A bilateral shear layer between two parallel Couette flows

TL;DR

This paper introduces a novel shear layer between two parallel Couette flows with lateral width variation, providing an analytic solution validated by numerical simulations and exploring stability and mixing phenomena.

Contribution

It derives an analytic solution for a new type of shear layer with lateral width variation, supported by numerical validation and preliminary instability analysis.

Findings

Analytic formula for shear zone width as a function of wall-normal coordinate.

Numerical solutions agree with the analytical model to better than 1%.

Preliminary instability analysis shows unsteady mixing at the interface.

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.