The propagation of a gravity current into a linearly stratified fluid

TLDR

The stratification is characterized by a density difference (ρ_b−ρ_0) and intrinsic frequency N, with the parameter R=(ρ_C−ρ_0)/(ρ_b−ρ_0) measuring the relative strength of the current to the stratification. Experiments and simulations show that the heavy gravity current propagates at a constant speed V whose dimensionless Froude number Fr=V/(NH) depends only on the density ratio R and not on lock length, and that the transition distance X_tr/h is a unique function of Fr; after this regime, subcritical Fr<1/π causes velocity oscillations from internal waves while supercritical Fr yields monotonic decay, with the numerical model matching experimental speeds within ±1.5%.

Abstract

The constant initial speed of propagation ( V ) of heavy gravity currents, of density ρ C , released from behind a lock and along the bottom boundary of a tank containing a linearly stratified fluid has been measured experimentally and calculated numerically. The density difference, bottom to top, of the stratification is (ρ b −ρ 0 ) and its intrinsic frequency is N . For a given ratio of the depth of released fluid ( h ) to total depth ( H ) it has been found that the dimensionless internal Froude number, Fr = V / NH , is independent of the length of the lock and is a logarithmic function of a parameter R = (ρ C −ρ 0 )/(ρ b −ρ 0 ), except at small values of h/H and R close to unity. This parameter, R , is one possible measure of the relative strength of the current (ρ C −ρ 0 ) and stratification (ρ b −ρ 0 ). The distance propagated by the current before this constant velocity regime ended ( X tr ), scaled by h , has been found to be a unique function of Fr for all states tested. After this phase of the motion, for subcritical values of Fr , i.e. less than 1/π, internal wave interactions with the current resulted in an oscillation of the velocity of its leading edge. For supercritical values, velocity decay was monotonic for the geometries tested. A two-dimensional numerical model incorporating a no-slip bottom boundary condition has been found to agree with the experimental velocity magnitudes to within ±1:5%.