Two-Dimensional Unsteady Gravity Currents

Since long it has been recognized, that even a small density surplus can have a significant effect on the motion of a dense fluid. Probably the first to report experimental data on this subject was W. Schmidt (1911). This author describes a number of laboratory experiments with cold air. These experiments show, that a gravity current is formed, when an amount of cold air is released on the ground. This current attains a velocity relative to the ambient lighter fluid, that is of the order \(\sqrt {g'H}\), where \(g' = g\Delta \rho /\rho\) is the reduced gravity, Δρ the density difference, ρ the density and H the depth of the current. Schmidt related his experimental results to the outflow of cold air in the atmosphere.