Remarks concerning the double cascade as a necessary mechanism for the instability of steady equivalent-barotropic flows

n a recent paper, Petroniet al. claim that a necessary condition for the instability of two-dimensional steady flows is a «double cascade» of energy and enstrophy respectively to larger and to smaller scales of motion. It is shown here that the analytical reasoning employed by Petroniet al. is flawed and that their conclusions are incorrect. What is true is that in any scale interaction (whether an instability or not), neither energy nor enstrophy can be transferred in one spectral direction only, but this result is extremely well known.