Compressible particle-driven gravity currents

Abstract

Large-scale particle-driven gravity currents occur in the atmosphere, often in the form of pyroclastic flows that result from explosive volcanic eruptions. The behaviour of these gravity currents is analysed here and it is shown that compressibility can be important in flow of such particle-laden gases because the presence of particles greatly reduces the density scale height, so that variations in density due to compressibility are significant over the thickness of the flow. A shallow-water model of the flow is developed, which incorporates the contribution of particles to the density and thermodynamics of the flow. Analytical similarity solutions and numerical solutions of the model equations are derived. The gas–particle mixture decompresses upon gravitational collapse and such flows have faster propagation speeds than incompressible currents of the same dimensions. Once a compressible current has spread sufficiently that its thickness is less than the density scale height it can be treated as incompressible. A simple ‘box-model’ approximation is developed to determine the effects of particle settling. The major effect is that a small amount of particle settling increases the density scale height of the particle-laden mixture and leads to a more rapid decompression of the current.