Marginal and weakly nonlinear stability in spatially developing flows

Abstract

This work is devoted to revealing the essence of near-critical phenomena in nonlinear problems with nonparallel effects. As a generalization of the well-known concept of linear stability in Fourier space for a parallel basic state, we introduce a new concept valid for nonparallel flows as well. The new picture allows one to demonstrate the possible singular limit to the parallel case. Also, on its basis we derive a weakly nonlinear model valid near criticality. The damped Kuramoto-Sivashinsky equation with variable coefficients is used to illustrate the application of the theory.