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The euler-type description of lagrangian water waves

Buldakov, EV; Taylor, PH; Eatock Taylor, R; (2005) The euler-type description of lagrangian water waves. In: WIT Transactions on the Built Environment. (pp. 501 - 510).

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Abstract

A new description of 2D continuous free-surface flows in Lagrangian coordinates is proposed. It is shown that the position of a fluid particle in such flows can be represented as a fixed point of a transformation in ℝ. Components of a transformation function satisfy the linear Euler-type continuity equation and can be expressed via a single function analogous to an Eulerian stream function. Fixed-point iterations lead to a simple recursive representation of a solution satisfying the Lagrangian continuity equation. Expanding the unknown function into a small-perturbation asymptotic expansion we obtain the complete asymptotic formulation of the problem in a fixed domain of Lagrangian labels. The method is then applied to a classical problem of a regular wave traveling in deep water, and the fifth order Lagrangian asymptotic solution is constructed. In contrast with early attempts of Lagrangian regular-wave expansions, the presented asymptotic solution is uniformly-valid at large times. © 2005 WIT Press.

Type:Proceedings paper
Title:The euler-type description of lagrangian water waves
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Civil, Environmental and Geomatic Engineering

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