INTRUSIVE GRAVITY CURRENTS

Intrusive gravity currents arise when a fluid of intermediate density intrudes into an ambient fluid. These intrusions may occur in both nat ural and human-made settings and may be the result of a sudden release of a fixed volume of fluid or the steady or time-dependent injection of such a fluid. In this article we analytically and numerically analy ze intrusive gravity currents arising both from the sudden release of a fixed volume and the steady injection of fluid having a density that is intermediate between the densities of an upper layer bounded by a free surface and a heavier lower layer resting on a flat bottom. For t he physical problems of interest we assume that the dynamics of the fl ow are dominated by a balance between inertial and buoyancy forces wit h viscous forces being negligible. The three-layer shallow-water equat ions used to model the two-dimensional flow regime include the effects of the surrounding fluid on the intrusive gravity current. These effe cts become more pronounced as the fraction of the total depth occupied by the intrusive current increases, To obtain some analytical informa tion concerning the factors effecting bore formation we further reduce the complexity of our three-layer model by assuming small density dif ferences among the different layers. This reduces the model equations from a 6 x 6 to a 4 x 4 system. The limit of applicability of this wea kly stratified model for various ranges of density differences is exam ined numerically. Numerical results, in most instances, are obtained u sing MacCormack's method. It is found that the intrusive gravity curre nt displays a wide range of flow behavior and that this behavior is a strong function of the fractional depth occupied by the release volume and any asymmetries in the density differences among the various laye rs. For example: in the initially symmetric sudden release problem it is found that an interior bore does not form when the fractional depth of the release volume is equal to or less than 50% of the total depth . The numerical simulations of fixed-volume releases of the intermedia te layer for various density and initial depth ratios demonstrate that the intermediate layer quickly slumps from any isostatically uncompen sated state to its Archimedean level thereby creating a wave of opposi te sign ahead of the intrusion on the interface between the upper and lower layers. Similarity solutions are obtained for several cases that include both steady injection and sudden releases and these are in ag reement with the numerical solutions of the shallow-water equations. T he 4 x 4 weak stratification system is also subjected to a wavefront a nalysis to determine conditions for the initiation of leading-edge bor es. These results also appear to be in agreement with numerical soluti ons of the shallow-water equations.