Intrusion into a density-stratified crossflow - a model for spreading volcanic ash cloud

Buoyant fluid from a steady source (such as a volcanic eruption) in a stratified environment (such as the atmosphere) rises to an equilibrium level where it spreads as a homogenous intrusion. Here the dynamics of such an intrusion in the presence of a mean ambient flow are examined with a semi-analytical model. The intrusive flow is irrotational, and is governed by mass conservation and a form of the Bernoulli equation that relates the cloud velocity and its thickness. In the absence of wind, the outward flow from the source is radially uniform and supercritical in the hydraulic sense, with decreasing thickness and increasing speed with distance from the source. In the presence of a crosswind, however, the picture is radically different. Unless the crosswind is very strong a stagnation point exists on the upstream side of the source, where the cloud thickness reaches a maximum. There are two types of flow solution: ones where the flow is wholly subcritical, and others where the flow is “transcritical”, being subcritical on the upstream side of the source, and supercritical on the downstream side. It is these transcritical solutions with a supercritical spreading tail that are relevant to volcanic ash clouds. For these flows the upstream stagnation point is quite close to the source, and its position is remarkably insensitive to the strength of the crossflow, relative to that of the source. The external flow is mostly directed horizontally around the cloud, much as if the latter were a rigid obstacle. The results have potential significance for interpretation of geological sediments.