Some problems of modern meteorology, no 5 the present position of the theory of turbulent motion in the atmosphere

Abstract

It is of significance, when one considers the failure of the classical hydrodynamics to account for the behaviour of the atmosphere near the ground, that practically no definite progress has yet been made with the general theory of eddy motion in fluids. Almost all motion in the atmosphere is turbulent, and consequently it would appear that it is not reasonable to expect the mathematics of streamline flow to give anything like a good approximation to the conditions which actually prevail in the lower layers of the atmosphere. I t must frankly be admitted that, as yet, very little progress has been made with the questions which arise consequent upon the turbulent condition of the air, but sufficient has been achieved to show that the problem is not as hopeless as might appear at first sight.The main problem is to give a quantitative explanation of the following phenomena-the variation of temperature with height near the ground, the frictional drag of the earth's surface on moving masses of air ( L e . , the problem of the variation of the wind velocity with height) and the phenomenon of atmospheric diffusion. If we do not take into account the action of the eddies we are faced with the problem of explaining how, by ordinary molecular conduction, the air above the surface is warmed so rapidly on a hot day; how molecular viscosity can account for the marked increase in the velocity of the wind with height; or how Brownian motion may cause a cloud of smoke to scatter across wind until it attains a width of hundreds of yards a mile or so from the source. Such phenomena are entirely inexplicable if we assume molecular agitation to be the sole agency at work. The meteorological problem then amounts to the investigation of the action of the eddies as the agents which cause mixing of the air masses in such a way as to transfer heat, momentum, particles of dust, water vapour, etc., from one stratum to another. Up to the present the trend of research has been to emphasize the analogy between eddy and molecular motion so that the sole difference is one of scale. It is now abundantly clear that the problem is not to be solved by such simple means, and that something far deeper is required.