A numerical investigation of constant-volume non-Boussinesq density currents

The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents of density ρc, released from a lock of height h₀ and length x₀ into a ambient of height H and density ρₐ, is considered. We use two dimensional Navier-Stokes simulations to cover a wide range of density ratio ρc/ρₐ (for both "heavy"-bottom and "light"-top currents) and geometric ratios (H*=H/h₀, λ=x₀/h₀). To our knowledge, the ranges of parameters and times of propagation considered here were not covered in previous experimental or numerical studies. In the first part, we set the lock aspect ratio to λ=18.75, and vary the density ratio 10-⁴<ρc/ρₐ<10⁴ and initial depth ratio 1≤H*≤50. The Navier-Stokes results are compared with predictions of a shallow-water model, in the regime of constant-speed (slumping) phase. Good agreement is observed in a large region of the parameter space (ρc/ρₐ; H*). The larger discrepancy is observed in the range of high-H* and low-ρc/ρₐ for which the shallow-water model overpredicts the velocity of the current. Two possible reasons are suspected, namely the fluid motion in the ambient fluid which is not accounted for in the model, and the choice of the model for the front condition. In the second part, we set the initial depth ratio to H*=10, and vary the density ratio 10-²<ρc/ρₐ<10² and lock aspect ratio 0.5≤λ≤18.75. In particular, we derive novel insights on the influence of the lock aspect ratio λ=x₀/h₀ on the shape and motion of the current in the slumping stage. It is shown that a critical value exists, λcrit; the dynamics of the current is significantly influenced by λ if below λcrit. We present a simple analytical model which support the observation that for a light current the speed of propagation is proportional to λ¼ when λ<λcrit

A numerical investigation of high-Reynolds-number constant-volume non-Boussinesq density currents in deep ambient

The time-dependent behaviour of non-Boussinesq high-Reynolds-number density currents, released from a lock of height h0 and length x0 into a deep ambient and spreading over horizontal flat boundaries, is considered. We use two-dimensional Navier–Stokes simulations to cover: (i) a wide range of current-to-ambient density ratios, (ii) a range of length-to-height aspect ratios of the initial release within the lock (termed the lock aspect ratio λ=x0/h0) and (iii) the different phases of spreading, from the initial acceleration phase to the self-similar regimes. The Navier–Stokes results are compared with predictions of a one-layer shallow-water model. In particular, we derive novel insights on the influence of the lock aspect ratio (λ) on the shape and motion of the current. It is shown that for lock aspect ratios below a critical value (λcrit ), the dynamics of the current is significantly influenced by λ. We conjecture that λcrit depends on two characteristic time scales, namely the time it takes for the receding perturbation created at the lock upon release to reflect back to the front, and the time of formation of the current head. A comparison of the two with space–time diagrams obtained from the Navier–Stokes simulations supports this conjecture. The non-Boussinesq effect is observed to be significant. While the critical lock aspect ratio (λcrit ) is of order 1 for Boussinesq currents, its value decreases for heavy currents and increases significantly (up to about 20) for light currents. We present a simple analytical model which captures this trend, as well as the observation that for a light current the speed of propagation is proportional to λ1/4 when λ<λcrit

Experimental study on radial gravity currents flowing in a vegetated channel

We present an experimental study of gravity currents in a cylindrical geometry, in the presence of vegetation. Forty tests were performed with a brine advancing in a fresh water ambient fluid, in lock release, and with a constant and time-varying flow rate. The tank is a circular sector of angle $30^circ$ with radius equal to 180 cm. Two different densities of the vegetation were simulated by vertical plastic rods with diameter $D=1.6; extrm{cm}$. We marked the height of the current as a function of radius and time and the position of the front as a function of time. The results indicate a self-similar structure, with lateral profiles that after an initial adjustment collapse to a single curve in scaled variables. The propagation of the front is well described by a power law function of time. The existence of self-similarity on an experimental basis corroborates a simple theoretical model with the following assumptions: (i) the dominant balance is between buoyancy and drag, parameterized by a power law of the current velocity $sim |u|^{lambda-1}u$; (ii) the current advances in shallow-water conditions; (iii) ambient-fluid dynamics is negligible. In order to evaluate the value of ${lambda}$ (the only tuning parameter of the theoretical model), we performed two additional series of measurements. We found that $lambda$ increased from 1 to 2 while the Reynolds number increased from 100 to approximately $6cdot10^3$, the drag coefficient and the transition from $lambda=1$ to $lambda=2$ are quantitatively affected by $D$, but the structure of the model is not

Models of internal jumps and the fronts of gravity currents:unifying two-layer theories and deriving new results

The steady speeds of the front of a gravity current and of an internal jump on a two-layer stratification are often sought in terms of the heights of the relatively dense fluid both up- and downstream from the front or jump, the height of the channel within which they flow, the densities of the two fluids and gravitational acceleration. In this study a unifying framework is presented for calculating the speeds by balancing mass and momentum fluxes across a control volume spanning the front or jump and by ensuring the assumed pressure field is single-valued, which is shown to be equivalent to forming a vorticity balance over the control volume. Previous models have assumed the velocity field is piecewise constant in each layer with a vortex sheet at their interface and invoked explicit or implicit closure assumptions about the dissipative effects to derive the speed. The new formulation yields all of the previously presented expressions and demonstrates that analysing the vorticity balance within the control volume is a useful means of constraining possible closure assumptions, which is arguably more effective than consideration of the flow energetics. However the new approach also reveals that a novel class of models may be developed in which there is shear in the velocity field in the wake downstream of the front or the jump, thus spreading the vorticity over a layer of non-vanishing thickness, rather than concentrating it into a vortex sheet. Mass, momentum and vorticity balances applied over the control volume allow the thickness of the wake and the speed of the front/jump to be evaluated. Results from this vortex-wake model are consistent with published numerical simulations and with data from laboratory experiments, and improve upon predictions from previous formulae. The results may be applied readily to Boussinesq and non-Boussinesq systems and because they arise as simple algebraic expressions, can be straightforwardly incorporated as jump conditions into spatially and temporally varying descriptions of the motion.</jats:p

Rotating planar gravity currents at moderate Rossby numbers: fully resolved simulations and shallow-water modelling - ERRATUM

This note is concerned with the paper published in JFM 867 "Rotating planar gravity currents at moderate Rossby numbers: fully-resolved simulations and shallow-water modeling" by Salinas, Jorge; Bonometti, Thomas; Ungarish, M.; Cantero, Mariano. We discovered a serious error in a significant equation; this produced some wrong numbers in a table and a related figure. The present erratum clarifies the error and provides the corrected results

Introduction to gravity currents and intrusions

The whole book is well written in a clear and pedagogical general style. &#x2026; the author has, in my opinion, produced the first comprehensive book entirely devoted to the modeling of gravity currents and intrusions. This book will be particularly useful to graduate and PhD students, as well as to academics and research engineers working in this field. It may be used as a self-consistent document to get a detailed idea of the state of knowledge about a given problem or a guide toward more specialized papers. It is rich with ideas regarding the direction in which further research is warranted. Thi