Experiments on convection of isolated masses of buoyant fluid

Abstract

Isolated masses of buoyant fluid were released in a water tank. Their width, 2r, and the distance travelled, z, were measured as functions of time and were found to follow roughly the laws $r = nz,\;\;\;\;\; w = C(g \overline {B}r)^ \frac{1}{2},$ where w is the vertical velocity, $\overline {B}$ the mean buoyancy, and n and C are constants. These equations are predicted by dimensional analysis, assuming viscosity to be negligible, and the constants appear to be independent of the Reynolds number. It is found that C [eDot ] 1·2 and n is in the neighbourhood of 4. Since the Froude number relating the buoyancy and inertia forces is the same as for isolated masses of buoyant air in the atmosphere, it is concluded that the constants will have the same value in this latter case. This is confirmed roughly by observation of cumulus cloud towers. Some of the characteristics of the motion observed in the experiments are described and comparison is made with vortex rings.