A theory for Rayleigh damping in the free troposphere

Description

In the weak-pressure-gradient (WPG) approximation for single-column models, the Rayleigh-damping time scale is the key tunable parameter. Rayleigh damping is also used in the Matsuno-Gill model and related toy models of atmospheric circulations. This damping is usually intended as an approximation of convective momentum transport. Typical values assigned to the damping time scale range from 1 to 10 days, although no theory has previously been given to explain these values. Here, such a theory is presented. It predicts a range of time scales from 1 to 10 days, and it also gives the dependence of the time scale on convective mass fluxes (or precipitation rate), convective entrainment rate, and the shape of the wind profile. The theory also predicts that long-wavelength components of the wind profile descend more slowly than short-wavelength components. These predictions are confirmed by large-eddy simulations.