Turbulent phase shift of rossby waves

The properties of turbulent flows are strongly modified by the presence of dispersive waves the period of which can be less than the eddy-turnover time of turbulence for sufficiently large scales. Using a systematic method due to Andre, 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 terms, 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 1000km and tends to a limit close to 0.3 for sufficiently small scales.