The Effects of Compressibility and Dissipation Heating on Boundary Layer Plumes

Abstract

This paper examines in detail some of the assumptions previously used by the author in modeling the convective boundary layer. It has been customary to mathematically model atmospheric convection with plumes and blobs in which the air is taken to be incompressible in analogy with the fluid in water tank models used in the past to justify much of this work. It is not always clear in formulating such equations what exactly are the approximations thus introduced as the physical foundation of the model, and this is a point of confusion detracting from the main work. This paper shows that the modification needed to accurately account for the compressibility of the air is simple and the changes resulting in the final variables negligible. The effect that turbulence and its decay to heat have on the density used in the model is discussed and its omission is shown to be justified.