Turbulent entrainment in jets with arbitrary buoyancy

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Abstract
Explosive volcanic jets present an unusual dynamic situation of reversing buoyancy. Their initially negative buoyancy with respect to ambient fluid first opposes the motion, but can change sign to drive a convective plume if a sufficient amount of entrainment occurs. The key unknown is the entrainment behaviour for the initial flow regime in which buoyancy acts against the momentum jet. To describe and constrain this regime, we present an experimental study of entrainment into turbulent jets of negative and reversing buoyancy. Using an original technique based on the influence of the injection radius on the threshold between buoyant convection and partial collapse, we show that entrainment is significantly reduced by negative buoyancy. We develop a new theoretical parameterization of entrainment as a function of the local (negative) Richardson number that (i) predicts the observed reduction of entrainment and (ii) introduces a similarity drift in the velocity and buoyancy profiles as a function of distance from source. This similarity drift allows us to reconcile the different estimates found in the literature for entrainment in plumes.

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