A bilateral shear layer between two parallel Couette flows
arXiv:1202.5842 · doi:10.1103/PhysRevE.85.036302
Abstract
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.
6 pages, 7 figures. Accepted for publication in Phys. Rev. E