A MATHEMATICAL THEORY OF CONVECTION

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Abstract
Since the motions of the atmosphere involve the presence of external heat sources and heat sinks, it is important to incorporate these effects into the hydrodynamical theory of air motions. In the discussion contained in this paper a method for accomplishing such a synthesis of hydrodynamics and thermodynamics is formulated for the case of two-dimensional motion. The use of the method is illustrated by an exact integration of the equations for the case of a circular vortex. Possible further elaborations of the method are discussed with a view of throwing light upon the fundamental nature of the general circulation of the atmosphere.

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