Weakly-nonlinear stage of instability development in shear flows with an inflection-free velocity profile and thin pycnocline

Abstract: Weakly stratified flows of the class under study have a wide 3D spectrum of unstable waves with very close growth rates. What is more, their phase velocities differ little and therefore their individual critical layers merge into a common one. On this basis, nonlinear evolution equations describing the perturbation development are derived and analyzed. Their solutions demonstrate that, throughout a weakly nonlinear stage of development, wave amplitudes grow explosively. During the first (three-wave) phase, the most rapidly growing are low-frequency waves whereas at the next phase, when numerous and diverse higher-order wave interactions come into play, the growth of high-frequency waves is accelerated and they overtake low-frequency waves. The results obtained are illustrated by numerical calculations for some ensembles of waves.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods