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Title: Particle-driven gravity currents in non-rectangular cross section channels

We consider a high-Reynolds-number gravity current generated by suspension of heavier particles in fluid of density ρ{sub i}, propagating along a channel into an ambient fluid of the density ρ{sub a}. The bottom and top of the channel are at z = 0, H, and the cross section is given by the quite general −f{sub 1}(z) ≤ y ≤ f{sub 2}(z) for 0 ≤ z ≤ H. The flow is modeled by the one-layer shallow-water equations obtained for the time-dependent motion which is produced by release from rest of a fixed volume of mixture from a lock. We solve the problem by the finite-difference numerical code to present typical height h(x, t), velocity u(x, t), and volume fraction of particles (concentration) ϕ(x, t) profiles. The methodology is illustrated for flow in typical geometries: power-law (f(z) = z{sup α} and f(z) = (H − z){sup α}, where α is positive constant), trapezoidal, and circle. In general, the speed of propagation of the flows driven by suspensions decreases compared with those driven by a reduced gravity in homogeneous currents. However, the details depend on the geometry of the cross section. The runout length of suspensions in channels of power-law cross sections ismore » analytically predicted using a simplified depth-averaged “box” model. The present approach is a significant generalization of the classical gravity current problem. The classical formulation for a rectangular channel is now just a particular case, f(z) = const., in the wide domain of cross sections covered by this new model.« less
Authors:
 [1]
  1. Department of Computer Science, Tel-Hai College, Tel-Hai (Israel)
Publication Date:
OSTI Identifier:
22482449
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 27; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY; FLUIDS; GEOMETRY; GRAVITATION; HEIGHT; LENGTH; MIXTURES; PARTICLES; REYNOLDS NUMBER; SUSPENSIONS; TIME DEPENDENCE; VELOCITY