The Growth of Instability Waves in a Slightly Nonuniform Medium
Kinematic wave theory, extended to include weak dissipation, higher-order amplitude dispersion, and weak nonlinearity, is used to calculate the long-time evolution of instability waves in a three-dimensional boundary layer. An unstable wave on a convected inhomogeneity reaches criticality when propagating at the velocity of the inhomogeneity; it then becomes absolutely unstable in that moving reference frame. A trapped such a wave is found to be governed by the Ginzburg-Landau equation within an inner region of size ε−172 times the wave lengt where ε << 1 measures the non-uniformity of the wave system or the background medium.
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