Rayleigh Damping in the Free Troposphere

Abstract

his paper explores whether cumulus drag (i.e., the damping of winds by convective momentum transport) can be described by an effective Rayleigh drag (i.e., the damping of winds on a constant time scale). Analytical expressions are derived for the damping time scale and descent speed of wind profiles as caused by unorganized convection. Unlike Rayleigh drag, which has a constant damping time scale and zero descent speed, the theory predicts a damping time scale and a descent speed that both depend on the vertical wavelength of the wind profile. These results predict that short wavelengths damp faster and descend faster than long wavelengths, and these predictions are confirmed using large-eddy simulations. Both theory and simulations predict that the convective damping of large-scale circulations occurs on a time scale of O(1?10) days for vertical wavelengths in the range of 2?10 km.