On the rise of turbulent plumes: Quantitative effects of variable entrainment for submarine hydrothermal vents, terrestrial and extra terrestrial explosive volcanism

The maximum height reached by a turbulent plume rising in a stratified environment is a key tool to estimate the flux released at its source, particularly for large-scale flows because flux can often be very hard to measure directly. This height is known to be mainly controlled by the stratification of the ambient fluid, source buoyancy flux, and the efficiency of turbulent mixing between the plume and the external fluid. The latter effect has been only superficially explored in spite of its fundamental control on the dynamics. Here we show that commonly used one-dimensional models incorporating a constant entrainment coefficient do not provide satisfying predictions. We propose a new model allowing for variable entrainment which gives excellent predictions of maximum heights reached by laboratory plumes in stratified environments. We then apply our formalism to natural plumes produced by explosive volcanic eruptions under terrestrial, paleo-Martian, and Venusian conditions and by submarine hydrothermal activity at mid-ocean ridges. Source mass discharge rates deduced from maximum volcanic column heights for terrestrial eruptions are found to be greater than those estimated with the commonly used constant entrainment parameterization by a factor of 2. In the paleo-Martian atmosphere, existing models overestimate plume heights by 14-27%. In the current atmosphere of Venus, the maximum height reached by a volcanic plume is also found to be smaller than previously estimated for large eruption rates. The source heat flux released by the TAG field (Atlantic Ocean) deduced from several submarine hydrothermal plumes is found greater by a factor 3 with our model.