Turbidity currents interacting with three-dimensional seafloor topography

Abstract

Direct numerical simulations are employed to investigate the interactions of bidisperse turbidity currents with three-dimensional seafloor topography in the form of Gaussian bumps. Results for two different bump heights are compared against currents propagating over a flat surface. The bump heights are chosen such that the current largely flows over the smaller bump, while it primarily flows around the taller bump. Furthermore, the effects of the settling velocity are investigated by comparing turbidity currents with corresponding compositional gravity currents. The influence of the bottom topography on the front velocity of turbidity currents is seen to be much weaker than the influence of the particle settling velocity. Consistent with earlier work on gravity currents propagating over flat boundaries, the influence of the Reynolds number on the front velocity of currents interacting with three-dimensional bottom topography is found to be small, as long as $\mathit{Re}\geq O(1000)$. The lobe-and-cleft structures, on the other hand, exhibit a stronger influence of the Reynolds number. The current/bump interaction deforms the bottom boundary-layer vorticity into traditional horseshoe vortices, with a downwash region in the centre of the wake. At the same time, the vorticity originating in the mixing layer between the current and the ambient interacts with the bump in such a way as to form ‘inverted horseshoe vortices’, with an upwash region in the wake centre. Additional streamwise vortical structures form as a result of baroclinic vorticity generation. The dependence of the sedimentation rate and streamwise vorticity generation on the height of the bump are discussed, and detailed analyses are presented of the energy budget and bottom wall-shear stress. It is shown that for typical laboratory-scale experiments, the range of parameters explored in the present investigation will not give rise to bedload transport or sediment resuspension. Based on balance arguments for the kinetic and potential energy components, a scaling law is obtained for the maximum bump height over which gravity currents can travel. This scaling law is validated by simulation results, and it provides a criterion for distinguishing between ‘short’ and ‘tall’ topographical features. For turbidity currents, this scaling result represents an upper limit. An interesting non-monotonic influence of the bump height is observed on the long-term propagation velocity of the current. On the one hand, the lateral deflection of the current by the bump leads to an effective increase in the current height and its front velocity in the region away from the bump. At the same time, taller bumps result in a more vigorous three-dimensional evolution of the current, accompanied by increased levels of dissipation, which slows the current down. For small bumps, the former mechanism dominates, so that on average the current front propagates faster than its flat bottom counterpart. For currents interacting with larger bumps, however, the increased dissipation becomes dominant, so that they exhibit a reduced front velocity as compared to currents propagating over flat surfaces.

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

“…23,24,38 A customized Immersed Boundary Method (IBM) can be combined with our high-order flow solver in order to model accurately 3D obstacles at the bottom of the computational domain. 39 The idea is to mimic the complex topographies observed in nature for turbidity currents and to see how the gravity currents are reacting to a specific topography.…”

“…There has been an intensive effort to study those structures, with many experimental investigations, 3,7,[12][13][14][15] theoretical approaches, 16,17 and more recently with numerical investigations based on Direct Numerical Simulations (DNS). [18][19][20][21][22][23][24] Experiments 3,7,12 investigating a) s.laizet@imperial.ac.uk lobe-and-cleft patterns have typically imaged the gravity current from below, allowing the growth, merging, and bifurcation of the structures to be tracked. This analysis identified the origin of the instability as the unstable stratification generated as ambient fluid is overrun by the current head, subject to a frictional surface.…”

“…23,27 They provide detailed and valuable information about the dynamics of turbidity currents with, for instance, the spatio-temporal evolution of the energy budgets, particle concentration field, or wall shear stress. Unfortunately, only very few DNS were carried out with a relatively high Reynolds number and with particle sedimentation.…”

High-resolution simulations of turbidity currents

“…(1)-(3) by a reference length scale, such as the domain half height H/2 of a lock-exchange flow (Meiburg et al 2015;Nasr-Azadani and Meiburg 2014;Necker et al 2002Necker et al , 2005, the current density ρ 1 , and the buoyancy velocity u b…”

Dynamic Lift on an Artificial Static Armor Layer During Highly Unsteady Open Channel Flow

“…Some unsteady flow experiments focus on velocity measurements, sediment transport behavior or studied the river as an ecosystem [3,[12][13][14][15][16][17]. Others address different types of flows, like gravity currents [18,19]. However, none addressed the direct influence of unsteadiness on bed shear stress and lift.…”