wind gradient, was derived. The resulting wind proﬁle is shown in Figure 4.1 with typical forest values of h= 20, d = 15 andϕ(h − d) = 0.6.

Using the expression developed in Paper I it was shown that the roughness length, z0, the integration constant that comes out of integrating Equation 4.1,

decreases with increasing stable stratiﬁcation. The stability dependence of

z0 was conﬁrmed by the measurements presented in Paper II, where a new

method of estimating z0without bias from a priori assumptions was presented.

Measurements from both Skogaryd (Paper I) and Ryningsnäs (Paper II), as well as the wind proﬁle expression developed in Paper I show a decrease of z0

by 50% going from neutral to stable stratification. The physical interpretation of this is that in stable conditions the wind above the forest feels a smoother surface than during unstable conditions. Since the trees themselves do not change with stratification, the effect of stability dependent roughness is rather coupled to flow in the lower parts of the forest decoupling from the flow aloft. Yi et al (2005) found evidence from field measurements of such a decoupling between the upper and the lower part of the canopy.

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Figure 4.1. Mean wind proﬁle in(a), stable, (b), neutral and (c), unstable, near

neu-tral. The dash-dotted line shows tower measurements from Skogaryd(z/h < 2) and Ryningsäs (z/h > 2), the dashed line shows measurements from LIDAR, the dotted line is the wind proﬁle from Peña et al (2009) and the full line is the wind proﬁle from paper I. The shaded area shows the standard deviation of the measurements.

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local time height (m) 12:00 00:00 12:00 00:00 12:00 00:00 12:00 0 500 1000 1500 2000 2500

Figure 4.2. Evolution of the boundary layer height during the radio-soundings

mea-surement campaign. The black triangles show the estimated height from soundings, the solid line is the Rossby-Montgommery expression with C= 0.15, the dashed line with C= 0.1 and the dash-dotted line is the expression recommended by Zilitinke-vich et al (2007). The gray shaded areas indicate time periods when the heat ﬂux was positive.

At higher heights, where the non-dimensional scale (z − d)/δ becomes large, it is necessary to include (z − d)/δ as an argument to Φ. In Paper II it was shown that several variables behaved in ways that could be explained by inﬂuence from the boundary layer depth. Wind veer was shown to be sig-niﬁcant, especially in stable conditions, the length scale of turbulence showed a limited growth with height and in stable conditions the wind speed did not increase with height as much as predicted by surface layer theory. It is thus interesting to see how similarity expressions that include(z − d)/δ as a pa-rameter compares to the measurements from Ryningsnäs.

During a short ﬁeld campaign aimed at providing insights to the structure and depth of the boundary layer at the Ryningsnäs site, several radiosondes were released. The resulting estimations ofδ is shown in Figure 4.2 together with similarity expressions forδ from Equation 2.5 (Rossby and Montgomery, 1935) and Equation 2.9 (Zilitinkevich et al, 2007). It was concluded from the comparison that a value of the constant C in the Rossby and Montgommery formulation, C = 0.1, resulted in good agreement with the soundings. The estimated value of C= 0.1 is lower the the standard value of C = 0.15 and implies that the boundary layer height over forests is not higher than over low vegetation.

Based on δ from the Rossby and Montgomery formulation, Peña et al (2009) developed an expression for the wind speed in the Ekman layer. Their expression is included as a reference in Figure 4.1. In Figure 4.1, U/u_∗ -profiles from Paper I and from Peña et al (2009) was determined for each 30-min value of L in the data-set. The individual profiles were then averaged within the same stability classes as the measurements. The reason for not cal-culating one single profile for the mean value of L in each stability class is the non-linear response to variations in L that would otherwise give a bias in the comparison.

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In addition to the tower measurements of U/u_∗, Figure 4.1 shows measure-ments from a Zephir LIDAR. The LIDAR measuremeasure-ments were scaled with corresponding u_∗ from the tower. The Zephir LIDAR had problems mea-suring in the turbulent conditions at Ryningsnäs and analysis of the LIDAR measurements revealed two main reasons for this. First, the Zephir type of LI-DAR can only measure|U| and must rely on reference measurements of wind direction at 2 m above ground to align the wind vector in the right direction. Since the LIDAR was placed in a clearing problems arose due to frequent ﬂow separation within the clearing and above. After correction, by instead using the 98 m tower measurement as reference, there was still a positive bias, with magnitude increasing with the turbulence intensityσu/U. The remaining bias

possibly consist of a systematic error in the algorithm used to translate laser backscatter data into wind speed (Bergström et al, 2013). From Figure 4.1 it can be concluded that the LIDAR measurements agreed better with the tower measurements in stable conditions when the turbulence level is lower. Further-more, the LIDAR measurements show that in stable conditions the wind speed does not continue to increase with height in the way predicted by surface-layer theory. It is thus necessary to include the scale(z−d)/δ to accurately describe the wind proﬁle. In neutral and unstable conditions the surface-layer theory is in good agreement with the tower measurements up to 140 m and the gradient agrees reasonably with the LIDAR measurements up 250 m.

A feature of the mean wind profile in the atmospheric boundary layer that is rarely discussed in surface-layer studies is the turning of mean wind direc-tion with height. A study based on the wind veer from Ryningsnäs showed that taking veer into account in the pitch-control of wind turbines can re-duce fatigue loads (Bergström et al, 2013). A theoretical description of the wind veer can be found by assuming a balance in the boundary layer be-tween Coriolis force, pressure gradient and divergence of the momentum flux. The classical solution to this problem is to represent the flux by a constant eddy viscosity, K, multiplied the wind gradient,∂uw/∂z = −K∂2U/∂z2and

∂v_w_{/∂z = −K∂}2_V_/∂z2_{(Ekman, 1905). This solution gives a 45}◦_wind

turn-ing called the Ekman spiral. Such large values are seldom observed, but usturn-ing a more realistic turbulence representation, where the eddy viscosity is allowed to slowly vary around an amplitude K0, Grisogono (2011) managed to ﬁnd an

expression that ﬁts observations better. In Figure 4.3 the Grisogono (2011) expression is shown together with measurements of the wind direction. The value of K0was found to agree reasonably with the measurements from

Ryn-ingsnäs using the function

K0= l κ

φm(l/L)

e1/2 (4.3)

where l is given by l= (115−1+δ−1)−1, andφmis the stability function from

Högström (1996). In the Grisogono (2011) proﬁle shown in Figure 4.3, L was taken from measurements andδ from the Rossby Montgomery formulation.

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Figure 4.3. Mean veer proﬁle in(a), stable, (b), neutral and (c), unstable, near

neu-tral. The dash-dotted line shows tower measurements from Skogaryd(z/h < 2) and Ryningsäs (z/h > 2), the dashed line shows measurements from LIDAR and the full line is the veer proﬁle from Grisogono (2011). The shaded area shows the standard deviation of the measurements.

Although it is obvious that the theory still overestimates the wind turning it gives realistic values, especially in stable stratification where the veer is sig-nificant. Within the forest the mean wind direction is much harder to measure accurately due to the high turbulence intensities. This is reflected in Figure 4.3 through the large standard deviation. In stable stratification the wind speed is so low within the forest that the main balance in the momentum equation is between the flux divergence and the pressure gradient only (Shinn, 1971). This causes the wind in the measurements to veer in average 60◦between the ground and 250 m height. A theoretical consideration gives 90◦ between the forest floor and the boundary-layer top.

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5. Turbulence statistics

In addition to the mean wind profile, turbulence statistics are very important to wind industry. Results from the measurements presented in this thesis in-dicate that wind turbines in forests might be exposed to more severe loads than what is currently covered by the most rigid industry standard (Bergström et al, 2013). Paper II was dedicated to reporting profiles of standard turbu-lence statistics up to 140 m for a wide range of background stratification. To the authors’ knowledge Paper II offers the most complete description of the turbulence in the boundary layer over forests published to this date and can be used as a valuable reference for models aimed to describe the atmo-spheric boundary layer over forests. In Paper II the diagonal terms in the Reynolds-stress tensor was shown to be close to height constant values with ratiosσu,v,w/u∗= 1.9,1.5,1.2, for the neutral class. Those values are in

agree-ment with values reported from the surface layer over low vegetation (Wyn-gaard, 2010), and indicate that above the roughness sublayer, turbulence be-haves much in the same way over forests as over smoother surfaces. In Figure 5.1 the six unique components of the Reynolds stress is shown, correspond-ing to Figure 5 of paper II, but here also includcorrespond-ing the same statistics from Skogaryd, giving values in the roughness sublayer and the canopy layer. Not much variation can be seen between the different stability classes, especially considering the scatter within each class. Within the forest turbulent energy is much more evenly distributed and the three velocity components show ap-proximately the same amount of variance. A detail is that the horizontal com-ponents has a local maximum in the proﬁle within the forest but the vertical component does not. This is analogous to other reports, which show that while the wind proﬁle within the forest has a local maximum beneath the tree trunks, the shear stress decays exponentially from the top of the forest to the ground (Yi, 2008). Close above the forest virtually all of the vertical shear stress is found in uw, and it is only at the highest heights, particularly in stable con-ditions, that vw becomes important. In Paper II the coupling between vw

and the wind veer is discussed and it was concluded that the veer is signiﬁcant where vwhas a signiﬁcant contribution to the shear stress.

Wind turbines rely on active-control units to adjust the pitch angle of the blade or the rotation speed in order to control the power output and the loads. If a turbulence model is used to tune such an active-control system it is im-portant that it properly describes the statistical properties of the wind. Several reports on third order moments in the roughness sublayer suggests that the skewness is non zero there, with the largest magnitude found close to tree tops

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Figure 5.1. Vertical proﬁles of (a) uu/u2_∗, (b) uv/u2_∗, (c) uw/u2_∗, (d) vv/u2_∗, (e) v_w_/u2

∗,( f ) ww/u2∗, with the lines showing stability-class mean in the diabatic

conditions: stable (blue), neutral (green) and unstable, close to neutral (orange). The shaded area shows the standard deviation of the measurements.

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and decaying towards the top of the roughness sublayer (Raupach et al, 1996; Finnigan, 2000; Segalini et al, 2013). As standard turbulence models assume a Gaussian distribution of the turbulence, a non-zero value of the skewness within the region of the turbine rotor could be problematic. To address this question, skewness was discussed in paper II and it was concluded that in the height span relevant to wind energy, skewness was indeed found to be very close to zero. In Figure 5.2 the skewness of all three velocity components is shown, including the measurements from Skogaryd. The same behaviour as reported in the literature is observed close to the canopy, including the decay of the skewness up to z≈ 2h. By studying Figure 5.1 and Figure 5.2 it is clear that the effect of the roughness sublayer on the second- and third-order mo-ments is conﬁned to the region below z/h ≈ 2, and is thus of minor importance to wind-energy applications.

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Figure 5.2. Vertical proﬁles of(a), skewness of u, (b), skewness of v, and (c),

skew-ness of w. The lines show the stability-class mean in the diabatic conditions: stable (blue), neutral (green) and unstable, close to neutral (orange). The shaded area shows the standard deviation of the measurements.

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6. Spectra

While the mean properties of turbulence above forests was examined in Paper II, Paper III is focussed on how the turbulent energy is distributed at different scales. Load calculation on wind turbines typically require that the wind field over the rotor is known as a function of time. To get the correct estimate of the loads it is necessary to know the spatial correlation pattern of the flow so that modelled winds at different locations can be combined in a realistic way. In a very influential paper Mann (1994) derived a model for the spectral correlation tensor,φi, j, which provides the correlations necessary to construct a realistic

wind field over the rotor. The Mann (1994) model was derived using the rapid distortion equations for homogeneous shear flow, where a background shear is allowed to act on an initially isotropic turbulence field for a certain amount of time,τ. The rapid distortion equations are linear, which enables an analyti-cal formulation of the spectral tensor and makes analyti-calculations computationally effective.

An obvious limitation of the Mann (1994) model is the lack of buoyancy, which means that stratification is not accounted for. In Paper III a new spectral correlation model is presented which follow the approach of Mann (1994), but starts with the inviscid rapid distortion equations for stratified shear flow, which can be written as

d dtuˆi= α 2kik1 k2 − δi1 ˆ u3+ kik3 k2 − δi3 ˆ ρ , (6.1) d dtρ = Nˆ 2_u_ˆ 3, (6.2)

where tensor notation is used and ˆui is a Fourier component of the wind,α is

the wind shear, k is the wave number, N is the Brunt-Väisälä frequency and ˆρ is a Fourier component of the ﬂuctuating density measure gρ/ρ0, where g is

the acceleration due to gravity. Furthermore, the evolution of the wave-number vector is

dki

dt + αk1δi,3= 0, (6.3) which implies that

k(t) = (k1, k2, k3) = (k1,0, k2,0, k3,0− αk1,0t) , (6.4)

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In Paper III an analytical solution to Equation 6.1 was developed using the solution of Equation 6.2 provided by Hanazaki and Hunt (2004). In Mann (1994) the proper integration time is suggested to be a typical lifetime of tur-bulent eddies,τ, and hence is wave number dependent. To expand τ to stable stratiﬁcation a new formulation was proposed,

τ = (τ−1

M94+ cN)−1, (6.5)

where τM94 is the original eddy lifetime proposed in Mann (1994) and c is

a constant. The idea of Equation 6.5 was to limit the eddy life time to N−1 which has been observed to be accurate in the stable boundary layer (Wyn-gaard, 2010), and at the same time converging to the values provided byτM94

in neutral conditions. The obtained tensor is then typically integrated numeri-cally over the lateral and vertical wave-number space so that the end product resembles a spectrum measured in in the atmosphere,

Fi j(k1;Δx2,Δx3) = RΦi j(τ;k)e ik2Δx2_eik3Δx3_dk 2dk3, (6.6) where_Rdk2dk3= _∞ −∞ _∞ −∞dk2dk3.

The model derived in Paper III has six parameters that needs to be known. Values of the model parameters was determined using single point spectra from Ryningsnäs and from another site, Maglarp, that in contrast had very low roughness (see Smedman and Bergström (1984) for details). It was shown that the only parameter sensitive to change in roughness was the magnitude of the initial isotropic spectra. This is natural since turbulence is more intense over forests. Otherwise the parameter optimization in Paper III conﬁrmed the results in Paper II, that when averaged in time, turbulence statistics behave the same way in the surface layer over forests as over low vegetation. Of the other parameters three was shown to be constant and the remaining two were proposed to be functions of background shear and stratiﬁcation.

Single point spectra calculated with the model are shown in Figure 6.1. They are shown as functions of longitudinal wave number, k1, scaled with

the length scale, L of the initial isotropic spectrum. Averaged spectra from the measurements at Ryningsnäs, used to optimize the parameters, are also included. The co-spectrum of longitudinal wind and temperature, F_uθ, that was not used in the optimization routine, is included as a measure of the model performance. By studying Figure 6.1 it is clear that only minor differences can be seen between the different stability classes. The small difference is not an indication that spectra are the same in neutral and stable conditions, but rather that scaling the spectra with proper scales makes them collapse to the same shape (Olesens et al, 1984). It should be pointed out that the main advantage of using a model such as the one described in Paper III is not the ability to predict single point spectra, but rather the possibility to ﬁnd cross-spectra between different variables and spatially separated points.

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10−1 100 101 102 −0.1 0 0.1 0.2 0.3 k1 Fij /σ 2 u k1L (a) 10−1 100 101 102 −4 −2 0 2 4 6 8 10 12x 10 −3 kF iθ /( σu T0 Fr 2 ) k1L (b) 10−1 100 101 102 −0.1 0 0.1 0.2 0.3 k1 Fij /σ 2 u k1L (c) 10−1 100 101 102 −0.01 −0.005 0 0.005 0.01 0.015 0.02 0.025 kF iθ /( σu T0 Fr 2) k1L (d) 10−1 100 101 102 −0.1 0 0.1 0.2 0.3 k1 Fij /σ 2 u k1L (e) 10−1 100 101 102 −0.02 −0.01 0 0.01 0.02 0.03 0.04 kF iθ /( σu T0 Fr 2) k1L (f)

Figure 6.1. Comparison of the spectra from measurements and from the present model

at z≈ 100 m and U(z) ≈ 7 ms−1for(a − b) Neutral conditions (Ri = 0.07), (c − d) Near-Neutral Stable conditions (Ri= 0.10) and (e− f ) Stable conditions (Ri = 0.14). Experimental data: (◦) Fuu,(+) Fvv,(∗) Fww,() Fuw,() Fuθ,() Fwθ. Model

prediction: (solid line) Fuu, Fuw, Fuθ, Fwθ. (dashed line) Fvv. (dotted line) Fww. Since

the model predicts only real single-point spectra, only the real part of the cross-spectra is shown. The ﬁgure is a reprint from Paper III

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The model presented in Paper III is eligible for wide use in wind-energy applications. Since the model parameters was only weakly sensitive to surface roughness the model may be used in smother terrain as well. Large Eddy Simulation (LES) of wake effect in off shore wind farms is an example where a realistic inlet turbulence field is necessary (Nilsson et al, 2014). Furthermore, it has been shown that the ambient turbulence has a large effect on the recovery of wind turbine wakes (Ivanell, 2009) and since the stable boundary layer reacts slowly (due to weak mixing) it is a benefit to have a good first guess of the turbulence at the upstream boundary of the LES domain.

The spectral tensor can also be utilized in a more direct way to generate time series for load calculations, using inverse Fourier transformation of frequency to time. The phase difference,

ϕi j= arctan ℑFi j(k1) ℜFii(k1) , (6.7)

between spatially separated components will then be transformed into time lags. The coherence,

γ2 i j= Fi j(k1) 2 Fii(k1)Fj j(k1), (6.8)

will determine how much coupling there is between two spatially separated points. It is thus crucial that the model can predict coherence and phase. Fig-ure 6.2 provides observed and modelledϕ and γ in moderately stable condi-tions and mean wind speed between 7-8 ms−1, for all three velocity compo-nents at 100 and 120 m height. The real (Co) and imaginary (Quadrature) parts of the cross-spectral density are also shown. It can be noted that the agreement is good in the real part of the spectra, but that the imaginary part of the model peaks at too high frequencies and that the anisotropy is too large. This discrep-ancy has effect on the magnitude of the coherence which is overestimated by the model, even though the model was generally able to capture the trend of the coherence. The phase difference is better estimated by the model, even at very high wave numbers. The inability of the model to accurately predict the spatially separated quadrature spectra may be explained by the fact that opti-misation of the parameters was done using single point spectra only. Further studies of the model performance may reveal if the overestimated coherence is a general discrepancy of the model or if it is a result limited to the conditions studied in Paper III.

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10−1 100 101 −0.05 0 0.05 0.1 0.15 0.2 k1 Fij /σ 2 u k1L (a) 10−1 100 101 −0.05 0 0.05 0.1 0.15 0.2 k1 Fij /σ 2 u k1L (b) 10−1 100 101 0 0.2 0.4 0.6 0.8 1 γ 2 ij k1L (c)

Figure 6.2. Comparison of the two-point velocity spectra from measurements and

from the present model for z1≈ 100 m, z2≈ 120 m and U(z1) ≈ 7 ms−1 for

Near-Neutral Stable conditions (Ri= 0.10). (a) Real part and (b) imaginary part of Fuu, Fvv

and Fww. (c) Coherence and (d) phase functions. See ﬁgure 6.1 for the list of used

symbols. The ﬁgure is a reprint from Paper III

10−1 100 101 −3 −2 −1 0 1 2 3 ϕij k1L (d)

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7. Wave structures in the wind

It was shown in Section 5 that the roughness-sublayer effects on the mean wind profile and on the third- and second-order turbulence statistics was con-fined to the region below z/h ≈ 2, and that higher up the surface layer behaved much like the surface layer above low vegetation. Much research on the effects of the roughness sublayer has however been done that does not only directly involve the turbulence moments. Several previous studies have been aimed at the development of the roughness sublayer and the cause of its characteristics (Finnigan, 2000). Raupach et al (1996) established the mixing layer theory which is the dominant explanation for the deviation between the surface layer and the roughness sublayer. The mixing layer theory suggests that unstable waves can develop due to the inflection point in the mean wind. The instabil-ity is centred where the profile goes from being exponential (within the for-est) to logarithmic (above the forfor-est). The amplitude of these unstable waves grow exponentially and the waves become subject to secondary instabilities, which lead to entanglement and formation of more complex structures. Using LES results, Finnigan et al (2009) showed that the initial wave disturbance developed into several partially overlapping horse-shoe vortices that were ef-ficient in transporting momentum and scalars. Segalini and Alfredsson (2012) showed evidence of coherent structures in the wind at Ryningsnäs which could be detected through the whole measurement array (up to 140 m). The study of Segalini and Alfredsson (2012) was performed with cup anemometers in neutral conditions.

In Paper IV situations with strong background stratiﬁcation was studied with the hypothesis that strong background stratiﬁcation would prevent the growth of the initial wave instability, so that wave patterns in the wind would be more consistent and easier to detect. Using Fourier and wavelet transforms, wave events were detected by relating the peak frequency of the spectra to the total variance. The observed wave events from Ryningsnäs resembled to a large extent the wave events reported over a forest by Lee et al (1997).

By studying the phase difference between u and w,ϕuw, it was evident that

when the wind proﬁle has a prominent kink above the forest in presence of a strong background stratiﬁcation ϕuw was often close to 90◦ at the frequency

of the wave. ϕuw ≈ 90◦ is an indication that the waves are of the

Kelvin-Helmholtz type (Nappo, 2002), and that they are created by the inflection point instability in the wind profile (Lee et al, 1997). The inflection point in the wind profile is always present over forests which implies that the mechanism creating the Kelvin-Helmholtz instability is always present. In Paper IV the

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the product between the wavelet transform of horizontal wind, Wu(s,t), and

the transform of vertical wind, Ww(s,t), where s is the scale of the wavelet and t is the time of detection, was used to construct the phase lag between u and w, ϕuw(s,t) = atan ℑ(Wu(s,t)Wu∗(s,t)) ℜ(Wu(s,t)Ww∗(s,t)) . (7.1) where W∗is the complex conjugate of W .

Using wavelet transform to create ϕ has the advantage over Fourier meth-ods that the temporal evolution ofϕ can be studied. In Figure 7.1 the phase lag between u and w at 120 m is shown for a time series of 2 hours recorded Oc-tober 15 2011 01:00-03:00 local time. The event was characterized by strong stratiﬁcation (L=43 m) and wave signals in the wind. Figure 7.1 shows the end of the wave event and by studying the wind proﬁle and the phase lag si-multaneously one can notice that the time period withϕuw≈ 90◦ ends at the

time where the wind shear becomes more homogeneous in the whole layer, at about 80 minutes.

It is not clear from Figure 7.1 though, if it is the lack of shear produced turbulence above 100 m that makes the wave more undisturbed (allowing the wave to keep the theoretical value ofϕuw= 90◦ at t< 80 minutes) or if it is

the actual weakening of the inﬂection point (the curvature of the wind speed is moved higher up) that weakens the wave growth so that the wave disappear (t> 80 minutes).

In Paper IV it was shown that linear wave theory could predict many fea-tures of the observed waves including period and vertical shape of the ampli-tude. In order to examine how important the curvature of the upper part of the wind profile is for the generation of Kelvin-Helmhotlz waves it is possi-ble to use the numerical method presented in Paper IV on two different wind profiles, and study the resulting wave amplitudes. The result can be found in Figure 7.2, where two wind profiles with different curvature of U above the forest has been used together with linear wave theory. The amplitude of the w oscillations was determined here using wind profiles from different stratifica-tion, but the actual density profile was disregarded as it showed no significant effect on the amplitude of the Kelvin-Helmholtz waves. The two wind pro-files were created using the new wind profile expression presented in Paper I, with L= 500 and L = 50 respectively. As can be noted in Figure 7.2 (a) the near neutral profile has considerably more curvature above the forest than the profile from stable condition. However, when comparing the amplitude of the w oscillations, the two wind profiles result in very similar amplitude pro-files (Figure 7.2 (b)), with just a slight upward shift in vertical position of the maximum amplitude and slightly lower magnitude of the amplitude.

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5 1 0 40 60 80 100 120 140

z [m]

5 1 0 5 1 0 5 1 0 5 1 0 5 1 0 5 1 0 5 1 0 5 1 0 5 1 0 5 1 0 5 1 0 0 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90 100 110 20 40 60 80 100 120 140

Period [s]

time [minutes]

F igur e 7.1. Phase dif ference between u and w from a 120 minute record. Upper panel: W ind speed between 40 and 140 m. Each proﬁle is the ten minute av erage corresponding to its place on the time axis of the lo wer panel. Lo wer panel: Phase dif ference between u and w at 120 m as a function of time and scale.

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10 20 30 40 0 50 100 150 U [ms−1] z [m] (a) 0 0.1 0.2 0.3 0 50 100 150 | ˆw| z [m] (b)

Figure 7.2. (a), Wind speed determined by the analytical expression proposed in

Paper I using L= 500 m (full line) and L = 50 m (dashed line). (b), Amplitude of the normal mode of the linear wave solution using the numerical method described in Paper IV. The full line is the result using the full-line wind profile in(a) and the dashed line is the result using the dashed wind profile in(a). The density profile has been disregarded in the calculations.

It can thus be concluded that it is likely the turbulent distortion of the wave which makes it difﬁcult to detect waves during large wind shear, rather than the production mechanism being weaker.

The results presented in Figure 7.2 and in Paper IV suggest that the mech-anism generating Kelvin-Helmholtz type of waves over forests from the back-ground wind profile is consistently present. Results in Paper I show that the influence of the roughness sublayer decreases with stratification (see Figure 2 (b) of Paper I). Provided that the mechanism creating the roughness sublayer is the KelvHelmholtz instability, this result indicate that as stratification in-creases the waves become less unstable, and thus contribute less to momentum transport.

In Paper IV several examples of wave occurrences was shown. The ex-amples had low shear in the upper part of the proﬁle (above 100 m height) and low ambient turbulence. Low shear and limited turbulence are conditions ideal to wind power production. The fact that waves was found to be frequent in such conditions suggests that the effect of waves on wind turbine loads need to be examined thoroughly and that standard turbulence models may need to be complemented with wave models when estimating loads on wind-turbines in forested areas. The frequency of the waves together with their repetitive na-ture implies that it may be possible to tune modern wind turbine controllers to limit the effects of Kelvin-Helmholtz type of waves on the wind-turbine loads. It was further shown in Paper IV, using linear theory, that waves with higher frequency than Kelvin-Helmholtz waves may develop when the background

N2 proﬁle has a local maximum. The occurrence of such high-frequency waves and their implications to loads in wind turbines need to be studied fur-ther.

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8. Outlook

Increased experience from wind-turbine siting in forested areas, togehter with previous and current research, leads to increasing knowledge of the wind con-ditions in the boundary layer over forests. This thesis is a contribution in terms of how turbulence behaves as well as by providing modelling tools. Still, there is very much to be done and the knowledge is needed quickly. Even during the five years leading to this thesis, wind turbines has grown so much that the height of the measurement tower at Ryningsäs, 140 m, is not enough to give a complete picture of the conditions that the turbines operate in. New measure-ments at higher heights are necessary to take the knowledge further. There is a need for better assessment of the boundary-layer height, as that height is be-coming a more relevant scale to the turbines than the height of the trees. The growing relative importance of outer scales such as the boundary-layer height means that traditional models focusing on surface properties may need to be complemented. The influence of the boundary-layer depth challenges us to further develop dynamical tools such as large eddy simulations and numerical weather prediction models, where the boundary-layer height can evolve. The adaptation of such models to forested areas require optimizing constants and developing schemes that handle surface roughness and forest density as well as radiation and fluxes of heat and water vapour. There is still much work to be done on this subject with the measurement data gathered from Ryningsnäs and Skogaryd. Especially interesting questions relates to how detailed the for-est must be resolved spatially. While airborne laser scans enable us to map the forest in very fine detail, it is not clear how important it is to include such de-tailed information when modelling the mean wind and the turbulence 100-200 m above ground. Furthermore, models that cannot resolve the forest in such detail need to represent the heterogeneous forest in some mean sense, and it is not clear in what way that is optimally done. While many pioneering attempts of explicitly including a forest in CFD models use ideal leaf area density pro-files, where most of the foliage is located in the upper part of the canopy, initial studies done with the airborne laser scans over Ryningsnäs and Skoga-ryd show that, when averaged over a large horizontal area, the leaf area density profile and the tree height distribution become much more evenly spread out. The many smaller trees growing in clear-cut areas could be making a signifi-cant contribution, but it is far from straight forward to determine how and to which extent. It is thus important with studies aimed at the optimal way of representing a forest in a model, so that the resulting model tools will become universal, and not just apply to a certain model resolutions or configurations.

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9. Summary

This thesis contains four scientific papers. Two of the papers include new analytical models describing the wind profile (Paper I) and spectra (Paper III) over forests. The two remaining papers describe the flow in the boundary layer over forests in terms of turbulence (Paper II) and wave activity (Paper IV).

In Section 1.1 the aim of this thesis was formulated by means of providing answers to speciﬁc research questions. The questions are repeated here, with the ﬁndings in this thesis below each question.

• How does the mean wind proﬁle behave over forests?

In the roughness sublayer (the layer directly above the trees) the mean wind proﬁle has less shear than predicted by surface-layer theory. This behaviour can be corrected for by using a correction factor (Paper I). The roughness sublayer, however, is generally found below the height span of a typical wind turbine rotor (Chapter 5 and Paper II).

Above the roughness sublayer the mean wind profile is well described by surface layer theory, up to a certain point when the proximity of the boundary-layer height limits the wind speed. The height of the boundary boundary-layer was found to be important for the mean wind profile in stable stratification (Paper II).

In stable stratiﬁcation the wind veer becomes prominent, the results in Paper II indicate a veer of more than 0.1◦m−1in average for stable conditions.

The aerodynamic roughness length was shown in both Paper I and II to decrease in stable stratiﬁcation. This leads to an underestimation of the wind speed in stable conditions when using the roughness length from neutral condi-tions. Stability dependent roughness is generally not accounted for in models, and including it would be an improvement.

• How does turbulence generated by forests decay with height?

Results in Paper II showed that standard deviations of the three velocity components decayed only weakly with height, except for σwin stable

condi-tions. The values of standard deviations scaled by u_∗was shown to be consis-tent with reports from the surface layer over low vegetation. In Chapter 5 it was shown that the modiﬁcation of scaled standard deviations in the roughness sublayer was conﬁned to the region below twice the tree height.

In very stable stratiﬁcation, the amplitude Kelvin-Helmholtz waves showed agreement with predictions from linear wave theory. Both measurements and linear theory showed that the amplitude was largest near 40 m height and de-cayed rapidly with vertical distance from this height.

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Two-point velocity Co-spectra showed good agreement between modelled and measured values up to separation distances of 40 m, using a new spectral model (Paper III). It was concluded that for larger separation distances the difference in spectral length scale between two points together with the non linearities of the wind and temperature proﬁle lead to overestimation of the cross correlation by the model.

• Is the turbulence over forests any different from that over low

vege-tation?

The answer to this question is two folded. In the surface layer, turbulence statistics was found to behave similarly over forests and low vegetation. Sim-ilarity theory developed over smooth surfaces was shown to agree with mea-surements over forests, in terms of spectral length scale (Paper III), and mo-mentum transport (Paper II). When the model developed in Paper III was tuned to measurements over low vegetation the only parameter to show signiﬁcant change was the magnitude of the turbulence.

On the other hand, Paper I and IV are dedicated to features that are espe-cially important and characteristic to forest flows, i. e. the roughness sublayer and canopy waves. The underlying mechanism of the roughness sublayer is thought to be the same as the mechanism responsible for the Kelvin-Helmholtz waves studied in Paper IV. It was shown that the influence of the roughness sublayer on momentum transport decreased in stable stratification (Paper I) and that, in very stable stratification, the contribution to momentum transport by Kelvin-Helmholtz waves was minimized due to the phase difference be-tween u and w (Paper IV). This suggests that the effect of the forest on the flow aloft depends on stratification and appears to be linked to the growth rate of the Kelvin-Helmholtz instability.

Another quantity that showed large dependence on stratiﬁcation is the aero-dynamic roughness length. This could be explained by ﬂow decoupling inside the forest, which means that the mechanism would also be possible in lower vegetation, but suggests that it becomes more important when the roughness elements are higher.

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10. Acknowledgments

Turbulence has always mesmerized me. When I was a child I took pleasure in pouring milk into tea and watching it mix. I made sure to stir a couple of times with the spoon before the milk was completely dissolved and it was no longer possible to see the eddies. I remember picking up the tea bag one day, and as I was watching it swing back and forth I formulated the hypothesis that every revolution took the same amount time, no matter the amplitude. I was ten years old and knew I wanted to become a scientist.

My deepest and most sincere thanks goes to my supervisor Hans Bergström. I want to thank you for giving me the opportunity to pursue my dream and to let my curiosity guide me in my research. You are my absolute role model when it comes academic work, and I admire you deeply as a researcher and person.

I want to thank all my supervisors, Hans Bergström, Anna Rutgersson and Stefan Söderberg for excellent guidance in the academic world. The numerous times you have read my poorly written texts and patiently corrected my errors has been more valuable than I can possibly express.

I would like to acknowledge Energimyndigheten and Vindforsk for ﬁnanc-ing my work as a PhD student.

Special Thank to Hans Bergström and Matthias Mohr for coordinating the research projects Wind Power in Forests and Forest Wind.

Very special thanks to co-authors Ebba Dellwik and Antonio Segalini. Over the years I have immensely enjoyed working with you and I offer you my deepest thanks for sharing your knowledge and thoughts with me. So much of my knowledge of research practice I owe to you. I want to thank you both for your care and for guiding me in my work and education, while at the same time always making me feel that my contributions were important. Also, I can’t believe how much fun we have had!

I would like to thank all persons involved in collecting the data used in this thesis. Ebba Dellwik for taking care of measurements in Skogaryd and Ryningsnäs, Hans Bergström for providing me with data from Jädraås and Maglarp, Leif Klemedtsson for putting the Skogaryd tower at our disposal, Vattenfall for allowing us to use their complementary measurements in Ryn-ingsnäs and Conny Larsson and Olof Öhlund for sharing their data from the forest tower in Ryningsnäs. Your contributions have been invaluable to this work.

Special thanks to Carmen Nappo for inspiring me to work on the forest wave project and for sharing your passion for waves in the atmosphere and your great expertise in the ﬁeld. It has been a pleasure to work with you.

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Furthermore I wish to thank many persons working at Geocentrum. Olof Öhlund, you have been there from the very ﬁrst meteorology lecture eight years ago, and your strive to understand the basic mechanisms of every aspect of meteorology has been an ever present joy. Our discussions has very much shaped me into the meteorologist I am today.

In addition to Olof I would like to thank Petra Thorsson and Jennie Persson Söderman for excellent company while sharing room with me.

I wish to thank senior meteorologists Ulf, Ann-Soﬁ, Sven, Conny, Hans, Anna R, Erik S, Cecilia, Monica, Anna S, Björn, Post-docs Gaëlle, Sindu and Dave, as well as fellow PhD students in meteorology, Olof, Petra, Eva, Andreas, Tito, Lichuan, Nina, Maria, Erik, Susanna, Alvaro, Adam and Jennie for interesting seminars, courses and discussion.

To all fellow PhD students at LUVAL, thank you for sharing your experi-ence with me and for the support you have given me.

Thanks to Thomas Nord and Simon Östling for making sure that my com-puter work, and for calming me down when it doesn’t. Thanks to the admin-istrative personal and people working with the facilities at Geocentrum.

I wish to thank Erik Nilsson for being my mentor as a PhD student and for all our interesting discussion on turbulence and boundary layer structure. I sincerely hope that we can continue our discussions for a long time.

I would like to acknowledge Ingemar Carlén for sharing his knowledge of wind turbines and for pushing me towards relevant research. I always feel enthusiastic after speaking with you!

Special thanks goes to Fritjof, Martin, Olof and Tom for accompanying me on the lunch runs. Even on the worst, rainy, grey days I always feel like a new person after chatting with you while running for an hour.

To Majken, my Samoyed dog, and her companion, Stella, even though you cannot read this I want to send you my deepest thanks. Greeting me overjoyed at noon has brought me so much happiness. All the best ideas I have had during these years I have either come up with while running or while out walking with you.

I would like to thank all my friends for cheering me up and giving me energy when things have been tough. Special thanks goes to Uppsalafamiljen and Löpgruppen for dinner company, cheerful texts and support.

I cannot in words express how deeply grateful I am to my family for their love and support. My parents Sören and Laila and my siblings, Madeleine, Mattias and Pontus with families. In turbulence you have been my steady ground.

Finally, my warmest thanks goes to my girlfriend Matilda Häggström. You have been with me before I even knew what a Cumulus cloud was. Thank you for putting up with my sometimes absent mind, and thank you for all your support when work has occupied most of my time. Most of all, thank you for the times when I have not been working.

Mean Wind and Turbulence Conditions in the Boundary Layer above Forests

Digital Comprehensive Summaries of Uppsala Dissertations

from the Faculty of Science and Technology

1212

Mean Wind and Turbulence

Conditions in the Boundary Layer

above Forests

JOHAN ARNQVIST

List of papers

Contents

1. Introduction

1.1 Aim of this thesis

2. Background

2.1 The atmospheric boundary layer over forests

2.2 Scaling parameters

3. Data and Measurement sites

3.1 Measurement sites

3.2 Data preparation

4. Mean wind proﬁle

5. Turbulence statistics

6. Spectra

7. Wave structures in the wind

z [m]

Period [s]

time [minutes]

8. Outlook

9. Summary

10. Acknowledgments