On intrusion in a linearly-stratified ambient: the asymmetric steady-state model

The behavior of the steady intrusive gravity currents spreading into a stratified ambient fluid is investigated. The intrusive gravity current of thickness $h$ and density $\rho_c$ which propagates with speed $U$ at the neutral buoyancy level of a long horizontal channel of height $H$ into a stratified ambient fluid whose density increases linearly from $\rho_o$ to $\rho_b$ is investigated. The intrusive and the ambient fluids are assumed to be asymmetric due to axis passing the stagnation point of the system. The Boussinesq, high-Reynolds number two-dimensional configuration is discussed. The Long's model combined with the flow-force balance over the width of the channel and the pressure balances over a density current are used to obtain the desired results. It is shown that the intrusion velocity decreases with decreasing the asymmetry of the system and approaches its minimum for the symmetric configuration. In additional, the comparison between asymmetric and symmetric configurations shows no significant differences between the models.