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The evolution of a mono-disperse gravity current in the lock-exchange configuration is investigated by means of direct numerical simulations for various Reynolds numbers and settling velocities for the deposition. We limit our investigations to gravity currents over a flat bed in which density differences are small enough for the Boussinesq approximation to be valid. The concentration of particles is described in an Eulerian fashion by using a transport equation combined with the incompressible Navier-Stokes equations. The most interesting results can be summarized as follows: (i) the settling velocity is affecting the streamwise vortices at the head of the current with a substantial reduction of their size when the settling velocity is increased; (ii) when the Reynolds number is increased the lobe-and-cleft structures are merging more frequently and earlier in time, suggesting a strong Reynolds number dependence for the spatio-temporal evolution of the head of the current; (iii) the temporal imprint of the lobe-and-cleft structures can be recovered from the deposition map, suggesting that the deposition pattern is defined purely and exclusively by the structures at the front of the current.

Hyperpycnal flows are produced when the density of a fluid flowing in a relatively quiescent basin is greater than the density of the fluid in the basin. The density differences can be due to the difference in temperatures, salinity, turbidity, concentration, or a combination of them. When the inflow momentum diminishes, the inflowing fluid eventually plunges under the basin fluid and flows along the bottom floor as an underflow density current. In the present work, 3-D turbulence-resolving simulations are performed for an hyperpycnal flow evolving at the bottom floor of a tilted channel. Using advanced numerical techniques designed for supercomputers, the incompressible Navier-Stokes and transport equations are solved to reproduce numerically the experiments of Lamb et al. (2010, https://doi.org/10.1130/B30125.1) obtained inside a flume with a long tilted ramp. This study focuses on presenting and validating a new numerical framework for the correct reproduction and analysis of the plunge phenomenon and its associated flow features. A very good agreement is found between the experimental data of Lamb et al. (2010), the analytical models of Parker and Toniolo (2007, https://doi.org/10.1061/(ASCE)0733-9429 (2007) 133:6(690)), and the present turbulence-resolving simulations. The mixing process between the ambient fluid and the underflow density current is also analyzed thanks to visualizations of vortical structures at the interface.

Numerical analysis of the immersed boundary method applied to the flow around a forced oscillating cylinder Abstract. In present paper, Navier-Stokes and Continuity equations for incompressible flow around an oscillating cylinder were numerically solved. Sixth order compact difference schemes were used to solve the spatial derivatives, while the time advance was carried out through second order Adams Bashforth accurate scheme. In order to represent the obstacle in the flow, the Immersed Boundary Method was adopted. In this method a force term is added to the Navier-Stokes equations representing the body. The simulations present results regarding the hydrodynamic coefficients and vortex wakes in agreement to experimental and numerical previous works and the physical lock-in phenomenon was identified. Comparing different methods to impose the IBM, it can be concluded that no alterations regarding the vortex shedding mode were observed. The Immersed Boundary Method techniques used here can represent the surface of an oscillating cylinder in the flow.