Turbulent Phase Shift of Rossby Waves

The properties of turbulent flows are strongly rnodified by the presence of dispersive waves the period of which can be less than the eddy-turnover time of turbulence for suffciently large scales. Using a systematic method due to Andr, we show that the presence of such waves induces complex damping rates in stochastic models like for instance the Eddy-Damped Quasi-Normal Markovian model: in other terrns, turbulence acts to renormalise both viscosity and frequency. This method is applied to spherical Rossby waves; it is found that the relative correction to Rossby frequencies, negligible at planetary scales, might become important around 1000b.m and tends to a limit close to 0.3 for suffciently small scales.