ENTRAINMENT INTO 2-DIMENSIONAL AND AXISYMMETRICAL TURBULENT GRAVITY CURRENTS

Entrainment of ambient fluid into both two-dimensional and axisymmetri c gravity currents is investigated experimentally using a novel neutra lization technique. The technique involves the titrative neutralizatio n of an alkaline gravity current which intrudes into and entrains an a cidic ambient, and is visualized using a pH indicator solution. Using this technique, we can determine quantitative results for the amount o f dilution in the head of the current. The head of the current is able to entrain ambient fluid both by shear instabilities on the current/a mbient interface and by over-riding (relatively light) ambient fluid. Guided by our experimental observations, we present two slightly diffe rent theoretical models to determine the entrainment into the head of the current as a function of distance from the source for the instanta neous release of a constant volume of fluid in a two-dimensional geome try. By dimensional analysis, we determine from both models that the d imensionless entrainment or dilution ratio, E, defined as the ratio of the volumes of ambient and original fluid in the head, is independent of the initial reduced gravity of the current; and this result is con firmed by our experiments in Boussinesq situations. Our theoretical ev aluation of E in terms of the initial cross-sectional area of the curr ent agrees very well with our experimental measurements on the incorpo ration of an entrainment coefficient alpha, evaluated experimentally t o be 0.063 +/- 0.003. We also obtain experimental results for constant -volume gravity currents moving over horizontal surfaces of varying ro ughness. A particularly surprising result from all the experiments, wh ich is reflected in the theoretical models, is that the head remains e ssentially unmixed - the entrainment is negligible - in the slumping p hase. Thus the heads of gravity currents with identical initial cross- sectional areas but different initial aspect ratios (lock lengths) wil l begin to be diluted by ambient fluid at different positions and henc e propagate at different rates. A range of similar results is determin ed, both theoretically and experimentally, for the instantaneous relea se of a fixed volume of (heavy) fluid in an axisymmetric geometry. By contrast, the results of our experiments with gravity currents fed by a constant flux exhibit markedly different entrainment dynamics due to the continual replenishment of the fluid in the head by the constant input of undiluted fluid from the tail.