# Vertical Transport of Heat by Turbulence in the Atmosphere

C. H. B. Priestley, W. C. Swinbank

## Abstract

A necessary consequence of the classical theory of the turbulent transfer of heat in the atmosphere is that the flux of heat is in the direction from high to low potential temperature, and this normally involves the flux being from low to high actual temperature. On examination this is shown to be consistent with the second law of thermodynamics. However, the theory assumes that an eddy may be regarded as a normal sample of the population at its level of origin; but when account is taken of buoyancy effects in a necessarily heterogeneous atmosphere it is clear that this assumption is incorrect. It also becomes apparent in the discussion that a definition of the concept 'level of origin' of an eddy more rigid than that given in the classical theory is necessary, and this has been given. It is shown that a component of heat flux, here called 'convective turbulence', must result from the buoyancy forces. This is always directed upwards and is thus opposed to the general downward transfer of mechanical turbulence. Records of the fluctuations in temperature at fixed levels show amplitudes which cannot be explained by mechanical turbulence. The traces further indicate that convective turbulence may at times completely dominate the direction of the flow of heat, a conclusion which is supported by reference to some synoptic examples. This result helps to explain the normal increase of potential temperature with height. Dimensional considerations provide a rough measure of the dependence of the buoyancy flux on the lapse rate and amplitude of fluctuations, and also allow the total flux to be written in the classical form $\rho$c$_{p}$K$^{\prime}\left(\frac{\partial T}{\partial z}+\Gamma \right)$. K$^{\prime}$, which may be positive or negative, will depend upon the synoptic situation. Some of the implications in synoptic and general theoretical meteorology are discussed in detail. The turbulent transfer of physical quantities other than heat is briefly considered.