[1] Estimates of volcanic source mass flux, currently deduced from observations of plume height, are crucial for ash dispersion models for aviation and population hazard. This study addresses the role of the atmospheric wind in determining the height at which volcanic plumes spread in the atmosphere and the relationship between source mass flux and plume height in a wind field. We present a predictive model of volcanic plumes that describes the bending over of the plume trajectory in a crosswind and show that model predictions are in accord with a dataset of historic eruptions if the profile of atmospheric wind shear is described. The wind restricts the rise height of volcanic plumes such that obtaining equivalent rise heights for a plume in a windy environment would require an order of magnitude increase in the source mass flux over a plume in a quiescent environment. Our model calculations are used to calibrate a semi-empirical relationship between the plume height and the source mass flux that explicitly includes the atmospheric wind speed. We demonstrate that the model can account for the variations in plume height observed during the first explosive phase of the 2010 Eyjafjallajökull eruption using independently measured wind speeds and show that changes in the observed plume height are better explained by changing meteorology than abrupt changes in the source mass flux. This study shows that unless the wind is properly accounted for, estimates of the source mass flux during an explosive eruption are likely to be very significant underpredictions of the volcanic source conditions.

[1] We develop descriptions of the key processes influencing tephra dispersal from strong volcanic plumes. These are characterized by the development of a subvertical eruption column in the atmosphere that forms a spreading current at a level of neutral buoyancy. We describe the propagation of the spreading current due to both gravity and wind advection using scaling arguments and a simplified geometry to model particle sedimentation in a windy as well as a wind-free environment. New parameterizations are used to describe the wind field below the spreading current, particle aggregation, and particle density variations. We conducted a broad study to investigate the effects of these processes and made comparisons with field observations. The greatest variations resulted from wind advection below the spreading current, which shifts the plumecorner mass accumulation and the position of transitions in fallout regimes downwind. Particle aggregation strongly depends on the initial grain-size distribution and significantly affects deposit thinning, depending on the aggregate size and density, and on the relative amount of aggregating particles. Small aggregates can reproduce secondary maxima of mass accumulation when sedimenting in a wind field. Variation of particle density also affects the resulting thinning trend. The model provides acceptable reproduction of observations of the propagation of the spreading current (tested with the Plinian phase of the 18 May 1980 eruption of Mount St. Helens) and of observed thinning of tephra fallout deposits (tested with deposits from Mount St.

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Entrainment of ambient fluid into both two-dimensional and axisymmetric gravity currents is investigated experimentally using a novel neutralization technique. The technique involves the titrative neutralization of an alkaline gravity current which intrudes into and entrains an acidic ambient, and is visualized using a pH indicator solution. Using this technique, we can determine quantitative results for the amount of 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/ambient interface and by over-riding (relatively light) ambient fluid. Guided by our experimental observations, we present two slightly different theoretical models to determine the entrainment into the head of the current as a function of distance from the source for the instantaneous release of a constant volume of fluid in a two-dimensional geometry. By dimensional analysis, we determine from both models that the dimensionless 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 confirmed by our experiments in Boussinesq situations. Our theoretical evaluation of E in terms of the initial cross-sectional area of the current agrees very well with our experimental measurements on the incorporation of an entrainment coefficient a, evaluated experimentally to be 0.063 f 0.003. We also obtain experimental results for constant-volume gravity currents moving over horizontal surfaces of varying roughness. A particularly surprising result from all the experiments, which is reflected in the theoretical models, is that the head remains essentially unmixedthe entrainment is negligiblein the slumping phase. Thus the heads of gravity currents with identical initial cross-sectional areas but different initial aspect ratios (lock lengths) will begin to be diluted by ambient fluid at different positions and hence propagate at different rates. A range of similar results is determined, both theoretically and experimentally, for the instantaneous release 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.

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