\[3,8\]         512
     $B08$      980    0.012    0.17    $7.9\times10^{-5}$   $2.5\times10^{-4}$     0.54            \[3,8\]         2048
     $B09$      2500   0.038    0.27    $7.4\times10^{-4}$   $8.0\times10^{-4}$     0.31            \[3,8\]         1024
     $B10$      670    0.0042   0.17    $8.5\times10^{-6}$   $2.5\times10^{-4}$     0.79            \[3,8\]         2048
   $B_{SW}11$   100    0.0039   0.14    $7.6\times10^{-6}$   $8.0\times10^{-4}$     0.96            \[3,8\]         512
   $B_{SW}12$   470    0.013    0.11    $9.0\times10^{-5}$   $3.2\times10^{-4}$     0.24            \[1,5\]         1024
  ------------ ------ -------- ------- -------------------- -------------------- ----------- --------------------- ------

  ------------ ------ -------- ------- -------------------- -------------------- ----------- --------------------- ------
   Simulation    Re      Fr     $D_s$         $N_l$              $h_0/L_0$        $f_0/U_0$   $[k_{f_1},k_{f_2}]$   $N$
     $C01$      1400   0.0067   0.27    $1.9\times10^{-5}$   $8.0\times10^{-4}$     0.56            \[3,8\]         1024
     $C02$      1400   0.0073   0.24    $2.4\times10^{-5}$   $7.0\times10^{-4}$     0.55            \[3,8\]         1024
     $C03$      1900   0.0092   0.31    $4.1\times10^{-5}$   $4.6\times10^{-4}$     0.54            \[3,8\]         2048
     $C04$      1400   0.0057   0.43    $1.6\times10^{-5}$   $6.4\times10^{-4}$     0.74            \[3,8\]         2048
     $C05$      470    0.0067   0.54    $2.2\times10^{-5}$   $8.0\times10^{-4}$      1.1            \[3,8\]         2048
  ------------ ------ -------- ------- -------------------- -------------------- ----------- --------------------- ------

We performed several numerical simulations of both the shallow water and the Boussinesq models. These were done using the GHOST code [@gomez_mhd_2005; @gomez_parallel_2005; @mininni_hybrid_2011], which uses a pseudospectral method with periodic boundary conditions on a $L_0 \times L_0 = 2 \pi \times 2 \pi$ sized box (with $L_0$ the box length), the “$2/3$ rule” for the dealiasing [@canuto_spectral_1988], explicit second order Runge-Kutta for time stepping, and is parallelized using MPI and OpenMP. 