Recovery of Stokes waves from velocity measurements on an axis of symmetry

Matioc, Bogdan–Vasile

doi:10.1088/1751-8113/48/25/255501

Cited by 4 publications

(1 citation statement)

References 35 publications

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“…[19] and [20] provided some new methods to determine solitary water wave profiles from pressure transfer functions. [23] derived a power series reconstruction formula from horizontal velocity on vertical symmetry axis for Stokes waves. However, as far as we know, there is less research for the determination of stratified steady water waves than steady water waves.…”

Section: Introductionmentioning

confidence: 99%

On symmetry and recovery of steady continuous stratified periodic water waves

Xu,

Zhang,

2020

Preprint

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This paper considers two-dimensional steady continuous stratified periodic water waves. Firstly, we prove that each streamline must be symmetric about the crest line when it is strictly monotonous between troughs and crests by exploiting the maximum principle and analysis of surface profile. Then, standard Schauder estimates are exploited on the uniform oblique derivative problems to show that all streamlines are real analytic (including the free surface). Based on above symmetry and regularity of streamlines, finally we provide an analytic expansion method to recover the water waves from horizontal velocity on the axis of symmetry and wave height. Most notably, all of results here are suitable not only for small amplitude but also for large amplitude.

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Section: Introductionmentioning

confidence: 99%