Cloud–Environment Interface Instability: Rising Thermal Calculations in Two Spatial Dimensions

Abstract

High resolution two-dimensional numerical experiments of rising thermals in a stably stratified environment were performed to study the cloud boundary instability. Unstable modes develop on the leading edge of the rising thermal, which are driven by the buoyant production of vorticity and lead to the type of entraining eddies that are thought to be responsible for observed dilution of convective clouds. These instabilities develop on the complex and evolving base state characterized by a nonparallel flow near the interface with a contractional component across the interface and a stretching component along it. An analytical model is presented which describes the temporal evolution of the shear layer prior to the onset of the instability. It is shown that the flow pattern associated with the thermal rise leads to an exponential increase of the shear normal to the interface and exponential decrease of the shear-layer depth, which at a certain stage can lead to the onset of shearing instabilities. The theoretical predictions are in good agreement with the numerical simulation results. A shearing velocity is found from this theory which is the product of the shear-layer vorticity and the shear-layer depth. This shearing velocity is independent of the diffusional mixing and represents at least one attractive parameter for field testing of the theoretical model. Once the shear layer collapses to a depth of about 40 m, instabilities are typically excited with characteristic scales between 100 and 200 m and exponential growth rates of about 40 s. The Richardson number at the upper-thermal interface is negative and both buoyant, and shear terms contribute to the kinetic energy of the instability. The scale selection and growth rates are in rough agreement with those for classical shearing instability. While growing, the instabilities migrate sideways along the interface, increasing their tangential scale. The size of the eddies into which instabilities finally develop depends not only on the scale of initial excitation, but also on the growth rate, thermal size, further evolution of the shear layer (which may allow finer-scale instabilities to be excited), and interaction of instabilities excited at different times. The spectrum of eddy sizes observed in the simulations ranged from about 50 to about 250 m. These findings provide further evidence of cumulus entrainment being driven by an inviscid baroclinic process.