Stratified periodic water waves with singular density gradients

Abstract

We consider Euler's equations for free surface waves traveling on a body of density stratified water in the scenario when gravity and surface tension act as restoring forces. The flow is continuously stratified, and the water layer is bounded from below by an impermeable horizontal bed. For this problem we establish three equivalent classical formulations in a suitable setting of strong solutions which may describe nevertheless waves with singular density gradients. Based upon this equivalence we then construct two-dimensional symmetric periodic traveling waves that are monotone between each crest and trough. Our analysis uses, to a large extent, the availability of a weak formulation of the water wave problem, the regularity properties of the corresponding weak solutions, and methods from nonlinear functional analysis.2010 Mathematics Subject Classification. 35Q35; 35B32; 76B70; 76B47.

Exact solutions and internal waves for the Antarctic Circumpolar Current in spherical coordinates

“…7,[16][17][18][19][20][21][22][23][24][25][26][27] . On a related note, we would like to point out the very recent results by Escher et al 28 on stratified water flows with singular density gradients.…”

Azimuthal equatorial flows in spherical coordinates with discontinuous stratification

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Global bifurcation of capillary-gravity water waves with overhanging profiles and arbitrary vorticity

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