Effects of Varying Ambient Stratification Strengths on the Dynamics of a Turbulent Buoyant Plume

Abstract

This paper presents the results of laboratory experiments conducted to study the effects of varying ambient stratification strengths, characterized by the buoyancy frequency N, on the dynamics of a buoyant plume propagating in a linearly stratified environment. The buoyancy frequency was varied between N=0.37–1.17 s−1, while the source velocity was constant at W0=26 cm s−1, giving a source bulk Richardson number of Rib=(π/4)0.25g′dj/W02=0.09–0.31. Bulk parameters such as maximum height, Zm, spreading height, Zs, and radial propagation of the plume, Rf, were measured to characterize the plume and understand the flow dynamics. Experimentally, it was observed that the maximum height and spreading height of a plume decreases with increasing N, a trend attributed to the reduction in the momentum and buoyancy flux due to the vigorous entrainment between the plume and ambient fluid. The radial propagation of the plume, Rf was insensitive to the variations in N and Rf∝t0.75 for all values of N. An empirical parameterization involving Rib and N was developed that gives the characteristic time for a plume to reach a steady-state spreading and maximum height. Further, the transient density profiles show that the mixing-layer thickness decreases with increasing N, thereby rendering the entrainment to occur in a shallow layer of fluid. Using empirical relations, it is shown that the entrainment coefficient is larger for higher values of N, thus becoming a function of the Richardson number. The results are expected to be useful in understanding the mixing and convective process in various environmental flows.