Convection from a Large Horizontal Surface

Abstract

A theory is put forward for convection from a large horizontal heated surface in a semi·infinite medium, by buoyant elements which are subject to continuous mixing with the environment by turbulence on a smaller scale. It is assumed, with support from similarity arguments, that the (potential) temperature 6 at sufficient height z above the surface obeys the form -(g/6)(iJ6/iJz)=Oz-a, where a and 0 are positive constants. It is then shown: (i) that a must in practice be close to 4/3 and equal to it under steady conditions, except in layers where radiational heating is large, where a will be smaller; (ii) that the rate of heat 1088 varies as 0 312 ; and (iii) that the r.m.S. temperature fluctuations are proportional to OZ-113. Experimental results from the. surface layers of atmosphere support these predictions quite well. The principal results are first suggested for free convection by dimensional and similarity arguments. They receive independent confirmation from the mechanistic theory, which extends into conditions when forced convection is present but not dominant. The theory also provides information about the multiplying constants in the above relationships, though it does not so far lead to a prediction of their exact values. The multiplying constants depend, inter alia, on the mass ratio between the ascending and descending air, and this remains constant through the layer of constant heat flux. The behaviour of the ascending elements and that of the descending air are shown to be quite differently governed.