Rayleigh Friction, Newtonian Cooling, and the Linear Response to Steady Tropical Heating

Abstract

A series of studies are performed to examine the response of the tropical atmosphere to a prescribed steady, large-scale, elevated heat source (i.e., a region of persistent precipitation). Special emphasis is placed on the surface wind response in two idealized cases in which dissipation is achieved exclusively by Rayleigh friction or by Newtonian cooling. Starting from the linearized equations on an equatorial beta plane, theoretical arguments are presented that suggest there are qualitative differences in the solutions of these two models. A dry spectral primitive equation model of the atmosphere is employed and confirms the results obtained from the analytical studies. The results from both the analytical study and the numerical simulations are consistent in showing that Rayleigh friction and Newtonian cooling play totally different roles in the tropical atmosphere. Newtonian cooling homogenizes the atmospheric motion in the vertical direction, and a strong, vertically uniform wind is found below the base of the heat source. When Rayleigh friction dominates, the circulation driven by the heat source is confined to the layer where the heat source is located. It is also shown that a strong Hadley circulation is associated with reasonable strong Rayleigh friction, but not with Newtonian cooling alone. Finally, the numerical solution is found for the case where Newtonian cooling acts uniformly in the vertical and Rayleigh friction is included in the lower atmosphere to mimic crudely the dissipation of momentum in the boundary layer. The introduction of the simple boundary layer dramatically reduces the surface circulation that was supported in the Newtonian cooling alone case. Together these results suggest a significant surface circulation is unlikely to be driven by an elevated heat source if it resides above the top of the boundary layer.