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Highly accurate direct numerical simulations have been performed fortwo-dimensional free-surface potential flows of an ideal incompressible fluidover a constant depth $h$, in the gravity field $g$. In each numericalexperiment, at $t=0$ the free surface profile was in the form $y=A_0\cos(2\pix/L)$, and the velocity field ${\bf v}=0$. The computations demonstrate thephenomenon of Fermi-Pasta-Ulam (FPU) recurrence takes place in such systems formoderate initial wave amplitudes $A_0\lesssim 0.12 h$ and spatial periods atleast $L\lesssim 120 h$. The time of recurrence $T_{\rm FPU}$ is well fitted bythe formula $T_{\rm FPU}(g/h)^{1/2}\approx 0.16(L/h)^2(h/A_0)^{1/2}$.

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