Compressible particle-driven gravity currents

Large-scale particle-driven gravity currents occur in the atmosphere, often in the form of pyroclastic flows that result from explosive volcanic erupt ions. The behaviour of these gravity currents is analysed here and it is sh own that compressibility can be important in flow of such particle-laden ga ses because the presence of particles greatly reduces the density scale hei ght, so that variations in density due to compressibility are significant o ver the thickness of the flow. A shallow-water model of the flow is develop ed, which incorporates the contribution of particles to the density and the rmodynamics of the flow. Analytical similarity solutions and numerical solu tions of the model equations are derived. The gas-particle mixture decompre sses upon gravitational collapse and such flows have faster propagation spe eds than incompressible currents of the same dimensions. Once a compressibl e current has spread sufficiently that its thickness is less than the densi ty scale height it can be treated as incompressible. A simple 'box-model' a pproximation is developed to determine the effects of particle settling. Th e major effect is that a small amount of particle settling increases the de nsity scale height of the particle-laden mixture and leads to a more rapid decompression of the current.