High-fidelity simulations of the lobe-and-cleft structures and the deposition map in particle-driven gravity currents

Abstract

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.

Lobe‐cleft instability in the buoyant gravity current generated by estuarine outflow

“…Lobes and clefts (LC) are morphological features that result from complex, three‐dimensional flow along the leading edge of the vast majority of gravity currents. Clefts are described by Simpson [] as V shaped indentations in the front that propagate and merge along the front, and lobes are described as “a series of localized bursts” along the front that appear as “projecting noses with bulges or buttresses which continually change shape.” LC have been associated with impacts ranging from elevated frontal mixing in gravity currents [ Simpson , ], erosional patterns in turbidites [ Allen , ], depositional patterns in turbidity currents [ Espath et al , ], and powder avalanche dynamics [ Jackson et al , ]. Gravity currents may either travel along a nonslip surface, such as a dense turbidity current propagating along the ocean floor [ Middleton , ; Cantero et al , ], or a free‐slip surface, such as a buoyant river plume propagating along the ocean surface [ Pritchard and Huntley , ; Kilcher and Nash , ].…”

A new highly scalable, high-order accurate framework for variable-density flows: Application to non-Boussinesq gravity currents

“…The code is further validated for 2D gravity currents both in and beyond the Boussinesq limit. For these flows, following Birman et al [36] and Espath et al [9,37], incompressibility is enforced and the density field is determined by a concentration as…”

“…where Sc = µ/ρ/D is the Schmidt number, set at a fixed value Sc = 1 for the present simulations, reflecting the value used in the reference data of Birman et al [36] and Espath et al [9,37]. This necessitates modification of the extrapolation step of the constant-coefficient Poisson solver as [36] and Espath et al [9,37].…”

“…A mesh convergence study is performed for each case on meshes of 257×33× 32, 513 × 65 × 64 and 1025 × 129 × 128 mesh nodes, the highest resolution being approximately equivalent to that used by Espath et al [9,37]. To assess mesh convergence the location of the dense front and conservation of total energy are used as indicators.…”

“…For brevity fig. 7 shows only the mesh convergence of ρ 2 /ρ 1 = 0.998 as, being in the Boussinesq limit, it also allows comparison with the non-sedimenting results of Espath et al [37].…”