Almost all simulations shown here were done on grids of $N^2=2058^2$ points, with a few on grids of $N^2=1024^2$ or $512^2$ points (with $N$ the linear resolution). As a result of dealiasing, the maximum resolved wavenumber is $$k_\textrm{max}=N/3 .
\label{dealising}$$ Note all magnitudes in the code are dimensionless, with the smallest wavenumber $k_\textrm{min}=2\pi/L_0=1$, and the largest wavenumber $k_\textrm{max}=2\pi/\lambda_\textrm{min}$ being associated with the minimum resolved scale $\lambda_\textrm{min}$.

All runs are direct numerical simulations, with all relevant space and time scales resolved explicitly. The pseudospectral method with the $2/3$ rule is equivalent to a purely spectral method [@canuto_spectral_1988]: it converges exponentially fast, it conserves all quadratic invariants of the equations (i.e., there is no numerical dissipation introduced by the method), and it also has no numerical dispersion. All this was verified explicitly during the development of the code, using several test problems for the SW and BQ equations.

Most previous numerical studies on wave turbulence in gravity waves were done at lower resolutions, with the exception of [@yokoyama_statistics_2004]. But the key difference between previous simulations and the ones presented here (besides the fact that these are for shallow flows, not for deep flows) is that the physical model we use does not 