The dependence of the Hadley circulation on the thermal relaxation time

Analytic and numerical solutions are found for the nonlinear Hadley circulation problem with respect to the dependence of the strength and the extent of the Hadley circulation on the thermal relaxation time. The dependence on the thermal relaxation time is a crucial parameter to investigate since the simplifications used in previous studies assumed a large thermal relaxation time, to justify the geostrophic assumption, but in the presence of moist convection, thermal relaxation may be fast in the convection regions. In this study, a primitive equation model is used to investigate the effect of different latitudinal distribution of thermal relaxation time on the extent of the circulation cells, the zonal wind, the temperature distribution, and the strength of the meridional circulations. It is found that the extent of the Hadley circulation is insensitive to the value of the thermal relaxation time t, while the strength of the circulation is very sensitive to t (but in a way that is predictable based on the 1/t scaling).