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Solitary Water Waves of Large Amplitude Generated by Surface Pressure

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Abstract

We consider exact nonlinear solitary water waves on a shear flow with an arbitrary distribution of vorticity. Ignoring surface tension, we impose a non-constant pressure on the free surface. Starting from a uniform shear flow with a flat free surface and a supercritical wave speed, we vary the surface pressure and use a continuation argument to construct a global connected set of symmetric solitary waves. This set includes waves of depression whose profiles increase monotonically from a central trough where the surface pressure is at its lowest, as well as waves of elevation whose profiles decrease monotonically from a central crest where the surface pressure is at its highest. There may also be two waves in this connected set with identical surface pressure, only one of which is a wave of depression.

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  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA

    Miles H. Wheeler

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  1. Miles H. Wheeler
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Correspondence to Miles H. Wheeler.

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Communicated by C. Dafermos

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Wheeler, M.H. Solitary Water Waves of Large Amplitude Generated by Surface Pressure. Arch Rational Mech Anal 218, 1131–1187 (2015). https://doi.org/10.1007/s00205-015-0877-7

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  • DOI: https://doi.org/10.1007/s00205-015-0877-7

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