Johan Arnqvist
Mean Wind and Turbulence
Conditions over Forests
Geotryckeriet, Uppsala 2013 Department of Earth Sciences Licentiate Thesis 2013 Johan Arnqvist
Mean Wind and
Turbulence Conditions over Forests
Department of Earth Sciences Licentiate Thesis
2013
Johan Arnqvist
Mean Wind and Turbulence
Conditions over Forests
Abstract
The forest landscape has become and attractive area for wind power exploita-tion following the growth of wind turbines. However, the increase in size of the turbines and the placement in forested terrain introduce new uncertainties in the wind resource estimation. Low vegetation and near the ground pro-cesses has for long been the norm in wind resource estimation on land, but measurements presented in this thesis show that it is not a sufficient boundary description to accurately describe wind and turbulence at the heights where wind turbines over forests operate.
In the layer of the atmosphere occupied by wind turbines the wind is heav-ily influenced by exchange processes between the ground and the atmosphere. Radiation and temperature distribution as well as fluxes of heat and moisture all contribute to a high degree to determining the nature of the wind. The sim-ilarity theory that is used to predict the wind states that only a certain number of parameters is necessary to describe the full behavior of the wind. In this thesis it is shown that the traditional set of parameters is not enough, and two additional parameters, the height of the trees and the height of the atmospheric boundary layer, are attached importance to understand the wind resource over forests.
A new expression to describe the influence of the forest on the wind up to 2-3 tree heights is proposed in the thesis. The new expression is shown to agree with measurements. Furthermore, the nature of the wind is studied by means of how the mean wind, the turning of the wind and the turbulence changes with height. The results are presented in such a way that they will be useful to future studies of models aimed to predict and understand the wind resource over forests.
Sammanfattning
Skogslandskapet har blivit ett attraktivt exploateringsområde för vindkraft ef-tersom vinkraftverk har blivit så höga att skogen inte längre utgör ett definitivt hinder för den. I takt med att vindkraftverken har ökat i storlek och placerats i skog har dock kunskapen om vindresursen minskat. Ytnära skikt över låg ve-gitation har länge varit normen för beräkningar av vindresursen över land, men mätningar som presenteras i den här avhandlingen visar att det är otillräckligt för att beskriva vind och turbulens på den höjd där vindkraftverk i skogsmiljö opererar.
I det skikt av atmosfären som vindkraftverk befinner sig i beror vindens natur till mycket stor del av utbytesprocesser mellan mark och atmosfär. Sol-strålning, temperaturfördelning samt flöden av värme och fukt är exempel på parametrar som är mycket viktiga för att bestämma hur det blåser på en viss höjd. Den similaritetsteori som används för att beräkna inflytandet av mark-nära processer på vinden bygger på att endast ett bestämt antal parametrar behövs. I avhandlingen visas att de parametrar som traditionellt används inte räcker till. Ytterligare två parametrar, höjden på träden och höjden på det at-mosfäriska gränsskiktet, tillskrivs betydelse för att förstå vindenresuresen över skog.
Ett nytt uttryck för att beskriva hur skogen ändrar vinden upp till 2-3 gång-er trädens höjd föreslås i avhandlingen. Det nya uttrycket visas stämma bra överens med mätningar.Vidare studeras vindens natur genom att undersöka hur medelvind, vindvridning och turbulens ändras med höjden. Resultaten har tagits fram på sådant sätt att de skall vara till nytta för kommande studier av modeller som använts till att förutsäga vindresursen över skog.
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, 2013. Flux-profile relation with roughness sublayer correction Submitted to Quarterly Journal of the Royal Meteorological Society
II Arnqvist J, Segalini A, Dellwik E and Bergström H, 2013. Wind statistics from a forested landscape Submitted to Boundary Layer Meteorology
In paper I the author had the main responsibility for developing the theory and analyzing the data. The author had the main responsibility for writing the text.
In paper II the author had a shared responsibility for preparing the data, analyzing the data, and writing the text.
Contents
1 Introduction . . . 9
2 Theory . . . 12
3 Data and Measurement sites . . . .16
4 Results . . . .20
4.1 Mean wind profile . . . 20
4.2 Turbulence statistics. . . .23
5 Concluding remarks . . . 28
6 Acknowledgments . . . .29
1. Introduction
Wind power is becoming big business. Increasing awareness of risk for hu-man induced climate change together with increasing energy dehu-mands have spawned the rise of wind industry. As the industry have grown over the last thirty years, so has the turbine sizes. The hub height of a typical wind turbine has grown, from being 20 metres in 1990 to around 120 metres twenty years later. The size of a modern wind turbines means that it is possible to install them in forested areas. This is of course interesting in Sweden, where more than half of the country is covered with forest. It also raises a series of ques-tions which facilitates the "make it or brake it" (not literary) for wind power in forested areas. Two main questions can be identified:
• How high must a wind turbine be over the forest to produce a sufficient amount of electricity?
• How high must a wind turbine be to withstand the turbulence created by the forest?
These two question are the base of the research project in which this Licen-tiate thesis is produced. The authors’ work is only covering the part of these questions that concern wind. How the turbine reacts to loads from turbulent wind gusts, and how the turbine can be optimized to produce best in forest conditions are not covered by this thesis. It is thus relevant to rephrase the questions in terms of the wind conditions.
• How does the mean wind profile behave over a forest?
• How does turbulence generated by the forest decay with height? • Is the turbulence over forests any different from that over low
vegeta-tion?
We will reconnect to these questions throughout this thesis, but first it is rele-vant with an overview of the present knowledge concerning winds over forests. Even a modern wind turbine with a hub height of over 100 metres is gener-ally operating in turbulent conditions. The lower part of the atmosphere where winds are characterized by turbulence is called the boundary layer. Within the boundary layer turbulence mixes the air so that anything that happens at the surface, e g. heating by the sun or a change in surface roughness, is com-municated thorough the boundary layer by turbulent eddies. This process is rapid and an approximate time scale for something to travel from the bottom of the boundary layer to the top of the boundary layer is approximately a turnover time of of a turbulent eddy spanning the boundary layer. Given that the bound-ary layer is approximately between 100 metres to 2 kilometres deep this time scale is from few minutes to an hour. Above the boundary layer the flow is much smoother.
The lowest 10% of the boundary layer is called the surface layer. Within the surface layer the air is almost in 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 turbulent 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 in the forest itself behaves differently, so the surface layer is lifted up a distance d, the so called displacement height.
Within the forest the turbulence intensity is very high, around 100%, mean-ing that a typical change of wind due to a turbulent gust is of the same size as the wind itself. 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 profile is close to exponential, which is obtained both from theo-retical considerations and observations. Above the forest, close to the forest edge, there is another layer, the roughness sublayer. The roughness sublayer is defined by the fact that it is above the forest, but observations there does not match the surface layer theory. This layer is something that differers forests from low vegetation and it is thus connected to the last of the research ques-tions presented above. One explanation for the roughness sublayer is that it is the kink, the inflection point in the wind profile where it goes from exponential (within the forest) to logarithmic (above the forest) that gives rise to vortices of about the same size as the forest itself that enhance the turbulent mixing there. A schematic picture of the turbulence in the surface layer, the rough-ness sublayer, the forest layer as well as a typical scale of forest to turbine is shown in Figure 1.1
Figure 1.1.A schematic picture of the flow regimes in forest terrain. The tree height (h) and the displacement height (d) are indicated by lines
2. Theory
The non-linear Navier-Stokes equations that govern all fluid dynamic prob-lems are, with our present knowledge unsolvable for virtually all practical ap-plications. The without question most frequent solution to this is to linearise the equations by introducing Reynolds averaging. By decomposing a variable ξ to ξ + ξ0, where o ξ is the mean and ξ0is the instantinous fluctuation, the number of non-linear terms can be reduced, but it is tantalizingly so that there is always at least one new that is created. This can be solved by expressing the new non-linear term (which in the first step is called the Reynolds-stress) as a function of even higher order terms. But, as there are always more non-linear terms created in the process it is a game that can go on forever. The dominant solution to this puzzle in the boundary layer community is similarity theory. First, by careful study of the boundary conditions for the flow some clever approximations can be made. Second, identification of scaling parameters are done. This process involves finding key parameter that are especially impor-tant for the flow. Third, constructing desired variables from the set of key parameters. If for example the key parameters velocity scale, u, and length scale, l, has been identified, a time scale, t, can be constructed on dimensional arguments by t = l/v. By this process, the problematic non-linear terms in the Navier-Stokes equations can be expressed as functions of other, known, parameters.
The concept of similarity then says that if the proper key parameters has been identified, all the other variables can be constructed, no matter the scale of the flow. In the atmospheric surface layer the key parameters are
Variable name Physical interpretation Dimension
z Height m
(u0w02+ v0w02)1/2 Vertical momentum flux m2s−2 −w0t0 Vertical temperature flux ms−1K
g/T0 Buoyancy ms−2K−1
The use of them in similarity theory is known as the Monin-Obukhov sim-ilarity theory (Wyngaard, 2010). In the surface layer, vertical derivatives of fluxes are neglected so they are typically evaluated just above the sur-face. It is conventional to rewrite the surface fluxes to a velocity scale u∗=
(u0w02+ v0w02)1/4, and a temperature scale T
∗= −w0t0/u∗.The last parameter,
gravitational acceleration, g, over background temperature, T0, can be given
further physical meaning by the hydrostatic equation and the gas law. It can then be written as a measure of the weight of a small vertical slab of the atmo-sphere, and is thus useful in creating a measure of how prone the atmosphere is to vertical movement.
If we take the Reynolds stress for example, Yaglom (1979) says that any moment of the three velocity components can be described by:
uiujuk... = u∗1,2,3...Φ(ξ1, ξ2, ξ3...), (2.1)
where Φ is a universal function of the argument ξ , which is in turn a non-dimensional group of the key parameters. ξ is a scale measure, so it measures the ratio of a variable compared to the scale constructed by the key parameters. If we instead like to now how the wind speed, U changes in the surface layer as a function of the variable z we must first construct a length scale, l, from the other key parameter 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 (2.2)
This scale was first identified by Obukhov in 1946, and its product with one over 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 di-mensional arguments
∂U ∂ z =
u∗
κ zφ (z/L). (2.3)
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 small correction that over forests the relevant height is not z, but rather (z − d), Equation 2.3 does describe the wind gradient accurately in the surface layer over a forest as we shall later see from the measurements. The problem is that at the heights now relevant for wind energy the surface layer key parameters are not enough. The similarity theory can be widened by in-troducing new key parameters in addition to the set that is valid for the surface layer. As the scale grows it is foremost the Coriolis parameter, f , that becomes important to describe the flow. It is now possible to construct new length scales from combinations of the key parameters. The simplest 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∗
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 −w0t0f 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= s g∂ θ θ0∂ z , (2.7)
where θ 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 a stable atmosphere. This results in yet another length scale formula-tion,
lbs=
u∗
| f N|1/2. (2.8)
lbs is a scale measure for the height of the long term stable boundary layer.
The boundary layer height can now be expressed as a combination of these three length scales. Zilitinkevich et al (2007) proposes
δ−2= (Clf)−2+ (Cnslns)−2+ (Cbslbs)−2, (2.9)
where C, Cnsand Cbsare empirical constants for the neutral, nocturnally stable
and long term stable boundary layer respectively.
Now that we have a measure of the boundary layer height we can further develop the the similarity theory to include a measure of the scale of z − d compared to δ . In the case of wind gradient the similarity is:
∂U ∂ z =
u∗
κ zΦ((z − d)/L, (z − d)/δ ). (2.10) 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 wind with height, veer, is something that we shall later see is a prominent feature in the measurements over the forest.
Closer to the forest, in the roughness sublayer, (z − d)/δ is small enough that we can ignore it, but it is instead another length scale that becomes rele-vant. The choice of this length scale is not a closed matter but in Paper I we argue that it is h − d, where h is the tree height, that is the relevant length scale 14
for the roughness sublayer. If we again take the example of wind shear, it can thus be written, for the whole boundary layer
∂U ∂ z =
u∗
κ zΦ((z − d)/L, (z − d)/δ , (z − d)/(h − d)). (2.11) 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.
3. Data and Measurement sites
Within the research project V-312 Wind over forests there has been three main measurement sites, two with atmospheric measurements and one in a wind tunnel. This thesis will only cover results from the atmospheric measurements. The locations of the measurement sites can be seen in Figure 3.1. The western site Skogaryd includes measurements in a 38 m high tower. The measurement set-up was focused on near- and within-canopy processes. 3D wind and virtual temperature was sampled at the heights 1, 6, 12, 18, 30.5 and 38 m at 20 Hz by USA-1 (Metek Gmbh) sonic anemometers. In addition the reference temperature was sampled at 1 and 6 m at 1 Hz by Risø PT-100 instruments. The mean tree height from inspection was 25 m. The campaign ran from October 2011 to June 2012.
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 LIDAR (LIght Detection And Ranging) (Natural Power, Zephir) 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. For the reference temperature, Risø PT-100 was used at 40, ,80, 98 and 138 m. The existing instrumentation in the tower, before the measurement campaign started, included 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 mature forest close to the tower. In the large scale there is patchy forest cover for more than two hundred kilometres 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 typ-ical in Swedish forestry and are likely to be dominant in any wind power site located in a Swedish forest. Directional analysis of the instruments were done in order to determine the most representative wind directions to analyse the measurements from. In addition to studying the 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 averaged in 5x5x1 m3 cubes, and the ground height was taken as the minimum value in each cube 5x5 m col-umn. The forest density was determined through the fraction of incoming light 16
Figure 3.1.A map of sweden with the location of the two field sites. X-marks indicate the positions of the measurement towers
intensity to outgoing light intensity in each layer and scaled between 0 and 1. The results 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 respec-tively.
The tree height from inspection was 20 m for Ryningsnäs and 25 m for Skogaryd. In Figure 3.3 the distribution of tree height from each 5x5 m col-umn, being in the selected sector and closer than 200 m to the tower is shown. For Skogaryd, the distribution has a peak at the same value as by visual inspec-tion. For Ryningsnäs the distribution also has a clear peak, but the LIDAR-scans suggest a slightly higher value than from visual inspection.
5001000 15002000 500 1000 1500 2000 50 100 150 200 250 distance [m] distance [m] height [m] 10 20 30 0.25 0.5 0.75 200 400 600 800 400 600 800 0 50 100 150 200 distance [m] distance [m] height [m] 0 10 20 30 0.25 0.5 0.75
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.
Tree height [m]
0 5 10 15 20 25 30
Figure 3.3.Distribution of the tree height in the selected sector within 200 m from the
4. Results
To study properties of the wind, the data was prepared for analyzis by carry-ing out a Reynolds decomposition. This was done in the same manner for both sites, with a 30 minute block average. Details regarding the statistical prepa-ration can be found in paper II. A short summary is that the coordinate system was aligned with the mean wind vector at each height and that the velocity components were decomposed as U, u0,V, v0,W and w0, where V = 0. To de-termine how the flow depends 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 by their value of (z − d)/L. But, as the Ekman layer, the forest layer, and the roughness sublayer have different length scales that can be used to create non-dimensional measures of stability, we put limits for the stability classes on 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 Neutral, −1000 < L < −100, is shown in the figures. Data from both sites has been filtered with a despiking algorithm in order to remove erroneous data due to snow or rime ice. The despiking algorithm is described in detail in paper II. Two flow conditions has been used for both sites based on measurements at z ≈ 40 m, one on the required stationarity and one on min-imum wind speed. The stationarity criterion required that the wind direction did not change more than 10◦ from one 30 minute average to adjacent ones and that the wind speed from the centre ten minute average did not deviate more than 10% from adjacent ones. The wind speed condition of U > 3ms−1 was used to ensure that the mechanical turbulence was large enough that the higher order statistics would would converge. The same height was used to determine u∗ and L, which is throughout this thesis considered as constants
for each 30 minute period.
4.1 Mean wind profile
As we saw in Chapter 2, from arguments of similarity theory, the mean wind gradient over forest can be written as
∂U ∂ z =
u∗
κ zΦ((z − d)/L, (z − d)/δ , (z − d)/(h − d)). (4.1) If we integrate Equation 4.1 with height, we have the mean wind profile. Close to the forest, the length scales L and h − d are the most important ones as 20
(z − d)/δ is small enough to be ignored. Several studies has been made in order to find a working expression for Φ (Cellier and Brunet, 1992; Physick and Garratt, 1995; Mölder et al, 1999; Harman and Finnigan, 2007; Ridder, 2009). The prevalent way is to write Φ=φm(z − d, L)ϕ(z − d, lf), where φmis
the non-dimensional gradient for surface layer and ϕ 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 have an analytical form of the integrated Equation 4.1. In paper I we follow Harman and Finnigan (2007) and use the central length scale h − d to represent the forest and develop a form of ϕ which has an analytical form of the integrated wind gradient. The resulting wind profile is shown in Figure 4.1 using typical forest values of h= 20, d = 15 and ϕ(h − d) = 0.6. A key finding in both paper I and paper II is the fact that surface roughness length, z0, the integration constant that
comes out of integrating Equation 4.1 decreases with increasing stability for stable stratification. Measurements from both Skogaryd and Ryningsnäs, as well as the wind profile expression developed in paper I show a decrease of z0
by 50% going from neutral to stable stratification.
When the non-dimensional scale (z − d)/δ becomes large it is necessary to include it as an argument to Φ. While we have not attempted this, in Paper II we have evaluated the formulation of δ from Rossby and Montgomery (1935) and Zilitinkevich et al (2007) against boundary layer heights deduced from radio soundings. We found that a value of the constant C in the Rossby and Montgommery formulation, C = 0.1, gave good agreement with the sound-ings. Based on δ from Rossby and Montgommery, Peña et al (2009) developed a formulation for the wind speed in the Ekman layer, and we have included it for reference in Figure 4.1. In the comparison in Figure 4.1, U /u∗-profiles
from paper I and from Peña et al (2009) was determined for each value of L in the data-set. The individual profiles were then averaged within the same stability classes as for the measurements. The reason why not just a single profile was calculated for the mean value of L in each stability class was to ensure that any non-linear response to a variation of L around a given mean value would not give a bias in the comparison.
Also in Figure 4.1 is the tower measurements of U /u∗and the measurents of
Ufrom the LIDAR. The LIDAR measurements were scaled with correspond-ing u∗ from the tower. The Zephir LIDAR had problems measuring in the
turbulent conditions at Ryningsnäs and studies of the results pointed out two main reasons for this. First, this type of LIDAR can only measure |U | and thus 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 this caused a problem due to frequent flow separation within the clearing and above. After correction, using the 98 m tower measurement as reference instead, there was still a positive bias, with magnitude increasing
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.
with the turbulence intensity σu/U . This problem was found to mainly consist
of a systematic error of the algorithm used to translate laser backscatter data into wind speed (Bergström et al, 2013).
A feature of the mean wind profile in the atmospheric boundary layer that is often overlooked is its turning with height. A study based on the wind veer from Ryningsnäs showed that taking the veer into account in the pitch-control of the turbine can reduce the fatigue loads (Bergström et al, 2013). A theoreti-cal description of the wind veer is found by assuming that there is a balance in the boundary layer between 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, times the wind gradient, so that the flux divergence, ∂ u0w0/∂ z = −K∂2U/∂ z2and ∂ v0w0/∂ z = −K∂2V/∂ z2 (Ek-man, 1905). This solution gives a 45◦wind turning within the Ekman layer, called the Ekman spiral. Such large values are seldom observed, but using 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 4.2 the Grisogono (2011) expression is shown using a value of
K0= l κ φm(l/L)
e1/2 (4.2)
where l is given by l = (115−1+ δ−1)−1, and φmis the stability function from
Högström (1996). This form of K0comes from theoretical considerations and
matching with the Ryningsnäs data. In the Grisogono (2011) profile shown in Figure 4.2, L was taken from measurements and δ from the Rossby Mont-gomery formulation. Although it is obvious that the theory still overestimates the wind turning it gives realistic values, especially in stable stratification were the veer is significant. Within the forest the veer is much harder to measure ac-curately due to the high turbulence intensities. This is reflected in Figure 4.2 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. A theoretical consideration gives 90◦between forest floor and boundary layer top.
4.2 Turbulence statistics
Apart from the mean wind profile the turbulent statistics are also important to wind industry. Results from the measurements presented here indicate that a wind turbine in a forest might be exposed to more severe loads than what is currently covered by the most rigid industry standard Bergström et al (2013). Figure 4.3 shows the six unique components of the Reynolds stress. Over
Figure 4.2. 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.
the forest the diagonal terms show close to height-constant values with ratios σu,v,w/u∗= 1.9, 1.5, 1.2, for the neutral class. Not much variation can be seen
between the different stability classes, especially considering the scatter within each class. Within the forest the turbulence is much more evenly distributed and the three velocity components carry approximately equally much turbulent energy. A detail is that the horizontal components show 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 (Yi, 2008). Close to the forest virtually all of the vertical shear stress is found in u0w0, and it is only at the highest heights, and particularly in stable conditions, that v0w0 becomes important. This is also the conditions in which we see the most wind veer.
Wind turbines rely on active-control units to adjust the pitch angle of the blade and the rotation speed to adjust the power output and the loads. If a wind model is used to tune such an active-control system it is important 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 magnitudes close to tree tops and decaying towards the top of the roughness sublayer (Raupach et al, 1996; Finnigan, 2000; Segalini et al, 2013). As most 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. In Figure 4.4 the skewness of all three velocity components is shown. The same behaviour as in the literature is observed close to the canopy, including the decay of the skewness up to z≈ 2h. As the lowest point of a typical turbine rotor is above that height it seems that the near-forest characteristics is of non-zero skewness is of minor importance to the wind industry. In the vertical interval of interest to wind power it is only the skewness of w that is significantly non-zero, but as an appropriate scaling is likely to include δ it is hard to draw conclusion from the results as L only implicitly affects δ .
Figure 4.3. Vertical profiles of (a) u0u0/u2∗, (b) u0v0/u2∗, (c) u0w0/u2∗, (d) v0v0/u2∗,
(e) v0w0/u2∗, ( f ) w0w0/u2∗with the lines as stability-class mean in diabatic conditions:
stable (blue), neutral (green) and unstable, close to neutral (orange). The shaded area shows the standard deviation of the measurements.
Figure 4.4.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 diabatic conditions: stable (blue), neutral (green) and unstable, close to neutral (orange). The shaded area shows the standard deviation of the measurements.
5. Concluding remarks
Wind power is a fast growing business, both in terms of economical growth and in terms of turbine size. The recent expansion of wind power into forested areas calls for increased knowledge of the atmospheric boundary layer over forests. In paper I the wind in the layer closest to the forest, the roughness sublayer has been studied. A new wind profile expression is proposed and is shown to work in various atmospheric stabilities over two measurement sites. Although it was shown in paper II that roughness sublayer effects is of minor importance at the heights of interest for wind power, the new wind profile expression presented in paper I also describes the wind profile within the forest, which could prove important if implemented in meso-scale models that currently have very poor forest description.
In paper II the wind profile up to 138 m was reported and compared to sur-face layer theory. Both paper I and paper II showed roughness lengths that decreased in stable stratification. In paper I the new wind profile expression could reproduce this result. The roughness length was found to decrease with 50% in both paper I and paper II, going from neutral to stable stratification. This is of high interest to the wind power industry as it affects the wind re-source estimation.
In paper II the often overlooked wind veer was presented and was shown to be of such a magnitude that it is important to consider for wind power. The wind veer is coupled to the boundary layer height, and a comparison of two different analytical models to boundary layer heights from radio soundings gave insight to model constants. The influence from the boundary layer height on second- and third-order turbulence statistics was discussed. In paper II it was also discussed why traditional surface layer scaling can be successful at higher heights despite that surface layer approximations are not valid.
The comprehensive results presented in paper II provide a wide basis for parametrization and validation of new models that aims to describe the flow in the boundary layer over a forest. It is the authors’ hope that it will be put to much use in the coming years.
6. Acknowledgments
I would like to thank my supervisors Hans Bergtröm, Anna Rutgersson and Stefan Söderberg for their full support. If it wasn’t for them this licentiate the-sis would never have been produced. A very special thanks to Hans for never being to busy for my questions, and for always providing such thoughtful an-swers.
Deep and gracious thanks to my co-authors Ebba Dellwik and Antonio Se-galini. During hours and hours of work, e-mail conversations and Skype talks it has always been a pleasure working with you. Thank you both for your patience with me. A special thanks to Antonio for your impressive speed and work capacity and a special thanks to Ebba for always encouraging me, and reminding me to never settle for less than doing my best.
Finally a big thanks to all the PhD students in meteorology, present and former, for shared laughs and shared burdens.
This licentiate thesis has been a part of the Vindforsk III project V-312, Wind power in forests.
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