High-resolution simulations of cylindrical density currents

Abstract

Three-dimensional highly resolved simulations are presented for cylindrical density currents using the Boussinesq approximation for small density difference. Three Reynolds numbers (Re) are investigated (895, 3450 and 8950, which correspond to values of the Grashof number of 105, 1.5 × 106 and 107, respectively) in order to identify differences in the flow structure and dynamics. The simulations are performed using a fully de-aliased pseudospectral code that captures the complete range of time and length scales of the flow. The simulated flows present the main features observed in experiments at large Re. As the current develops, it transitions through different phases of spreading, namely acceleration, slumping, inertial and viscous Soon after release the interface between light and heavy fluids rolls up forming Kelvin–Helmholtz vortices. The formation of the first vortex sets the transition between acceleration and slumping phases. Vortex formation continues only during the slumping phase and the formation of the last Kelvin–Helmholtz vortex signals the departure from the slumping phase. The coherent Kelvin–Helmholtz vortices undergo azimuthal instabilities and eventually break up into small-scale turbulence. In the case of planar currents this turbulent region extends over the entire body of the current, while in the cylindrical case it only extends to the regions of Kelvin–Helmholtz vortex breakup. The flow develops three-dimensionality right from the beginning with incipient lobes and clefts forming at the lower frontal region. These instabilities grow in size and extend to the upper part of the front. Lobes and clefts continuously merge and split and result in a complex pattern that evolves very dynamically. The wavelength of the lobes grows as the flow spreads, while the local Re of the flow decreases. However, the number of lobes is maintained over time. Owing to the high resolution of the simulations, we have been able to link the lobe and cleft structure to local flow patterns and vortical structures. In the near-front region and body of the current several hairpin vortices populate the flow. Laboratory experiments have been performed at the higher Re and compared to the simulation results showing good agreement. Movies are available with the online version of the paper.

Stabilized edge‐based finite element computation of gravity currents in lock‐exchange configurations

“…Moreover, for the cylindrical case, the mixture intensity tends to diminish according to the front evolution, whereas at the initial stages there exists an abrupt concentration of inertia and vorticity in regions close to the flow head with the formation of a big bulb that pushes the fluid forward and promotes an increase in the contact between the fluid phases. Consequently, more mixing and dissolution effects take part as described in [10,12,37,46]. In this case, the flow dynamics is much similar to when a cloud of heavy gas is discharged in the atmosphere.…”

“…The problem considered here consists of a cylindrical column of dense fluid centralized in a circular domain. Since this flow tends to develop quasi-axisymmetrically, we have used, following [12,37], a model corresponding to a 90 • sector as illustrated in Figure 5. The domain dimensions are L x = 20.0, L y = 20.0 and h = 2.0.…”

“…Validations of the present approach are performed for head current position and velocity against DNS and LES simulations previously presented in [7,8,10,12,14,37] for planar and cylindrical lock-exchange configurations. For the planar case, we also compare our results with the experiments of Shin et al [4].…”

Direct numerical simulation of cylindrical particle-laden gravity currents

“…The simulation is carried out inside a rectangular box of dimensions L x × L y × H = 30 × 30 × 1 using a spectral code that has been extensively validated [4,5]. Periodic boundary conditions are imposed along the sidewalls for the continuous and particle phases.…”

Numerical investigation of continuous, high density turbidity currents response, in the variation of fundamental flow controlling parameters

“…Up to present, there are various numerical investigations dealing with such flows, providing valuable results [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. However most of these previous works treat turbidity currents with a quasi-single-phase approach, solving one set of continuity and momentum equations for the ambient fluid and treating the transport of sediment particles through an advection-diffusion equation for sediment concentration.…”