Bidisperse Particle-Driven Gravity Currents in Power-Law Cross-Section Channels

Abstract

Particle-driven gravity currents are suspensions of dense particles that spread into an ambient fluid due to the difference between the density of the suspension and that of the ambient fluid. In most of the analytical works, it has been assumed that the suspension of particles possess a single settling velocity. However in many situations this is a considerable simplification and in virtually all real situations there is a range of particle sizes, and hence settling velocities. In the present work we consider the propagation of a high-Reynolds-number gravity current driven by a bi-disperse distribution of two types of particles in fluid of density ρ a propagating along a channel into an ambient fluid of the density ρ a . The bottom and top of the channel are at z = 0, H and the cross-section is given by the power-law f(z). The flow is modeled by the one-layer shallow-water equations. We solve the problem by the finite-difference numerical code to present typical height h(x,t), velocity u(x,t) and volume fractions of particles profiles. We demonstrate that in some regimes it is sufficient to deduce the behavior of the suspension to the corresponding monodisperse suspension of average settling velocity. The numerical results are confirmed by recent experimental results.