Mixing in gravity currents

Abstract

The dynamics of buoyancy-driven flows are investigated focusing on the mixing processes occurring between the dense current and the surrounding fluid. This kind of flows widely occurs in the environment, due both to natural and anthropic causes: examples are sea breeze fronts, oceanic overflows, and pollutant discharges in water bodies. In this study steady and unsteady gravity currents are analysed by means of laboratory experiments and Large Eddy Simulations. Unsteady gravity currents propagating over horizontal and up-sloping boundaries are generated by the lock-exchange technique, and are studied by a combination of laboratory experiments and numerical simulations. Steady gravity currents are reproduced experimentally by the release of a constant discharge of dense fluid in a lighter ambient fluid. The gravity current is then allowed to flow down a rough inclined bottom, in a rotating environment. A total of 12 laboratory experiments and 16 LES of lock-released gravity currents are performed, varying the initial reduced gravity g′0, the aspect ratio of the initial volume of the dense fluid in the lock R, and the inclination of the bottom boundary . A good agreement is found between the numerical LES results and the experimental measurements. Different phases during the propagation of the dense current are observed: a slumping phase followed by a self-similar phase and an eventual viscous phase are detected. The visualization of the three-dimensional density iso-surface shows the presence of two kinds of instability characterizing all the simulated cases: Kelvin-Helmholtz billows and lobe-and-cleft structures, and it is found that their development strongly affects mixing. The increase in velocity of the front of the gravity current is visible with the increase of g′0 or with a decrease of R. On the contrary, as expected, increasing the steepness of the bottom, the dense current slows down. Furthermore, in gravity currents propagating up a slope, the presence of a reversed flow close to the bottom of the domain is clearly visible, which causes an accumulation of dense fluid in the lock region of the tank. Mixing processes occurring between the dense current and the ambient fluid are analysed according to different approaches: two entrainment parameters are defined (Elocal and Ebulk) and the energy budget method of Winters et al. [1995] is applied. The analysis shows that a greater amount of mixing is observed as R decreases. In addition, as expected, a decrease of mixing with the increase of the steepness of the bottom is observed. Turbulent quantities are analysed, finding that turbulence is more pronounced at the interface between the dense and the ambient fluids, particularly in the head region and and in correspondence of the Kelvin-Helmholtz billows, indicating the occurrence of significant mixing in these regions. The dynamics of steady gravity currents flowing down an incline on a rough bottom boundary in a rotating environment are investigated by laboratory experiments, focusing on the effects on mixing of the variations of the roughness and of the inclination of the slope s. A total of 68 experiments are performed and different flow regimes are observed, depending on s and on the density of the roughness c. During the laminar regime, low values of the entrainment parameter are found. For higher values of s, non-breaking wave regime and breaking-wave regime occur, during which a great amount of ambient fluid is entrained by the gravity current. The higher values of E are observed during the turbulent regime, which is found in presence of high values of s. In the experiments performed on the same roughness, the increase of E with the increase of s is distinctly detected. The presence of a rough bottom causes the occurrence of two different mechanisms acting oppositely: additional turbulence is generated due to the presence of the roughness, which acts enhancing mixing, but, at the same time, the velocities in the flow decrease for the presence of the rough elements, and consequently, turbulent structures are inhibited. In general, the presence of a rough bottom acts increasing the entrainment. A good correspondence is observed between the present study and the investigations on flows propagating within aquatic vegetation [Nepf , 2012]. The analysis of the density measures taken at different heights during the experiments shows a stratification within the body of the gravity current which is in agreement with the Nepf [2012] classification: increasing the density of the roughness, the stratification within the body of the dense current becomes more visible, until significant differences in density between the parts of the fluid belonging to the regions inside and outside the roughness are observed for high values of c.