The Mathematical Theory of Permanent Progressive Water-Waves

Okamoto, Hisashi; Shoji, Masataka

doi:10.1142/4547

Cited by 123 publications

(155 citation statements)

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“…The review by [20] shortly summarises in great lines what has been known on this subject at the end of the twentieth century. Monographs by [39] and by [44] are other exhaustive sources of informations on various types of capillary-gravity waves.…”

Section: Introductionmentioning

confidence: 99%

A plethora of generalised solitary gravity–capillary water waves

Clamond¹,

Dutykh

Durán

2015

J. Fluid Mech.

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The present study describes, first, an efficient algorithm for computing solutions in terms of capillary–gravity solitary waves of the irrotational Euler equations with a free surface and, second, provides numerical evidences of the existence of an infinite number of generalised solitary waves (solitary waves with undamped oscillatory wings). Using conformal mapping, the unknown fluid domain, which is to be determined, is mapped into a uniform strip of the complex plane. In the transformed domain, a Babenko-like equation is then derived and solved numerically.

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Section: Introductionmentioning

confidence: 99%

A plethora of generalised solitary gravity–capillary water waves

Clamond¹,

Dutykh

Durán

2015

J. Fluid Mech.

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“…Jones & Toland [38] introduced and studied a version of Nekrasov's equation for periodic gravity-capillary waves which has become the basis for a large number of analytical and numerical existence theories revealing a much more complex local and global bifurcation picture than that for pure gravity waves. A comprehensive survey of current results in this area is given by Okamoto & Shoji [53]. The mathematical problem for rotational Stokes waves is rather different.…”

Section: Further Resultsmentioning

confidence: 99%

Steady Water Waves

Groves¹

2004

JNMP

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“…All these works strongly use the assumption that the flow in the bulk is irrotational, whereby one may reformulate the problem in terms of quantities defined at the fluid surface. We encourage the interested reader to some excellent surveys [Tol96,OS01,BT03,Gro04,Str10].…”

Section: Stokes Wavesmentioning

confidence: 99%

On the recovery of traveling water waves with vorticity from the pressure at the bed

Hur

Livesay

2016

European Journal of Mechanics - B/Fluids

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Abstract. We propose higher-order approximation formulae recovering the surface elevation from the pressure at the bed and the background shear flow for small-amplitude Stokes and solitary water waves. They offer improvements over the pressure transfer function and the hydrostatic approximation. The formulae compare reasonably well with asymptotic approximations of the exact relation between the pressure at the bed and the surface wave in the zero vorticity case, but they incorporate the effects of vorticity through solutions of the Rayleigh equation. Several examples are discussed.

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The Mathematical Theory of Permanent Progressive Water-Waves

Cited by 123 publications

References 0 publications

A plethora of generalised solitary gravity–capillary water waves

A plethora of generalised solitary gravity–capillary water waves

Steady Water Waves

On the recovery of traveling water waves with vorticity from the pressure at the bed

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