Streak growth and breakdown in a boundary layer with steady uniform suction

Streak growth and breakdown in a boundary layer with steady uniform suction

E. N. Davidsson

Turbulent flow processes play an important role in many flow systems. To optimize and control energy losses of such systems, knowledge of the mechanisms leading to and maintaining turbulence is required. Steady, uniform suction through porous materials is one control method known to stabilize the flat plate boundary layer flow.

As wall suction is applied, the growth of Tollmien-Schlichting waves are decreased and a critical Reynolds number of 54000 is reported

. Wind tunnel experiments show that also disturbances arising due to free stream turbulence are dampened by wall suction

. A common observation for parallel shear flows, and boundary layers in particular, is that streamwise streaks pre-date transition to turbulence

. Thus a numerical study of streak instabilities and breakdown is a natural step in elucidating the stabilizing effects of wall suction.

In this work, several scenarios of breakdown to turbulence of a flat plate bound- ary layer with wall suction is studied. Calculations have been performed by means of direct simulations of the Navier-Stokes equations in the temporal domain. This approach allow for the study of the evolution of periodic disturbances such as streaks and oblique waves found in figure 1. The studied disturbances are found to trigger transition to turbulence by similar mechanisms as other flows. Energy thresholds for transition to turbulence is calculated and transition at the lowest energy is provided by the oblique wave scenario for all investigated Reynolds numbers. The next step of the investigation is to study the flow further into the turbulent state, which requires the simulation code to be run in a spatial setup.

∗Lule˚a University of Technology, SE-971 87 Lule˚a, Sweden.

1Hocking, Q. J. Mech. Appl. Math. 28, 341 (1975).

2Fransson and Alfredsson, J. Fluid Mech. 482, 51 (2003).

3Yoshioka et al., Phys. Fluids 16, 3530 (2004).

4Matsubara and Alfredsson, J. Fluid Mech. 430, 149 (2001)

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Figure 1: Initial optimal disturbances. (a) Cross-flow plane of the optimal stream- wise vortices. (b) Contours of normal disturbance velocity of the oblique waves in a horizontal plane.

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