ON THE DIRECTION AND DIVERGENCE OF THE SMALL-SCALE TURBULENT HEAT FLUX

Abstract

The equation describing the production or decay of temperature fluctuations of the nth moment is derived and applied toward the determination of the sign of the small-scale heat flux and its vertical divergence in the atmosphere. It is found that an upward heat flux is possible within a sub-adiabatic layer surmounting a super-adiabatic layer if the potential temperature does not increase with height by more than about 0.2C within the layer. The vertical divergence of the heat flux in an unstable surface layer is found to be positive close to the ground, thereby compensating somewhat for strong radiational heating. It is found to be negative higher above the surface where the potential temperature decreases much more slowly with height provided the temperature variance diminishes with height. The divergence appears to be positive (negative) at the lower (upper) surface of an inversion and could therefore be a mechanism of maintenance of such a surface against the destructive effect of radiation.