of rotating [@galtier_weak_2003] and of magnetohydronamic [@galtier_weak_2000] flows). However, the SW model is non-dispersive, and as a result the resonance condition is only satisfied for collinear wave vectors. Resonant interactions can then only couple modes that propagate in the same direction (i.e., along the ray of the wave), and non-resonant interactions must be taken into account to consider other couplings. But more importantly, dispersion is crucial in weak turbulence theory to have decorrelation between different waves: without dispersion, all modes propagate with the same velocity, and the modes initially correlated remain correlated for all times (see, e.g., [@lvov_statistical_1997] for a discussion of these effects in the context of acoustic turbulence).

![[*(Color online)*]{} Total energy as a function of time for simulation $A06$ (see Table \[table1\]). As the fluid starts from rest and the forcing is applied, energy increases until it reaches a turbulent steady state (note energy at $t=0$ is different from zero, as the flow potential energy is never zero). All the analysis of the simulations was performed after the simulations reached the turbulent steady state. [*Inset:*]{} Energy balance as a function of time (see Eq. ). Note the balance is satisfied up to the seventh decimal place. []{data-label="eng_cons"}](Figure2.eps){width="48.00000%"}

