The dynamics of intrusions into a density-stratified crossflow

Abstract

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 semi-analytical models. The intrusive flow is irrotational, and is governed by mass conservation and a form of the Bernoulli equation that relates the intrusion velocity and its thickness. Two types of source are considered—one in which the initial flow from the source is radially symmetric, which is appropriate for weak crosswinds, and another in which it is unidirectional, which also applies to strong crosswinds. In the absence of wind, the outward flow from the radial 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, unless the crosswind is very strong a stagnation point exists on the upstream side of the radial source, where the intrusion thickness reaches a maximum. There are two types of flow solution: those 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 flows from isolated sources. 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. As a consequence, the position of this stagnation point gives a direct measure of the strength of the source. The external flow is mostly directed horizontally around the intrusion, much as if the latter were a rigid obstacle. The behaviour of the flow in the far-field tail of the intrusion is analysed for both the inviscid case, and for the more realistic one in which the intrusive flow is affected by the drag of its motion relative to that of the environment. The second type of flow, from the unidirectional source, has the same asymptotic behaviour, but the near-field flow changes with increasing distance, from one with maximum thickness on the centerline to one with minimum thickness there. Apart from the fluid dynamical aspects, the results have potential significance for interpretation of geological sediments.