Gravity currents supplied with constant volume fluxes into a fluid of different density are examined in a series of numerical computations. The Navier-Stokes equation for an inhomogeneous fluid with the transport equation for solute is solved by the finite volume method. The results show that initially the gravity currents propagate with the constant speeds after the starting of the release of fluid. The initial current speeds vary with the flow rate to the power of 0.41, approximately. Afterwards, two types of the development of gravity current are found: In the first type, the current becomes thin. A strong mixing occurs in the head due to the vortices generated there. The gravity current keeps almost constant speed for a long time in this case.
A gravity current appears when a fluid of one density propagates into another fluid of different density. The current is driven by the gravitational acceleration in the vertical direction caused by the density difference, but to propagate mainly in the horizontal direction. Since it transports in horizontal direction the substances dissolved such as nutrients or oxygen, and in addition, it suppresses the vertical mixing with the stratified layer created behind the head, it is important to investigate the propagation and the process of the mixing around the gravity current. There have been many numerical and experimental studies of gravity currents (Simpson 1987, Ungarish 2009). The lock-exchange set-up is a typical configuration for studying the evolution of gravity currents. Various types of gravity currents are seen in the field of the ocean engineering. In most of them, the volume of the released fluid is not fixed: the fluid is released continuously, such as a influx of freshwater from rivers, a discharge from power plants or factories, and an oil spillage from a wrecked tanker.
