  Freak waves are very large, rare events in a random ocean wave train. Here we
study the numerical generation of freak waves in a random sea state
characterized by the JONSWAP power spectrum. We assume, to cubic order in
nonlinearity, that the wave dynamics are governed by the nonlinear Schroedinger
(NLS) equation. We identify two parameters in the power spectrum that control
the nonlinear dynamics: the Phillips parameter $\alpha$ and the enhancement
coefficient $\gamma$. We discuss how freak waves in a random sea state are more
likely to occur for large values of $\alpha$ and $\gamma$. Our results are
supported by extensive numerical simulations of the NLS equation with random
initial conditions. Comparison with linear simulations are also reported.
