
VOLUME 93  ISSUE 4 
PAGE 213

Numerical study of FermiPastaUlam 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 twodimensional freesurface 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 , and the velocity field v=0. The computations demonstrate the
phenomenon of FermiPastaUlam (FPU) recurrence takes place in such systems
for moderate initial wave amplitudes and spatial periods
at least . The time of recurrence T_{ FPU} is well
fitted by the formula
.


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