condition $$\begin{gathered}
    \frac{h_0}{\lambda_\textrm{min}} = h_0 \frac{k_\textrm{max}}{2
      \pi} < 1 \nonumber \\
    \Rightarrow h_0 < \frac{6 \pi}{N} .
    \label{cond_disp}\end{gathered}$$ where $\lambda_\textrm{min}$ is, as already mentioned, the shortest wavelength resolved by the code in virtue of the condition given by Eq. .

\[results\] Results
===================

Description and classification of the simulations
-------------------------------------------------

The spectral behavior of the flow in the simulations depends on the external parameters. We can independently control the height of the fluid at rest $h_0$, the viscosity $\nu$, the gravity acceleration $g$, the amplitude of the forcing $f_0$, the range of wavenumbers in which the force is applied, and the linear resolution $N$. However, all these parameters can be reduced to a smaller set of dimensionless controlling parameters.

One of these parameters is the Froude number $$\textrm{Fr}=\frac{U_0}{\sqrt{g h_0}},$$ which measures the ratio of inertia to gravity acceleration in the momentum equation, and where $U_0$ is the r.m.s. velocity.

Another dimensionless parameter is the non-linear number, $N_l$. In order to be in the regime of weak turbulence, nonlinearities should be small. The effect of nonlinearities can be measured by how large perturbations in $h$ are compared to $h_0$, so we define $N_l$ as $$N_l=\frac{h_\textrm{rms}-h_0}{h_0},$$ where $h_\textrm{rms}$ is the r.m.s. value 