Direct numerical simulation of starting-plume cloud-flows

Abstract

In the present work, we study the effect of off-source volumetric heating on a starting plume in an attempt to understand the fluid dynamics of clouds. Clouds play a major role in weather and climate. In the tropics cumulus clouds are particularly prominent. They generally form due to condensation of water vapor in the moist air that rises from heat sources or hot spots on the ground. Previous work (as reviewed by Narasimha & Bhat (2008))has shown that off-source volumetric heating of a self-similar jet or a plume results in cloud like flow characteristics. A starting plume is particularly relevant to clouds as the life cycle time of a single cloud is of the order of a few hours and is usually not long enough to generate completely self-similar flows. We carry out Direct Numerical Simulation (DNS) of the Navier-Stokes equations under the Boussinesq approximation to study such flows. We start with two-dimensional (2D) simulations to explore suitable algorithms and boundary conditions. A clustered Cartesian grid is used for the computation. The equations are solved using the projection method and finite difference schemes. For integration in time, second order Adams-Bashforth and Crank-Nicolson methods are used for advection and viscous diffusion respectively. The code is verified by demonstrating conservation of buoyancy flux and satisfaction of the divergencefree condition. The 2D simulation of the starting-plume model gives results broadly similar to those seen in the experiments on round jets and plumes. In the heatinjection zone the spread rate of the plume decreases. Immediately above the heat-injection zone instabilities begin to reappear and the spread rate tends to recover.