ONSET OF NONLINEAR INSTABILITIES IN MONOTONIC VISCOUS BOUNDARY LAYERS

In this paper, we study the nonlinear stability of a shear layer profile for Navier-Stokes equations near a boundary. More precisely, we investigate the effect of cubic interactions on the growth of the linear instability. In the case of the exponential profile, we obtain that the nonlinearity tames the linear instability. We thus conjecture that small perturbations grow until they reach a magnitude O(\nu¹/⁴) only, forming small rolls in the critical layer near the boundary. The mathematical proof of this conjecture is open.