Existence of capillary-gravity water waves with piecewise constant\n vorticity

2013/02/22 by Calin Iulian Martin, Martin, Calin Iulian, Bogdan–Vasile Matioc +1 · 1 citation
Earth and Planetary Sciences · Engineering · #47J15 #76B03 #76B45 #76B70 #Analysis of PDEs (math.AP) #Coastal and Marine Dynamics #FOS: Mathematics #Ocean Waves and Remote Sensing #Wave and Wind Energy Systems

paper · pdf · doi:10.48550/arxiv.1302.5523

openalex publication_date 2013/02/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

In this paper we construct periodic capillarity-gravity water waves with a\npiecewise constant vorticity distribution. They describe water waves traveling\non superposed linearly sheared currents that have different vorticities. This\nis achieved by associating to the height function formulation of the water wave\nproblem a diffraction problem where we impose suitable transmission conditions\non each line where the vorticity function has a jump. The solutions of the\ndiffraction problem, found by using local bifurcation theory, are the desired\nsolutions of the hydrodynamical problem.\n

Cited by

• Bifurcation analysis of Stokes waves with piecewise smooth vorticity in deep water

Related

• Steady periodic water waves with unbounded vorticity: equivalent formulations and existence results
• Global bifurcation for steady finite-depth capillary-gravity waves with constant vorticity
• Bifurcation of gravity-capillary Stokes waves with constant vorticity
• On the existence of steady periodic capillary-gravity stratified water\n waves
• Existence of capillary-gravity waves that are perturbations of Crapper's waves