Penetrative convection in stably stratified fluids

The downward convection of discrete masses of heavy fluid, called thermals, in a gravitationally stable environment is studied experimentally. For simplicity the ambient stratification is chosen to have a discontinuous two-layer structure with fluid of uniform density in each layer. When released into the homogeneous upper layer the thermal acquires the circulation of a turbulent ring vortex as reported earlier. For weak stratifications, which are however capable of halting the thermal, this circulation is destroyed in a dramatic fashion during the penetration of the lower layer; restoring buoyancy forces then develop a reversed circulation as the thermal flattens and spreads. For strong stratifications no reversal of the circulation occurs, rather the flattening and spreading of the thermal is associated with a gradual decay of the original circulation.

A dimensional argument is proposed to indicate the parameters which determine the extreme penetration of the thermal into the lower layer: this is confirmed by experiment.

In order to generalize the results to more realistic geophysical cases a mechanistic description of thermal behaviour is put forward. The treatment is shown to rationalize the data for environments with (a) neutral stratification, (b) a discontinuous two-layer structure and (c) constant density gradient. Thermal behaviour in a stratification consisting of (a) surmounted by (c) is then predicted.

Observations made by the author of the penetration of tall cumulus clouds into the sub-tropical stratosphere permit a test of the applicability of this model in one geophysical area. For every 1 km of penetration it is deduced that convective motions have an average vertical intensity of 10 m/sec: this prediction is shown to be in good agreement with the limited observational data.