Spectral imbalance in the inertial range dynamics of decaying rotating turbulence

Abstract: Direct numerical simulations of homogeneous decaying turbulence with mild background rotation show the existence of a systematic and significant imbalance between the non-linear energy cascade to small scales and its dissipation. By starting the decay from a statistically stationary and fully developed rotating turbulence state, where the dissipation and the energy flux are approximately equal, the data shows a growing imbalance between the two until a maximum is reached when the dissipation is about twice the energy flux. This dichotomy of behaviours during decay is reminiscent of the non-equilibrium and the equilibrium regions previously reported for non-rotating turbulence [P.C. Valente, J.C. Vassilicos, Phys. Rev. Lett. {\bf 108} 214503 (2012)]. Note, however, that for decaying rotating turbulence the classical scaling of the dissipation rate $\epsilon \propto u'^3/L$ (where $u'$ and $L$ are the root mean square fluctuating velocity and the integral length scale, respectively) does not appear to hold during decay, which may be attributed to the effect of the background rotation on the energy cascade. On the other hand, the maximum energy flux holds the scaling $\Pi_{max} \propto u'^3/L$ in the initial stage of the decay until the maximum imbalance is reached.