Abstract

Three-dimensional numerical experiments were performed with thermals rising in a stably stratified environment to study the cloud-environment boundary instability. This work extends that reported in Part I. It is shown that the analytical theory developed in Part I, which describes the evolution of the laminar interface between the thermal and its environment, applies to the three-dimensional case with only minor modifications. As in the two-dimensional case, the scale selection and growth rate of the unstable modes appear to depend upon the depth and velocity change across the shear layer near the interface, which is in rough agreement with classical linear theory developed for the case of planar geometry.

Analysis is presented that indicates further evolution of the three-dimensional eddies results in a transition to turbulence. A decrease of the Taylor-microscale Reynolds number and leveling off of the average enstrophy and velocity-derivative skewness is observed in the numerical experiments, which is typical for the development of numerical isotropic homogeneous turbulence. This transition is also associated with an increase (from about 0.5 to about 2) in the ratio between the vortex stretching and baroclinic production term of the enstrophy equation, with the magnitude of the stretching term approaching a value close to that for isotropic homogeneous turbulence.

Implications for the problem of cumulus entrainment are discussed. A heuristic argument based on the results of this study is given to explain why entrainment in cumuli and in high Reynolds number laboratory thermals is associated with the presence of large structures, not much smaller than the size of a cloud or thermal.

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