In this paper, the three-dimensional structure of the thermally forced tropical atmosphere on an equatorial beta-plane is investigated. Special emphasis is placed on the relations between the vertical structure of the heating and the horizontal structure of the response.
By solving the vertical eigenvalue-eigenfunction problem in a vertically semi-bounded domain, we obtain a complete set of the vertical eigenfunctions that includes a single barotropic (external) mode and a continuous spectrum of baroclinic (internal) modes. These eigenfunctions are used to decompose the vertical heating profiles for two types of tropical heating: 1) deep heating representing the convective plume heating (CP); and 2) shallow heating representing mature cloud cluster heating (MC). By examining the spectral energy density of the heating profile, the contributions of each vertical mode to the overall structure is explored for each case and the difference between the responses to these two profiles of heating is discussed. A dry spectral primitive equation numerical model of the atmosphere is employed to verify the analytical results.
The results from both the analytical and the numerical simulations are consistent in showing that the vertical structure of the heating is fundamental to the structure of the response. The CP is deep relative to the MC. Thus, the CP projects onto the vertical eigenfunctions of relatively larger equivalent depth than does the MC. As a result the CP-forced signals propagate away from the heat source much faster than those forced by the MC. Hence, when the atmosphere is subjected to the same linear dampings (Rayleigh friction and Newtonain cooling), the spatial (mainly in the horizontal) decay rate of the signals forced by the CP is significantly smaller than that of the signals forced by the MC heating and the CP-forced signals extend further.
To what extent a shallow water system of a specified vertical mode (e.g., the Gill Model) can approximate the three-dimensional response is also examined. Results show that the effective gravity wave speed of the multi-mode system varies greatly with location. Hence, it is extremely difficult to select a globally suitable equivalent depth so that a one-mode shallow water system can approximate the spatially three-dimensional structure of the response to a given heating.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics