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JETP Letters

, Volume 93, Issue 4, pp 195–198 | Cite as

Numerical study of Fermi-Pasta-Ulam recurrence for water waves over finite depth

  • V. P. Ruban
Plasma, Hydro- and Gas Dynamics

Abstract

Highly accurate direct numerical simulations have been performed for two-dimensional free-surface potential flows of an ideal incompressible fluid over a constant depth h, in the gravity field g. In each numerical experiment, at t = 0 the free surface profile was in the form y = A 0cos(2πx/L), and the velocity field v = 0. The computations demonstrate the phenomenon of Fermi-Pasta-Ulam (FPU) recurrence takes place in such systems for moderate initial wave amplitudes A 0 ≲ 0.12h and spatial periods at least L ≲ 120h. The time of recurrence T FPU is well fitted by the formula T FPU(g/h)1/2 ≈ 0.16(L/h)2(h/A 0)1/2.

Keywords

Soliton JETP Letter Water Wave Spatial Period Shallow Water Wave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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