A Simplified Model for Levee Formation by Turbidity Currents
Turbidity currents are known to form channels, and in some cases to generate levees by deposition... more Turbidity currents are known to form channels, and in some cases to generate levees by deposition of sediments from channel overflows. The levees may follow a power law or exponential decay in thickness perpendicular to the channel. In the present study we provide a simple analytical model to describe the levee shape as function of the governing flow parameters. Entrainment of ambient fluid is found to have an important influence on the shape of the levee. Two-dimensional numerical simulations are conducted to provide supporting evidence to the theoretical model.
Navier-Stokes based linear stability analysis of submarine channel formation by turbidity currents
Submarine channels represent common features on the continental shelf. They are formed, and in tu... more Submarine channels represent common features on the continental shelf. They are formed, and in turn affect, sediment transport from shallow to deeper waters. We perform a Navier-Stokes based linear stability analysis, based on the Boussinesq approximation, to assess turbidity currents as a potential mechanism for the initiation of such channels. A one-dimensional base state is assumed for the streamwise velocity and the particle loading, and the fluid/substrate interface evolves according to a balance of erosion and sedimentation. The stability analysis demonstrates that a perturbation of this balance results in local variations of particle concentration, which in turn lead to the formation of counterrotating, streamwise vortex pairs. These modify the local balance of erosion and sedimentation such as to amplify the initial perturbation. Dispersion relationships are presented in order to evaluate the influence of the governing dimensionless parameters. The ratio of the particle concentration and velocity boundary layer thicknesses is seen to be important.
Sediment wave formation by unstable internal waves in a turbidity current boundary layer
The bedform of sediment that is deposited from turbidity currents onto the ocean floor is often f... more The bedform of sediment that is deposited from turbidity currents onto the ocean floor is often found to exhibit long-wavelength variations, with crest lines perpendicular to the flow direction (``sediment waves''). A temporal stability analysis, based on the 2D Navier--Stokes equations, reveals the presence of unstable internal waves in the bottom boundary layer of a turbidity current. Instability arises from the interaction between the current and the sediment bed, via the competing effects of particle deposition and erosion. Due to the velocity and density variations within the boundary layer, near-stationary internal waves near the bottom may exist under both sub- and supercritical outer flow conditions. Unstable internal waves display long wavelengths and are typically found to slowly travel upstream. Both features are in qualitative agreement with field observations on sediment waves.
Inverse modeling: reconstructing the initial conditions of a turbidity current
A new approach is introduced for generating models of submarine sediment deposits laid down by tu... more A new approach is introduced for generating models of submarine sediment deposits laid down by turbidity currents (turbidites). Initial conditions of the original turbidity current are reconstructed via a derivative-free optimization algorithm based on information of the deposit properties at isolated control points; where the problem is in the subsurface (e.g. in an oil or gas field), this information is typically obtained from well data. Towards this end, results from successive numerical flow simulations are matched against the available partial well data. Upon convergence, these simulations provide a process-based estimation of the properties of the entire deposit. The validity of the approach is demonstrated in the context of particle-driven lock-exchange flows, simulated via DNS.
We explore the formation of sediment waves by turbidity currents, based on a linear stability ana... more We explore the formation of sediment waves by turbidity currents, based on a linear stability analysis of the bottom boundary layer in a turbidity current. The analysis employs the 2D Navier-Stokes equations for the fluid, and it accounts for the coupled interaction of fluid and suspended particle motion with the erodible bed below. Wavy perturbations of the bottom topography may either be amplified or leveled out under the competing effects of sediment deposition and erosion. The destabilizing effect of the base flow on the stability of the bedform is modulated by the perturbation eigenmodes of sediment deposition and of erosive shear stress. The phase relation between these two perturbation fields determines the total growth rate and phase velocity of the sediment wave. Upstream-traveling waves are dominantly caused by preferred erosion of sediment into the flow along the downstream side of the interface wave, in qualitative agreement with existing experimental and numerical investigations. Results indicate that both short- and long-wavelength modes are amplified. The associated short-wavelength eigenmodes travel at negative phase velocities over parameter regimes that are typical of turbidity currents.
The linear stability of an erodible sediment bed beneath a turbidity current is analyzed, in orde... more The linear stability of an erodible sediment bed beneath a turbidity current is analyzed, in order to identify mechanisms for the formation of longitudinal channels. Based on the Navier-Stokes equations, the analysis accounts for the coupled interaction of the three-dimensional fluid and sediment motion with the erodible bed. For instability to occur, the suspended sediment base concentration profile needs to decay more slowly away from the sediment bed than the base flow shear stress. This destabilizing effect of the base flow is modulated by the stabilizing perturbation of the suspended sediment concentration, and by the shear stress due to a secondary flow in the form of counterrotating streamwise vortices. These are stabilizing for small Reynolds numbers, and destabilizing for large values. For a current height of 10m, we obtain a most amplified wavelength of about 250m, which is consistent with field observations. In contrast to previous analyses based on depth-averaged equations, the instability mechanism identified here does not require any assumptions about sub- or supercritical flow, nor does it require the presence of a slope.
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Papers by Brendon Hall