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Variational principles for water waves from the viewpoint of a time-dependent moving mesh

Bridges, TJ and Donaldson, NM (2010) Variational principles for water waves from the viewpoint of a time-dependent moving mesh Mathematika, 57. pp. 147-173.

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Abstract

The time-dependent motion of water waves with a parametrically defined free surface is mapped to a fixed time-independent rectangle by an arbitrary transformation. The emphasis is on the general properties of transformations. Special cases are algebraic transformations based on transfinite interpolation, conformal mappings, and transformations generated by nonlinear elliptic partial differential equations. The aim is to study the effect of transformation on variational principles for water waves such as Luke’s Lagrangian formulation, Zakharov’s Hamiltonian formulation, and the Benjamin–Olver Hamiltonian formulation. Several novel features are exposed using this approach: a conservation law for the Jacobian, an explicit form for surface re-parameterization, inner versus outer variations and their role in the generation of hidden conservation laws of the Laplacian. Also some of the differential geometry of water waves becomes explicit. The paper is restricted to the case of planar motion, with a preliminary discussion of the extension to three-dimensional water waves.

Item Type: Article
Authors :
NameEmailORCID
Bridges, TJt.bridges@surrey.ac.ukUNSPECIFIED
Donaldson, NMUNSPECIFIEDUNSPECIFIED
Date : 19 November 2010
Identification Number : https://doi.org/10.1112/S0025579310001233
Related URLs :
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:01
Last Modified : 17 May 2017 15:00
URI: http://epubs.surrey.ac.uk/id/eprint/833666

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