  We study the long-time evolution of gravity waves on deep water exited by the
stochastic external force concentrated in moderately small wave numbers. We
numerically implement the primitive Euler equations for the potential flow of
an ideal fluid with free surface written in canonical variables, using
expansion of the Hamiltonian in powers of nonlinearity of up to fourth order
terms.
  We show that due to nonlinear interaction processes a stationary energy
spectrum close to $|k| \sim k^{-7/2}$ is formed. The observed spectrum can be
interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of
energy.
