The growth of point source plumes at Rayleigh numbers up to 10⁸ and Prandtl numbers up to 1000

Two-dimensional numerical simulations were conducted of the growth of thermal plumes from a point heat source at Rayleigh numbers up to 10⁸ and Prandtl numbers up to 1000. Scaling the convection equations by the free fall velocity rather than the thermal diffusivity, increased the Prandtl number range available to numerical simulation by one order of magnitude from Prandtl number 100 to 1000. We present animations showing how the plumes grow with time for different Prandtl numbers. Plumes with Prandtl numbers around 7 (water) were found to be unstable to sinuous instabilities; whereas those at Prandtl numbers of 1000 had straight stems and fewer sinuous instabilities. Wavelet analysis was used to analyze the scales at which plumes initiated, and the scales at which sinuous instabilities occurred. The scale of both the plume structures and instabilities was found to decrease with Prandtl number.