We present numerical simulations of two-dimensional viscous incompressible flows past flat plates having different kind of wedges: one tip of the plate is rectangular, while the other tip is either a wedge with an angle of \(30^\circ \) or a round shape. We study the shear layer instability of the flow considering different scenarios, either an impulsively started plate or an uniformly accelerated plate, for Reynolds number \(Re = 9500\). The volume penalization method, with either a Fourier spectral or a wavelet discretization, is used to model the plate geometry with no-slip boundary conditions, where the geometry of the plate is simply described by a mask function. On both tips, we observe the formation of thin shear layers which are rolling up into spirals and form two primary vortices. The self-similar scaling of the spirals corresponds to the theoretical predictions of Saffman for the inviscid case. At later times, these vortices are advected downstream and the free shear layers undergo a secondary instability. We show that their formation and subsequent dynamics is highly sensitive to the shape of the tips. Finally, we also check the influence of a small riblet, added on the back of the plate on the flow evolution.
Instability of shear layers Vortex dynamics Computational methods in fluid dynamics Free shear layers Wavelets Spectral methods
Mathematics Subject Classification (2000)
Primary 65M85 Secondary 76D17 65T60 65M70
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We thank Thomas Leweke and Monika Nitsche for their fruitful discussions, and Dmitry Kolomenskiy for comments on the paper.
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