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Short-wavelength instabilities of edge waves in stratified water. (English) Zbl 1302.76070

Summary: In this paper we make a detailed analysis of the short-wavelength instability method for barotropic incompressible fluids. We apply this method to edge waves in stratified water. These waves are unstable to short-wavelength perturbations if their steepness exceeds a specific threshold.

MSC:

76E99 Hydrodynamic stability
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B70 Stratification effects in inviscid fluids
35Q35 PDEs in connection with fluid mechanics
35B36 Pattern formations in context of PDEs
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
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