VERTICAL EDDY FLUX OF HEAT IN THE ATMOSPHERE

Abstract

The thermodynamics of open systems is developed for a special atmospheric system in order to obtain a precise definition of the vertical eddy flux of heat. The upward eddy flux of heat per unit area is ??V?zh?, where ? is density, V?z is a specially defined fluctuation of the vertical component of velocity, and h is specific enthalpy. In terms of the eddy diffusivity K1, the unit-area flux of sensible heat is ?K??δ?d/δz1, where z is height and Yd ≡ cpT + ? and, in turn, cp is isobaric specific heat, T is temperature, and ? is geopotential. The heat flux including the latent-heat flux due to the flux of water vapor is ?K??δ?t/δz, where Yt ≡ cpdTe + ? and, in turn, cpd is the isobaric specific heat of dry air and Te, is equivalent temperature. Other expressions can replace these general expressions under stated conditions. Under some conditions the rate of loss of heat from the ocean surface by evaporation and conduction to the air, for a given distribution of eddy diffusivity, depends only on the mean surface temperature Ta and on the mean wet-bulb temperature T?wb at a chosen, short distance above. The rate of loss of heat is proportional to the difference in corresponding equivalent temperatures, T?ea ? T?eb