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Pré-Publication, Document De Travail Année : 2014

A plethora of generalised solitary gravity-capillary water waves

Didier Clamond
Angel Durán
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Résumé

The present study describes, first, an efficient algorithm for computing gravity-capillary solitary waves solutions of the irrotational Euler equations and, second, provides numerical evidences of the existence of (likely) an infinite number of generalised solitary waves (i.e. 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. A Babenko-like equation is then derived from a Lagrangian expressed in the transformed domain. The Babenko equation is then solved numerically using a Levenberg-Marquardt algorithm. Various interesting solutions are computed, some of them being known, some seem to be new. The emergence of generalised solitary waves is shown when the Bond number is increased.
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Dates et versions

hal-01081798 , version 1 (11-11-2014)
hal-01081798 , version 2 (01-07-2015)
hal-01081798 , version 3 (07-10-2015)

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  • HAL Id : hal-01081798 , version 1

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Didier Clamond, Denys Dutykh, Angel Durán. A plethora of generalised solitary gravity-capillary water waves. 2014. ⟨hal-01081798v1⟩
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