  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 $T_{\rm FPU}(g/h)^{1/2}\approx 0.16(L/h)^2(h/A_0)^{1/2}$.
