NATURAL-CONVECTION AS A HEAT ENGINE - A THEORY FOR CAPE

On many planets there is a continuous heat supply to the surface and a continuous emission of infrared radiation to space by the atmosphere. Since the heat source is located at higher pressure than the heat sin k, the system is capable of doing mechanical work. Atmospheric convect ion is a natural heat engine that might operate in this system. Based on the heat engine framework, a simple theory is presented for atmosph eric convection that predicts the buoyancy, the vertical velocity, and the fractional area covered by either dry or moist convection in a st ate of statistical equilibrium. During one cycle of the convective hea t engine, heat is taken from the surface layer (the hot source) and a portion of it is rejected to the free troposphere (the cold sink) from where it is radiated to space. The balance is transformed into mechan ical work. The mechanical work is expended in the maintenance of the c onvective motions against mechanical dissipation. Ultimately, the ener gy dissipated by mechanical friction is transformed into heat. Then, a fraction of the dissipated energy is radiated to space while the rema ining portion is recycled by the convecting air parcels. Increases in the fraction of energy dissipated at warmer temperatures, at the expen se of decreases in the fraction of energy dissipated at colder tempera tures, lead to increases in the apparent efficiency of the convective heat engine. The volume integral of the work produced by the convectiv e heat engine gives a measure of the statistical equilibrium amount of convective available potential energy(CAPE) that must be present in t he planet's atmosphere so that the convective motions can be maintaine d against viscous dissipation. This integral is a fundamental global n umber qualifying the state of the planet in statistical equilibrium co nditions. For the earth's present climate, the heat engine framework p redicts a CARE value of the order of 1000 J kg(-1) for the tropical at mosphere. This value is in agreement with observations. It also follow s from our results that the total amount of CAFE present in a convecti ng atmosphere should increase with increases in the global surface tem perature (or the atmosphere's opacity to infrared radiation).