The characterization of the dynamics of a continuous gravity current

The present work investigates the dynamical characteristics of a gravity current produced by a continuous and steady release of a dense fluid, with a source density 0, into a lighter ambient fluid, with density a< 0. A planar geometry is considered in which the ambient fluid is initially at rest inside a rectangular tank and the dense current is continuously released from a source located at the bottom-left corner of the tank. The released current propagates along the horizontal bottom boundary of the domain displacing the ambient fluid. This configuration has been considered experimentally by Sher Woods (2017). A numerical study has been carried out using the Direct Numerical Simulations (DNS) of the governing equations via the NEK5000 solver. Instantaneous three-dimensional velocity, pressure and density fields were extracted and two-dimensionalized by width-averaging. The state of the release is characterized by the source Froude number Fr0= u0/ (g'0h0 ) with u0being the velocity of the release, h0being the height at the inlet, and g'0= g (0- a)/a being the source buoyancy. Throughout the series of simulations, we control the state of the current at the source by only varying the source density 0, resulting in a range of source Froude number between 0.6 < Fr0 < 2.7, and we seek to record the effects of this variation on the dynamics. The source discharge Q0= u0h0and buoyancy flux B0= Q0g'0 are kept constant over time. The front speed, uf, was shown to remain steady; a well-known feature of continuous gravity currents. A dimensionless parameter, = uf/B01/3, that characterizes the front speed was computed as a function of Fr0 and the result shows a good agreement with the range recorded by Sher Woods (2017). The entrainment of ambient fluid into the current is parametrized with two methods. First, we estimate the rate of change of the volume of the current, dV/dt, and we recorded the range 1.8Q0< dV/dt < 2.1Q0for the selected Fr0 range. Secondly, the theory of inclined plumes introduced by Ellison Turner (1959) was considered to estimate a local entrainment parameter, E, as a function of the local stratification represented by the local Richardson number Ri. The well-known relation, E proportional to Ri-1, was held when Ri < 0.8; otherwise, the entrainment parameter tends to near-zero values.