Boussinesq plumes and jets with decreasing source strengths in stratified environments

Abstract

Solutions to the equations of Morton et al. (Proc. R. Soc. Lond. A, vol. 234, 1956, p. 1) describing turbulent plumes and jets rising in uniformly stratified environments are identified for the first time. The evolution of plumes and jets with sources whose driving flux decreases with time is considered in a stratified environment. Numerical calculations indicate that as the source buoyancy flux, for a Boussinesq plume (or source momentum flux, for a Boussinesq jet), is decreased, a transitional narrowing region with characteristic spreading angle tan -1 (2α/3) is formed, where α is the well-known entrainment coefficient. The plume or jet dynamics are modelled well by a separable solution to the governing equations which predicts stalling in the plume at a critical stall time t s = π/N and stalling in the jet at a critical stall time t s = π/(2N), where N is the buoyancy frequency of the ambient background stratification. This stall time is independent of the driving source conditions, a prediction which is verified by numerical solution of the underlying evolution equations.