|Copyright||Cambridge University Press 2015|
|Author(s)||Nouguier Frederic1, 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|
|WOS© Times Cited||1|
|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.|
Nouguier Frederic, Chapron Bertrand, Guerin Charles-Antoine (2015). Second-order Lagrangian description of tri-dimensional gravity wave interactions. Journal Of Fluid Mechanics, 772, 165-196. Publisher's official version : http://doi.org/10.1017/jfm.2015.179 , Open Access version : http://archimer.ifremer.fr/doc/00274/38476/