Inverse cascade of gravity waves in the presence of condensate: numerical simulation

During the set of direct numerical simulations of the forced isotropic turbulence of surface gravity waves in the framework of primordial dynamical equations, the universal inverse cascade spectrum was observed. The slope of the spectrum is the same (in the margin of error) for different levels of pumping and nonlinearity as well as dissipation present in the system. In all simulation runs formation of the inverse cascade spectrum was accompanied by appearance of strong long wave background (condensate). The observed slope of the spectrum $\sim k^{-3.07}$ is different from the constant wave action flux solution predicted by the Theory of Wave Turbulence $\sim k^{-23\mathrm{/}6}$.