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VOLUME 93 | ISSUE 4 | PAGE 213
Numerical study of Fermi-Pasta-Ulam recurrence for water waves over finite depth
V. P. Ruban
L.D. Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
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  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 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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