# Nonlinear Interactions Between Oblique Instability Waves on Nearly Parallel Shear Flows

## Abstract

Asymptotic methods are used to describe the nonlinear self interaction between pairs of oblique instability modes that eventually develops when initially linear, spatially growing instability waves evolve downstream in nominally two-dimensional, unbounded or semi bounded, laminar shear flows. The first nonlinear reaction takes place locally within a so-called “critical layer” with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves together with an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy a pair of integral differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.

### Keywords

Vortex Convection Explosive Vorticity Lution## Preview

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