Second-order Lagrangian description of tri-dimensional gravity wave interactions

Type Article
Date 2015-06
Language English
Author(s) Nouguier FredericORCID1, Chapron Bertrand2, Guerin Charles-Antoine1
Affiliation(s) 1 : Aix Marseille Univ, CNRS, Univ Toulon, MIO,IRD,UM 110, F-83957 La Garde, France.
2 : IFREMER, Lab Oceanog Spatiale, F-29280 Plouzane, France.
Source Journal Of Fluid Mechanics (0022-1120) (Cambridge Univ Press), 2015-06 , Vol. 772 , P. 165-196
DOI 10.1017/jfm.2015.179
WOS© Times Cited 2
Keyword(s) surface gravity waves, waves/free-surface flows
Abstract We revisit and supplement the description of gravity waves based on perturbation expansions in Lagrangian coordinates. A general analytical framework is developed to derive a second-order Lagrangian solution to the motion of arbitrary surface gravity wave fields in a compact and vectorial form. The result is shown to be consistent with the classical second-order Eulerian expansion by Longuet-Higgins (J. Fluid Mech., vol. 17, 1963, pp. 459-480) and is used to improve the original derivation by Pierson (1961 Models of random seas based on the Lagrangian equations of motion. Tech. Rep. New York University) for long-crested waves. As demonstrated, the Lagrangian perturbation expansion captures nonlinearities to a higher degree than does the corresponding Eulerian expansion of the same order. At the second order, it can account for complex nonlinear phenomena such as wave-front deformation that we can relate to the initial stage of horseshoe-pattern formation and the Benjamin-Feir modulational instability to shed new light on the origins of these mechanisms.
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