"Consider the [turbidity] current as ... a river" R. A. Bagnold (1962); foundation of contemporary deep marine sedimentology. Gravity currents, such sediment-laden turbidity are ubiquitous natural flows that driven by density difference. Turbidity currents have provided vital motivation to advance understanding this class because their enigmatic long run-out and driving mechanisms not properly understood. Extant models assume material transport gravity is dynamically similar fluvial flows....

An inertial gravity current released within a topographic depression may climb up the incline from lower to an upper plateau if it is sufficiently energetic and then continue flow unsteadily away step while simultaneously draining back into depression. This density-driven motion investigated theoretically using shallow-water equations simulate smooth horizontal plane compute volume of fluid that escapes It shown possible for all drain down escaped diminishes with power-law dependence on...

The collision of a gravitationally-driven horizontal current with barrier following release from confining lock is investigated using shallow water model the motion, together sophisticated boundary condition capturing local interaction. permits several overtopping modes: supercritical, subcritical, and blocked flow. analysed both mathematically numerically to reveal aspects unsteady motion compute proportion fluid trapped upstream barrier. Several problems are treated. Firstly, idealised...

Gravity currents are a ubiquitous density driven flow occurring in both the natural environment and industry. They include: seafloor turbidity currents, primary vectors of sediment, nutrient pollutant transport; cold fronts; hazardous gas spills. However, while energetics critical for their evolution particle suspension, they included system scale models only crudely, so we cannot yet predict explain dynamics run-out such real-world flows. Herein, novel depth-averaged framework is developed...

Summary The unsteady reflection of dam-break flow along a horizontal channel by remote barrier is modelled using the nonlinear shallow water equations. interaction generates an upstream moving bore that connects collapsing reservoir fluid to rapidly deepening layer adjacent barrier. These motions are modified when released into containing pre-wetted layer, because oncoming itself headed alters initial reflection. Solutions for these flows calculated quasi-analytical techniques utilise method...

When released from rest in a cylindrical reservoir, relatively dense fluid flows radially and may drain freely over an edge or propagate along the underlying boundary as gravity current. Here we show that both scenarios unsteady motions develop same supercritical state, phenomenon does not occur equivalent two-dimensional which strongly influences ensuing dynamics, even at long times after release. In particular, demonstrate onset persistence of outflow when drains edge, development internal...

Turbidity currents, seafloor flows driven by the excess density of suspended particles, are key conveyors sediment, nutrient, and pollutant from continental margins to deep ocean, pose critical submarine geohazard risks. Due their vast scale extreme aspect ratio, extant models constrained highly simplified depth-averaged theory fail capture observed behaviour. We propose a novel model capturing internal energy balance vertical profiles velocity, depth, turbulent kinetic energy. The change as...

Finite volume schemes for hyperbolic balance laws require a piecewise polynomial reconstruction of the cell averaged values, and is termed `well-balanced' if it able to simulate steady states at higher order than time evolving states. For shallow water system this involves reconstructing in surface elevation, which modifications must be made as fluid depth becomes small ensure positivity, many modification inertial field also required velocities are bounded. We propose here based on convex...

Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we so called 'well balanced' scheme. For shallow water system this involves reconstructing in surface elevation, which modifications must be made as fluid depth becomes small ensure positivity. We investigate scheme proposed Skevington (2021) though experiments, demonstrating its ability resolve near at high accuracy. also...

We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow a broad class differential algebraic conditions. Our approach is similar Thompson (1987), where values were simulated by combining characteristic equations time derivative conditions, but differs in two important regards. Firstly, when one fields Thompson's method can fail produce reasonable values. extrapolation which ensures convergence....

"Consider the [turbidity] current as ... a river" R. A. Bagnold (1962); foundation of contemporary deep marine sedimentology. Gravity currents, such sediment-laden turbidity are ubiquitous natural flows that driven by density difference. Turbidity currents have provided vital motivation to advance understanding this class because their enigmatic long run-out and driving mechanisms not properly understood. Extant models assume material transport gravity is dynamically similar fluvial flows....

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

Abstract “Consider the [turbidity] current as that of a river” R. A. Bagnold (1962);the foundation contemporary deep marine sedimentology.Submarine sediment-laden buoyancy-driven flows, or turbidity currents, are critical key vectors for material, nutrient, and pollutant dispersal in world’s oceans. Extant models currents assume material transport is dynamically similar to open-channel flows. Here, 70 years empirical research integrated with new data, show by fundamentally different from...

The collision of a gravitationally-driven horizontal current with barrier following release from confining lock is investigated using shallow water model the motion, together sophisticated boundary condition capturing local interaction. permits several overtopping modes: supercritical, subcritical, and blocked flow. analysed both mathematically numerically to reveal aspects unsteady motion compute proportion fluid trapped upstream barrier. Several problems are treated. Firstly, idealised...