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

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

2010-12-15

arxiv.org/abs/1012.3246v2

JETP Letters 93(4), 195-198 (2011)

Physics

Fluid Dynamics

revtex4, 4 pages, 12 figures; references and new material added; Pis'ma v ZhETF 93(4), 213 (2011)

Scientific paper

10.1134/S0021364011040126

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 $y=A_0\cos(2\pi x/L)$, and the velocity field ${\bf v}=0$. The computations demonstrate the phenomenon of Fermi-Pasta-Ulam (FPU) recurrence takes place in such systems for moderate initial wave amplitudes $A_0\lesssim 0.12 h$ and spatial periods at least $L\lesssim 120 h$. The time of recurrence $T_{\rm FPU}$ is well fitted by the formula $T_{\rm FPU}(g/h)^{1/2}\approx 0.16(L/h)^2(h/A_0)^{1/2}$.

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