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- W2147542870 abstract "A new description of two-dimensional 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 . Components of the 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 in 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 the classical problem of a regular wave travelling in deep water, and the fifth-order Lagrangian asymptotic solution is constructed, which provides a much better approximation of steep waves than the corresponding Eulerian Stokes expansion. In contrast with early attempts at Lagrangian regular-wave expansions, the asymptotic solution presented is uniformly valid at large times." @default.
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- W2147542870 date "2006-08-14" @default.
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- W2147542870 title "New asymptotic description of nonlinear water waves in Lagrangian coordinates" @default.
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- W2147542870 doi "https://doi.org/10.1017/s0022112006001443" @default.
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