Oblique Instability Waves in Nearly Parallel Shear Flows

Abstract

We are interested in the nonlinear interaction between a pair of oblique instability waves that develop when an initially linear, spatially growing instability waves evolve downstream in a nominally two-dimensional, unbounded or semi-bounded, laminar shear flows. It is appropriate to suppose that the Reynolds number R is large enough so that the flow is nearly parallel, and we also suppose that some sort of small-amplitude harmonic excitation (i.e. an excitation of a single frequency) is imposed on the flow (see Figure 1). Then the initial motion just downstream of the excitation device will also have harmonic time dependence and, within a few wavelengths or so, will be well described by linear instability theory.KeywordsInstability WaveCritical LayerAmplitude EquationFree Shear LayerNonlinear RegionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.