Particle-driven gravity currents: asymptotic and box model solutions

We employ shallow water analysis to model the flow of particle-driven gravi ty currents above a horizontal boundary. While there exist similarity solut ions for the propagation of a homogeneous gravity current, in which the den sity difference between the current and ambient is constant, there are no s uch similarity solutions for particle-driven currents. However, because the settling velocity of the particles is often much less than the initial vel ocity of propagation of these currents, we can develop an asymptotic series to obtain the deviations from the similarity solutions for homogeneous cur rents which describe particle-driven currents. The asymptotic results rende r significant insight into the dynamics of these flows and their domain of validity is determined by comparison with numerical integration of the gove rning equations and also with experimental measurements. An often used simp lification of the governing equations leads to 'box' models wherein horizon tal variations within the flow are neglected. We show how to derive these m odels rigorously by taking horizontal averages of the governing equations. The asymptotic series are then used to explain the origin of the scaling of these 'box' models and to assess their accuracy. (C) 2000 Editions scienti fiques et medicales Elsevier SAS.