Structure of Head of a Gravity Current

Abstract

The structure of the head of gravity currents is investigated in the experiment and the computation of lock-exchange flow. A finite volume of fluid was released instantaneously in another fluid of slightly different density in an open rectangular channel when a lock gate was opened. A box model was introduced to describe different regimes of a developing gravity current on the basis of energy argument.Visualization experiments were made by the shadowgraph method and with dye to trace the head of gravity currents, the results of which validate the box model. The initial depth and volume of the released fluid affect the front speed. At the first stage the released fluid spreads at a constant speed, and then it slows down so that the frontspeed decreases with time to the power of -1/3 in self-similar regime. The current that has begun to be dominated by viscosity slows down further in the final stage during which the front speed decreases with time to the power of -4/5.The computation was also made in the same condition as the experiments to study the structure of the head of currents in different regimes. The incompressible Navier-Stokes equation for an inhomogeneous fluid together with the transport equation for solute was solved by the finite volume method developed in the previous paper. The computation produces the transition between the development regimes so that the front speed obtained from the computed density field is in good agreement with the experimental result. The computational results indicate that the transition to the next regime is accompanied by remarkable changes in the geometry and the inner structure of the head. The head has maintained a sharp density interface even at low Reynolds number and the relatively large-scale entrainment of ambient fluid across the upper interface causes strong mixing behind the head. The models with the inviscid boundaries failed to catch the transition to the second stage, which suggests that the transition may require some stimulus associated with viscous motions. The result for the case of short lock-length shows the sudden decrease in the volume and in the density of the head brought about by the vortex shedding along the upper interface, which may be one of the mechanism to account for the strong mixing in the first and the second regimes.