The effect of turbulence on fog formation

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Abstract
Of prevalent conceptions of the physics of fog formation, the “classical” theory of the mixing of air masses of different temperatures seems to the present author to be the most convincing. In view of the fact that turbulent exchange implies a mixing of eddies of different origins, it is clear that the theory of turbulence applied to saturated air should result in some basic ideas of fog formation. For simplification of the problem to be studied, the author assumes that the inertia of the drops of fog can be neglected and that they are transferred by eddies in the same way as vapour. On that assumption, the mixing ratio of the total water content, i.e. the mixing ratio of liquid water plus vapour, and the potential wet-bulb temperature are two elements of air that remain constant in eddies irrespective of whether these are saturated or unsaturated by vapour. By putting each of the elements into the differential equation of eddy exchange, the basic formulae for estimation of fog density are obtained. The boundary conditions of integration determine the alternative kinds of fog, for example advection fog and radiation fog. Finally, some important modifications are obtained if regard is paid to the black-body emissivity of the drops of the fog. Thus, the density of the fog is considerably increased by a rise of the level of radiative heat loss from the ground surface to the top of the fog.

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