| Type |
Article |
| Date |
2015-06 |
| Language |
English |
| Author(s) |
Nouguier Frederic 1, 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 |
8 |
| 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. |
| Full Text |
| File |
Pages |
Size |
Access |
|
32 |
1 MB |
Access on demand |
| Author's final draft |
32 |
2 MB |
Open access |
|
