The Linear Response of a Global Atmosphere to Mobile Heating

Part 2: Dependency on Rayleigh Friction and Newtonian Cooling

Abstract

The circulation patterns induced by mobile global heating are investigated by using linearized shallow-water equations on the sphere when the Rayleigh friction rate (α) is different from the Newtonian cooling rate (c). The other parameters involved in this system are Lamb parameter (i. e., the parameter representing the effect of planetary rotation) and the velocity of the heat source. Numerical solutions for a wide range of these parameters are obtained directly from the simultaneous equations which are calculated from the shallow-water equations by expanding variables and the heating distribution in a series of normalized spherical harmonics.
When the motion of the heat source is not fast, the circulation patterns obtained strongly depend on α rather than c. The circulation, which is zonally uniform only in the height field, appears only when both α and c are sufficiently small. Further, both the height and divergence fields become zonally uniform when α is sufficiently large, c is small. This pattern never appears for steady heating. The circulation patterns also become zonally uniform for rapidly mobile heating, unless c is large. These results suggest that the assumption of α=c is applicable to a planetary atmosphere of α≠c such as the earth's one, if α is neither extremely smaller nor larger than c.
This investigation may be applied to the Venusian lower atmosphere where α is supposed to be considerably larger than c. When the relaxation time of the dynamical damping process (=1/α) is shorter than 100 days, it is suggested that the direct circulation between the day and night sides appears independent of c.