Global Circulation in an Axially Symmetric Shallow Water Model Forced by Equinoctial Differential Heating

Abstract

Solutions of an axially symmetric inviscid shallow-water model (SWM) on the earth forced by equinoctial differential heating are constructed using numerical integration of the time-dependent equations and analysis of their steady states. The study also maps the physical initial conditions and parameter values for which the solutions approach steady states at long times, demonstrating strong dependence of the SWM on initial conditions. The model admits states of uniform angular momentum, including superrotation, in the tropics and radiative equilibrium at high latitudes. The asymptotic properties of the subtropical jets and tropical fluxes are explicitly calculated and it is shown that all solutions of the previously studied nearly inviscid theories are particular solutions of the present theory. The model?s results relate the location and intensity of the subtropical jet in the steady states to properties of the SWM on a sphere, such as the conservation of angular momentum. The exact form of the differential heating is secondary in determining these properties and its main role is to transform any initial state to the vicinity of the steady states. When mass is assumed to be supplied to the fluid from an underlying motionless layer (this model is termed the 1½-SWM), the angular momentum in the tropics is not uniform (so the local Rossby number is smaller than 1), the height of the tropopause is nearly uniform there, the steady states do not depend on the initial conditions, and the zonal velocity vanishes on the equator. Accurate and simple estimates that are determined only by the value of a thermal Rossby number are derived in this case for the location and intensity of the subtropical jet.