PLUMES WITH NONMONOTONIC MIXING BEHAVIOR

We develop a model for the behaviour of continuous releases (plumes) of fluid which, upon mixing with the ambient fluid, undergo a non-monotonic change in density. This model serves as an analogue for the behaviour of volcanic eruption clouds and hydrothermal plumes. If, at the source, the plume is initially actually a negatively buoyant jet, but has the potential on mixing to become buoyant, we identify a criterion for collapse of the plume that is verified by experiment (see Woods and Caulfield, 1992). In a stratified environment, we show that a nonlinearly mixing plume always attains a lower maximum height than a conventional, linearly mixing plume whose initial buoyancy flux is equal to the potential buoyancy flux of the nonlinearly mixing plume. The potential buoyancy flux is defined as the maximum buoyancy Bur that the plume fluid can develop through mixing at large distances from the source, as the mass flux becomes large due to entrainment. For sufficiently small initial mass fluxes, the height of rise is predicted to decrease as the momentum flux is increased from zero, analogous to the results reported in Morton (1959). We explain this effect in terms of the behaviour of plumes in an unstratified ambient fluid. For a given buoyancy flux, increasing the initial mass flux always reduces the height of rise.