arXiv subjects

Edward W. G. Skevington

Publications and source records attributed to Edward W. G. Skevington.

8 recordsLinked to original sources

arXiv2025

Gravity current energetics and particle suspension

Gravity currents are a ubiquitous density driven flow occurring in both the natural environment and in industry. They include: seafloor turbidity currents, primary vectors of sediment, nutrient and pollutant transport; cold fronts; and hazardous gas spills. However, while the energetics are critical for their evolution and particle suspension, they are included in system scale models only crudely, so we cannot yet predict and explain the dynamics and run-out of such real-world flows. Herein, a novel depth-averaged framework is developed to capture the evolution of volume, concentration, momentum, and turbulent kinetic energy from direct integrals of the full governing equations. For the first time, we show the connection between the vertical profiles, the evolution of the depth-averaged flow, and the energetics. The viscous dissipation of mean-flow energy near the bed makes a leading order contribution, and an energetic approach to entrainment captures detrainment of fluid through particle settling. These observations allow a reconsideration of particle suspension, advancing over 50-years of research. We find that the new formulation can describe the full evolution of a shallow dilute current, with the accuracy depending primarily on closures for the profiles and source terms. Critically, this enables accurate and computationally efficient hazard risk analysis and earth surface modelling.

physics.flu-dyn↗

arXiv2023

Self-stratifying turbidity currents

Turbidity currents, seafloor flows driven by the excess density of suspended particles, are key conveyors of sediment, nutrient, and pollutant from the continental margins to deep ocean, and pose critical submarine geohazard risks. Due to their vast scale and extreme aspect ratio, extant models are constrained to highly simplified depth-averaged theory and fail to capture observed behaviour. We propose a novel depth-averaged model capturing the internal energy balance and the vertical profiles of velocity, depth, and turbulent kinetic energy. The vertical profiles change as the current evolves: it self stratifies. This enables the critical new insight that turbidity current propagation is enabled by bidirectional cascades between mean-flow kinetic, turbulent, and gravitational potential energies. The model is generalised for fully confined `canyon' flow (no lateral overspill), and partially confined `channel' flow (lateral overspill over bounding levees). `Quasi-equilibrium' solutions for self-stratifying turbidity currents are constructed. These solutions are weekly unstable and connected to a slowly evolving manifold, wherein environmental currents are likely found. Equilibrium solutions, found for channel flow, are not stable either. Levee overspill removes dilute, low momentum fluid, rejuvenating the flow, which can cause a positive feedback loop where the fluid becomes increasingly concentrated. We test the new theory by modelling flow in the Congo canyon-channel system, for the first time simulating a supercritical turbidity current that travels 100s km to the distal reaches of a real-world system. It is shown that self-stratification enhances material and momentum fluxes, determining the environmental impacts and risks from such flows.

physics.flu-dyn↗

arXiv2023

The unsteady overtopping of barriers by gravity currents and dam-break flows

The collision of a gravitationally-driven horizontal current with a barrier following release from a confining lock is investigated using a shallow water model of the motion, together with a sophisticated boundary condition capturing the local interaction. The boundary condition permits several overtopping modes: supercritical, subcritical, and blocked flow. The model is analysed both mathematically and numerically to reveal aspects of the unsteady motion and to compute the proportion of the fluid trapped upstream of the barrier. Several problems are treated. Firstly, the idealised problem of a uniform incident current is analysed to classify the unsteady dynamical regimes. Then, the extreme regimes of a very close or distant barrier are tackled, showing the progression of the interaction through the overtopping modes. Next, the trapped volume of fluid at late times is investigated numerically, demonstrating regimes in which the volume is determined purely by volumetric considerations, and others where transient inertial effects are significant. For a Boussinesq gravity current, even when the volume of the confined region behind the barrier is equal to the fluid volume, $30\%$ of the fluid escapes the domain, and a confined volume $3$ times larger is required for the overtopped volume to be negligible. For a subaerial dam-break flow, the proportion that escapes is in excess of $60\%$ when the confined volume equals the fluid volume, and a barrier as tall as the initial release is required for negligible overtopping. Finally, we compare our predictions to experiments, showing a good agreement across a range of parameters.

physics.flu-dyn↗

arXiv2023

Inadequacy of fluvial energetics for describing gravity current autosuspension

"Consider the [turbidity] current as ... a river" R. A. Bagnold (1962); the foundation of contemporary deep marine sedimentology. Gravity currents, such as sediment-laden turbidity currents, are ubiquitous natural flows that are driven by a density difference. Turbidity currents have provided vital motivation to advance understanding of this class of flows because their enigmatic long run-out and driving mechanisms are not properly understood. Extant models assume that material transport by gravity currents is dynamically similar to fluvial flows. Here, empirical research from different types of particle-driven gravity currents is integrated with our experimental data, to show that material transport is fundamentally different from fluvial systems. Contrary to current theory, buoyancy production is shown to have a non-linear dependence on available flow power, indicating an underestimation of the total kinetic energy lost from the mean flow. A revised energy budget directly implies that the mixing efficiency of gravity currents is enhanced.

physics.flu-dyn↗

arXiv2021

A Well Balanced Reconstruction with Bounded Velocities and Low-Oscillation Slow Shocks for the Shallow Water Equations

Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For the shallow water system this involves reconstructing in surface elevation, to which modifications must be made as the fluid depth becomes small to ensure positivity. We investigate the scheme proposed in Skevington (2021) though numerical experiments, demonstrating its ability to resolve steady and near steady states at high accuracy. We also present a modification to the scheme which enables the resolution of slowly moving shocks and dam break problems without compromising the well balanced property.

math.NA↗

arXiv2021

The implementation of a broad class of boundary conditions for non-linear hyperbolic systems

We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is similar to that of Thompson (1987), where the boundary values were simulated by combining characteristic equations with the time derivative of the algebraic conditions, but differs in two important regards. Firstly, when the boundary is a characteristic of one of the fields Thompson's method can fail to produce reasonable values. We propose a method of combining the characteristic equations with extrapolation which ensures convergence. Secondly, the application of algebraic conditions can suffer from $O(1)$ drift-off error, and we discuss projective time-stepping algorithms designed to converge for this type of system. Test problems for the shallow water equations are presented to demonstrate the result of simulating with and without the modifications discussed, illustrating their necessity for certain problems.

math.NA↗

arXiv2021

A well-balanced reconstruction with bounded velocities for the shallow water equations by convex combination

Finite volume schemes for hyperbolic balance laws require a piecewise polynomial reconstruction of the cell averaged values, and a reconstruction is termed `well-balanced' if it is able to simulate steady states at higher order than time evolving states. For the shallow water system this involves reconstructing in surface elevation, to which modifications must be made as the fluid depth becomes small to ensure positivity, and for many reconstruction schemes a modification of the inertial field is also required to ensure the velocities are bounded. We propose here a reconstruction based on a convex combination of surface and depth reconstructions which ensures that the depth increases with the cell average depth. We also discuss how, for cells that are much shallower than their neighbours, reducing the variation in the reconstructed flux yields bounds on the velocities. This approach is generalisable to high order schemes, problems in multiple spacial dimensions, and to more complicated systems of equations. We present reconstructions and associated technical results for three systems, the standard shallow water equations, shallow water in a channel of varying width, and a shallow water model of a particle driven current. Positivity preserving time stepping is also discussed.

math.NA↗

arXiv2020

Wetting Fronts in Porous Media

The dynamics of the wetting front are considered during the imbibition of a fluid into a porous substrate through a circular drawing area. A mathematical model of this process, assuming incompressible Darcy flow, is presented, before the full finite element scheme for solving this set of equations is given allowing the reader to reproduce all presented results. Asymptotic analysis is performed revealing contradictions between the assumptions of Darcy's equation and the solutions it produces, along with qualitative results for the behaviour of the wetting front and macroscopic contact angles. Velocity and pressure distributions across the wetted region are presented, as well as plots of the evolution of the wetting front and parameters with discussion.

physics.flu-dyn↗