Gravity currents from a line source in an ambient flow

Abstract

We present a mainly theoretical study of high-Reynolds-number planar gravity currents in a uniformly flowing deep ambient. The gravity currents are generated by a constant line source of fluid, and may also be supplied with a source of horizontal momentum and a source of particles. We model the motion using a shallow-water approximation and represent the effects of the ambient flow by imposing a Froude-number condition in a moving frame. We present analytic and numerical expressions for the threshold ambient flow speed above which no upstream propagation can occur at long times. For homogeneous gravity currents in an ambient flow below threshold, we find similarity solutions in which the up- and downstream fronts spread at a constant rate and the current propagates indefinitely in both directions. For gravity currents consisting of both interstitial fluid of a different density to the ambient and a sedimenting particle load, we find long-time asymptotic solutions for ambient flow strengths below threshold. These consist of a steady particle-rich near-source region, in which settling and advection of particles balance, and an effectively particle-free frontal region. The homogeneous behaviour of the fronts ensures that they also spread at a constant rate and therefore can propagate upstream indefinitely. For gravity currents driven solely by a sedimenting particle load, we find numerically that a single regime exists for ambient flow strengths below threshold. In these solutions, settling balances advection near the source leading to a steady region, which joins on to a complex frontal boundary layer. The upstream front progressively decelerates. Our solutions for homogeneous and particle-driven gravity currents compare well with published experimental results.