Traveling gravity water waves with critical layers

Abstract

We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with critical layers and an arbitrary number of crests and troughs in each minimal period. An important part of the analysis is a fairly complete description of the local geometry of the so-called kernel equation, and of the small-amplitude solutions. Finally, we investigate the asymptotic behavior of the bifurcating solutions.

arXiv comment31 pages

References in corpus (6)

• Steady periodic water waves with constant vorticity: regularity and local bifurcation
• Steady water waves with multiple critical layers: interior dynamics
• Traveling water waves with compactly supported vorticity
• Trimodal steady water waves
• Solitary gravity-capillary water waves with point vortices
• Global bifurcation of steady gravity water waves with critical layers

Cited by in corpus (4)

• Solitary waves on rotational flows with an interior stagnation point
• An existence theory for small-amplitude doubly periodic water waves with vorticity
• Large-amplitude steady gravity water waves with general vorticity and critical layers
• Global bifurcation of capillary-gravity water waves with overhanging profiles and arbitrary vorticity