Extrema of the dynamic pressure in a solitary wave

2016/12/23 by François Genoud, Genoud, François
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Coastal and Marine Dynamics #Navier-Stokes equation solutions #Ocean Waves and Remote Sensing #math.AP #msc:35Q31 #msc:76B15 #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.1612.07918

a couple of remarks about zero vs. non-zero vorticity included; some references added

arxiv created 2017/01/11 · arxiv updated 2017/01/12

Abstract

We study the dynamic pressure in an irrotational solitary wave propagating at the surface of water over a flat bed, under the influence of gravity. We consider the nonlinear regime, that is, the case of waves of moderate to large amplitude. We prove that, independently of the wave amplitude, the maximum of the dynamic pressure is attained at the wave crest, while its minimum is attained at infinity.

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