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

Abstract

[1] 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 onedimensional 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.

Analysis and modeling of hydrothermal plume data acquired from the 85°E segment of the Gakkel Ridge

“…This implies that the rise height seems to be a function of heat flux only, when heat is fully conserved as in our model. The error in maximum rise height for the scaling expression is about 50% according to Carazzo et al [2008] and we suggest that the lack of heat conservation might explain part of the error, although further studies are required in order to draw definite conclusions.…”

“…A constant entrainment coefficient has been employed in many other studies [e.g., McDougall, 1990;Rudnicki and Elderfield, 1992;Speer and Rona, 1989]. Carazzo et al [2008], however, showed that a more sophisticated buoyancy dependent entrainment parameterization yields more accurate model results. Unfortunately, the implementation of a variable entrainment reduced our model run speed to such an extent that the large number of model runs carried out here would have been impractical.…”

A three‐dimensional numerical simulation of spreading umbrella clouds

“…where C 1 , C 2 and C 3 are the proportionality constants [e.g., Morton et al, 1956;Sparks, 1986;Carazzo et al, 2008].…”

Submarine vortices derived from natural gas hydrate conversion: a mechanism for ocean mixing

“…Where Ri is the Richardson number and C = shear stress, parameters A and B depend on flow properties, and specifically describe the shapes of velocity, buoyancy, and turbulent shear stress profiles while in the upper plume R = radius and U = velocity (Carazzo et al, 2008).…”

“…Drag at the edge of the plume is responsible for mixing inward from the margin of the plume via the entrainment coefficient α e , a constant proportional to the velocity at a particular elevation (Carazzo et al, 2008):…”