Energy cascades and rogue waves in superfluid 4He

We report the results of recent experiments on second sound in a high Q resonator. Nonlinear wave interactions give rise to a form of acoustic turbulence in which there is a Kolmogorov-like cascade of energy through the frequency scales from the frequency at which it is injected towards higher frequencies until, eventually, dissipative processes come to dominate and terminate the energy flux. We report that that, under some circumstances, an inverse energy cascade occurs, whereby there is a steady flux of energy towards lower frequencies, a wholly unexpected result that bears on the suggestion that rogue waves on the ocean may arise through nonlinear interactions between conventional wind-blown waves.