ON THE DYNAMICS OF GRAVITY CURRENTS IN A CHANNEL

We attempt to clarify the factors that regulate the propagation and st ructure of gravity currents through evaluation of idealized theoretica l models along with two-dimensional numerical model simulations. In pa rticular, we seek to reconcile research based on hydraulic theory for gravity currents evolving from a known initial state with analyses of gravity currents that are assumed to be at steady state, and to compar e these approaches with both numerical simulations and laboratory expe riments. The time-dependent shallow-water solution for a gravity curre nt propagating in a channel of finite depth reveals that the flow must remain subcritical behind the leading edge of the current (in a frame work relative to the head). This constraint requires that h(f)/d less- than-or-equal-to 0.347, where h(f) is the height of the front and d is the channel depth. Thus, in the lock-exchange problem, inviscid solut ions corresponding to h(f)/d=0.5 are unphysical, and the actual curren ts have depth ratios of less than one half near their leading edge and require dissipation or are not steady. We evaluate the relevance of B enjamin's (1968) well-known formula for the propagation of steady grav ity currents and clarify discrepancies with other theoretical and obse rved results. From two-dimensional simulations with a frictionless low er surface, we find that Benjamin's idealized flow-force balance provi des a good description of the gravity-current propagation. Including s urface friction reduces the propagation speed because it produces diss ipation within the cold pool. Although shallow-water theory over-estim ates the propagation speed of the leading edge of cold fluid in the 'd am-break' problem, this discrepancy appears to arise from the lack of mixing across the current interface rather than from deficiencies in B enjamin's front condition. If an opposing flow restricts the propagati on of a gravity current away from its source, we show that the propaga tion of the current relative to the free stream may be faster than pre dicted by Benjamin's formula. However, in these situations the front p ropagation remains dependent upon the specific source conditions and c annot be generalized.