  We examine and discuss the spatial evolution of the statistical properties of
mechanically generated surface gravity wave fields, initialised with
unidirectional spectral energy distributions, uniformly distributed phases and
Rayleigh distributed amplitudes. We demonstrate that nonlinear interactions
produce an energy cascade towards high frequency modes with a directional
spread and triggers localised intermittent bursts. By analysing the probability
density function of Fourier mode amplitudes in the high frequency range of the
wave energy spectrum, we show that a heavy-tailed distribution emerges with
distance from the wave generator as a result of these intermittent bursts,
departing from the originally imposed Rayleigh distribution, even under
relatively weak nonlinear conditions.
