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

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

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

Cited by in corpus (2)

• Counter-diabatic driving in the classical $\beta$-Fermi-Pasta-Ulam-Tsingou chain
• Spatially quasi-periodic water waves of finite depth