A bilateral shear layer between two parallel Couette flows

Details A bilateral shear layer between two parallel Couette flows A bilateral shear layer between two parallel Couette flows

2012-02-27

arxiv.org/abs/1202.5842v1

Physics

Fluid Dynamics

6 pages, 7 figures. Accepted for publication in Phys. Rev. E

Scientific paper

We consider a shear layer of a kind not previously studied to our knowledge. Contrary to the classical free shear layer, the width of the shear zone does not vary in the streamwise direction but rather exhibits a lateral variation. Based on some simplifying assumptions, an analytic solution has been derived for the new shear layer. These assumptions have been justified by a comparison with numerical solutions of the full Navier-Stokes equations, which accord with the analytical solution to better than $1\%$ in the entire domain. An explicit formula is found for the width of the shear zone as a function of wall-normal coordinate. This width is independent of wall velocities in the laminar regime. Preliminary results for a co-current laminar-turbulent shear layer in the same geometry are also presented. Shear-layer instabilities were then developed and resulted in an unsteady mixing zone at the interface between the two co-current streams.

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