In this review article, we discuss recent progress with regard to modeling gravity-driven, high Reynolds number currents, with the emphasis on depth-resolving, high-resolution simulations. The initial sections describe new developments in the conceptual modeling of such currents for the purpose of identifying the Froude number–current height relationship, in the spirit of the pioneering work by von Karman and Benjamin. A brief introduction to depth-averaged approaches follows, including box models and shallow water equations. Subsequently, we provide a detailed review of depth-resolving modeling strategies, including direct numerical simulations (DNS), large-eddy simulations (LES), and Reynolds-averaged Navier–Stokes (RANS) simulations. The strengths and challenges associated with these respective approaches are discussed by highlighting representative computational results obtained in recent years.

Modeling Gravity and Turbidity Currents: Computational Approaches and Challenges

The behaviour of a gravity current propagating into a two-layer stratified ambient fluid is described in detail. A comprehensive description is given of the different flow regimes, with particular emphasis on the front condition linking the thickness of the gravity current to its speed of propagation and the transfer of energy to upstream disturbances in the form of internal bores and nonlinear solitary waves. Hydraulic theory analogous to that of two-layer flow over topography (Baines, J. Fluid Mech., vol. 146, 1984, pp. 127–167) is extended to the gravity current problem to classify frontal behaviour into the following regimes: Type I, subcritical currents; Type II, currents that generate upstream undular bores; Type III, currents that generate an upstream monotonic bore connected by a rarefaction; Type IV, supercritical fronts with a large-amplitude trapped solitary-wave-like disturbance; and Type V, supercritical gravity currents. Over 200 two-dimensional Boussinesq–Euler simulations spanning a range of gravity current properties demonstrate good agreement, for both the behavioural regime and the front condition , with hydraulic theory that extends original work by Rottman & Simpson (Q. J. R. Meteorol. Soc., vol. 115, 1989, pp. 941–963) to arbitrary ambient layer thickness, and uses an improved closure for the upstream bore that correctly predicts the behaviour in the limit of large bore amplitude. In addition, the energy balance is analysed, and it is shown that the energy transfer from the gravity current to upstream disturbances is significant, and consistent with the hydraulic theory. The results demonstrate a clear connection to the problem of upstream resonance in two-layer flow over topography, and have significant implications for interpreting field observations of nonlinear internal waves generated by atmospheric density currents and coastal river plumes.

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A general description of a gravity current front propagating in a two-layer stratified fluid

We present an experimental investigation, supported by a theoretical model, of the motion of lock-release, constant inflow, and time varying inflow gravity currents (GCs) into a linearly stratified ambient fluid at large Reynolds number. The aim is the experimental validation of a simple model able to predict the slumping phase front speed and the asymptotic self-similar front speed for rectangular and circular cross section channels. The first investigated system is of Boussinesq type with the dense current (salt water dyed with aniline) released in a circular channel of 19 cm diameter and 400 cm long (605 cm in the inflow experiments), half-filled of linearly stratified ambient fluid (salt water with varying salt concentration). The second system has the same components but with a channel of rectangular cross section of 14 cm width, 11 cm ambient fluid depth, and 504 cm length. The density stratification of the ambient fluid was obtained with a computer controlled set of pumps and of mixing tanks. For t...

Gravity currents in a linearly stratified ambient fluid created by lock release and influx in semi-circular and rectangular channels

Experiments of hypopycnal and mesopycnal currents demonstrate that the microscopic transport of fresh water in viscous boundary layers surrounding the settling particles significantly impacts the macroscopic current evolution.

Particle-bearing currents in uniform density and two-layer fluids

We develop a vorticity-based approach for modelling quasi-steady, supercritical gravity currents propagating into a finite-height channel with arbitrary density and velocity stratification. The model enforces the conservation of mass, horizontal and vertical momentum. In contrast to previous approaches, it does not rely on empirical, energybased closure assumptions. Instead, the effective energy loss of the flow can be calculated a posteriori. The present model results in the formulation of a second-order, nonlinear ordinary differential equation (ODE) that can be solved in a straightforward fashion to determine the gravity-current velocity, along with the downstream ambient velocity and density profiles. Comparisons between model predictions and direct numerical simulations (DNS) show excellent agreement. Furthermore, they indicate that, for high Reynolds numbers, the gravity-current height adjusts itself so as to maximize the loss of energy.

Gravity currents propagating into ambients with arbitrary shear and density stratification: vorticity-based modelling

We consider the propagation of a gravity current of density ρc at the bottom of a two-layer stratified ambient in a horizontal channel of height H, in the high-Reynolds number Boussinesq domain. The study emphasizes theoretical-analytical modeling, however, experimental and Navier-Stokes simulation data are also presented and their comparison with theory is discussed. The stratification parameters are S = (ρ1 − ρ2)/(ρc − ρ2) where ρ is the fluid density, and φ = h1R/H where h1R is the (unperturbed) ambient interface height. Here, 1 and 2 denote, respectively, the lower and upper layer and c denotes the gravity current. The reduced gravity is defined as g′ = (ρc/ρ2 − 1)g. Rigorous results are obtained for the steady-state analogue of the classical problem of Benjamin [J. Fluid Mech. 31, 209 (1968)]10.1017/S0022112068000133, in which the half-infinite gravity current has thickness h and speed U. We thereby demonstrate that the Froude number F=U/(g′h)1/2 is a function of a = h/H, S, and φ. In general, two so...

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Gravity currents in a two-layer stratified ambient: The theory for the steady-state (front condition) and lock-released flows, and experimental confirmations

A. W. Tan

Papers

Gravity currents in a two-layer stratified ambient: The theory for the steady-state (front condition) and lock-released flows, and experimental confirmations