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Sediment Transport and Deposition from a Two‐layer Fluid Model of Gravity Currents on Sloping Bottoms
Author(s) -
Moodie T. B.,
Pascal J. P.,
Swaters G. E.
Publication year - 1998
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/1467-9590.00076
Subject(s) - mechanics , decoupling (probability) , turbulence , geology , flow (mathematics) , volume fraction , density contrast , scaling , physics , geometry , thermodynamics , mathematics , control engineering , astronomy , engineering
This article reports on a theoretical and numerical study of noneroding turbulent gravity currents moving down mildly inclined surfaces while depositing sediment. These flows are modeled by means of two‐layer fluid systems appropriately modified to account for the presence of a sloping bottom and suspended sediment in the lower layer. A detailed scaling argument shows that when the density of the interstitial fluid is slightly greater than that of the ambient and the suspension is such that its volume fraction is of the order of the aspect ratio squared, for low aspect ratio flows a two‐layer shallow‐water theory is applicable. In this theory there is a decoupling of particle and flow dynamics. In contrast, however, when the densities of interstitial and ambient fluids are equal, so that it is the presence of the particles alone that drives the flow, we find that a consistent shallow‐water theory is impossible no matter how small the aspect ratio or the initial volume fraction occupied by the particles. Our two‐layer shallow‐water formulation is employed to investigate the downstream evolution of flow and depositional characteristics for sloping bottoms. This investigation uncovers a new phenomenon in the formation of a rear compressive zone giving rise to shock formation in the post‐end‐wall‐separation phase of the particle‐bearing gravity flow. This separation of flow from the end wall in these fixed volume releases differs from what has been observed on horizontal surfaces where the flow always remains in contact with the end wall.