Numerical analysis of flow metrics and overall mixing in density current using large eddy simulation

The overall mixing in density-driven density current has fundamental importance for understanding the dynamics of flow evolution, formation, transport, and distribution of the flow properties in numerous manmade and natural environments. Improved understandings of the dynamics of entrainment of those currents are insufficient in literature especially when dense currents flow over a slope and rough surface. In this numerical study, we investigated the flow metrics implicating the overall mixing in density currents over horizontal and sloping surfaces generated from dense overflows and lock-exchange systems employing high resolution large eddy simulations (LES). Inspiring by Beghin et al. (1981) theory, of flow evolution dependency on lock aspect ratio for lock-exchange cases, low and high lock aspect ratio lock-exchange cases have been investigated in terms of flow properties, flow structures and energetics employing 2D LES simulations. In this study, a novel entrainment metric based on fluid volume which compatible with both lock-exchange and constant flux density current flows have been presented. To evaluate entrained ambient fluid into dense current, two convincing and robust approaches are introduced. Shear interface is identified using density threshold value in one scheme which is defined as "interface identification approach" and density parcels are redistributed from heavy to light in order to get entrained fluid in another method, we name "sorting approach". An analytical relation has been proposed between entrainment rate and mixing efficiency for lock-exchange systems. Employing 3D LES simulations, the flow properties, 2D/3D flow structures, energetics, and mixing for different phases of lock-exchange cases are investigated for comprehensive understanding. The dense overflow case in terms of flow properties, flow structures, energetics, and mixing are also investigated similar to lock-exchange, and finally it has been concluded that the energetic and mixing pattern are approximating the behavior of lock-exchange case in inertial and viscous phase, TKE production and mixing happening around the leading head only. Our numerical study is also focused on entrainment and dense currents dynamics over a range of rough bottoms, in which the shape (square and sinusoidal), and spacing (k-type and d-type) of the roughness elements is varied. It has been showed that the roughness elements ejected more disturbances and instabilities besides the shear interface in fluids due to enhanced form drag around rough bottom which is apparently account for higher entrainment in rough bottom cases. We also explained that the shape and spacing of roughness elements has potential importance on generating turbulence and thus enhance the mixing on rib (square) cases compare to ripple (sinusoidal) cases. Finally, similar to the smooth cases, we observed the trend of increasing entrainment with increasing Re, Fr and the product of Fr and Re.