A COMPUTATIONAL MODEL FOR THE RISE AND DISPERSION OF WIND-BLOWN, BUOYANCY-DRIVEN PLUMES .2. LINEARLY STRATIFIED ATMOSPHERE

A multi-dimensional computational model of wind-blown, buoyancy-driven flows is applied to study the effect of atmospheric stratification on the rise and dispersion of plumes. The model utilizes Lagrangian tran sport elements, distributed in the plane of the plume cross section no rmal to the wind direction, to capture the evolution of the vorticity and density,field, and another set of elements to model the dynamics i n the atmosphere surrounding the plume. Solutions are obtained for a c ase in which atmospheric density changes linearly with height. Computa tional results show that, similar to the case of a neutrally stratifie d atmosphere, the plume acquires a kidney-shaped cross section which p ersists for a long distance downstream the source and may bifurcate in to separate and distinct lumps. Baroclinic vorticity generated both al ong the plume boundary and in the surroundings is used to explain the origin of the distortion experienced by the plume and the inhibiting e ffect of a stratified atmosphere, respectively. The vorticity within t he plume cross section forms two large-scale coherent eddies which are responsible for the plume motion and the entrainment. Prior to reachi ng the equilibrium height, the computed plume trajectory is found to f ollow the two-thirds law when extended to include the initial plume si ze, reasonably well. Entrainment and added mass coefficients equal to 0.49 and 0.7, respectively, are obtained from the numerical results ov er a wide range of the buoyancy ratio, defined as the ratio between th e plume buoyancy and the degree of background stratification. In the c ase of strong stratification, the plume trajectory shows weak, fast de caying oscillations around the equilibrium height.