Axisymmetric intrusions in two-layer and uniformly stratified environments with and without rotation

Abstract

Lock-release laboratory experiments have been performed to examine the collapse of a localized cylindrical mixed patch of fluid in both two-layer and uniformly stratified ambients. The experiments were performed with and without rotation. Unlike bottom propagating gravity currents, non-rotating intrusions typically propagated many lock radii at constant speed, sometimes stopping abruptly due to interactions with internal waves generated by the return flow into the lock. The initial front speeds of the resulting approximately axisymmetric intrusions emanating from locks of comparable depth and radius were found to be 30%–35% less than the predictions of rectilinear theory. Rotation had no impact on the intrusion's initial speed. However, it limited the maximum distance propagated by the intrusion and caused the patch to expand and contract as it approached geostrophic balance.

Sustained axisymmetric intrusions in a rotating system

“…The dimensionless Coriolis parameter is defined by [15], in which only ∼ 4% of the flow energy was transferred to internal waves. This contrasts with other flows, such as intrusions generated by a sudden collapse of mixed fluid, in which internal waves can play a more significant role [9]. Large-scale experiments may be necessary to determine conclusively how internal waves and other disturbances to the ambient stratification interact with the volcanic intrusions that motivate this study [3].…”

“…Similar behaviour occurs in flows in continuously stratified environments [9], with the final state, after many rotations, exhibiting an ellipsoidal shape [8], which continues to grow slowly if fed by a sustained source [10,11,12]. Continuously stratified fluids support the propagation of internal waves, and while these can significantly influence the transient behaviour of intrusions [9], they do not alter the geostrophic balance underlying this final ellipsoidal shape.…”

“…Equation (16) admits also another solution for u 2 and h 2 , in which the sign of the square roots is swapped; but this solution, which corresponds to subcritical motion, is not realised in time-dependent flows because it is not compatible with the boundary condition at the flow front (9).…”

“…When the current nose is retreating (dr N /dt < 0), the dynamic condition (9) can no longer be justified [8], and the appropriate boundary condition at the nose is that the boundary moves at the same speed as the c + characteristic, specified by setting h N (t) = 0. We integrate the system of equations arising from the spatial discretisation of the flow domain, along with those for h N (t), u N (t) and r N (t), using a second-order Runge-Kutta method, with a CFL number of 1/4.…”

Influence of lock aspect ratio upon the evolution of an axisymmetric intrusion

“…Like symmetric rectilinear intrusions, the collapsing lock fluid excites a mode-2 cylindrical solitary wave that then transports the lock-fluid radially outward at constant speed until the fluid in the leaky core is depleted and the head abruptly halts. This result was extended to examine full-and partial-depth lock-release experiments in stratified ambients (Holdsworth, Barrett & Sutherland 2012). Because mode-2 internal waves in uniform stratification have faster radial phase speeds than the speed of fulldepth intrusions the waves were able to carry energy away from the intrusion more efficiently and, as a consequence, the intrusion stopped a shorter distance from the lock.…”