Evolution of vortices in 2D boundary layer and in the Couette flow

Abstract

A 2D incompressible laminar boundary layer and the Couette flow having the low velocity fluctuations are considered using asymptotic methods at high Reynolds number. Two classes of solutions for the first order inviscid perturbations have been derived. The integral-differential equation with initial data describing evolution of vortices in time have been solved numerically. It was found that the discontinuities are formed in a smooth solution for a vertical velocity component with the time increase. This first type solution explains instability mechanism in the Couette flow. The second class of solutions contains a singularity at the boundary layer bottom which reminds a source-sink with a variable intensity. The singularity can absorb the fluid from the main part of the boundary layer and eject it back with a possibly “new” vorticity.