Publisher's Note: “Gravity currents in non-rectangular cross-section channels: Analytical and numerical solutions of the one-layer shallow-water model for high-Reynolds-number propagation” [Phys. Fluids 25, 026601 (2013)]

2013 ◽  
Vol 25 (3) ◽  
pp. 039901
Author(s):  
T. Zemach ◽  
M. Ungarish
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
High Reynolds Number ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Gravity Currents ◽  
Water Model ◽  
Shallow Water Model ◽  
High Reynolds ◽  
The One

Axisymmetric, constantly supplied gravity currents at high Reynolds number

2011 ◽  
Vol 675 ◽  
pp. 540-551 ◽  
Author(s):  
ANJA C. SLIM ◽  
HERBERT E. HUPPERT
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Threshold Value ◽  
Gravity Currents ◽  
Water Model ◽  
Closure Condition ◽  
Area Source ◽  
Radial Extent ◽  
Long Time ◽  
High Reynolds

We consider theoretically the long-time evolution of axisymmetric, high Reynolds number, Boussinesq gravity currents supplied by a constant, small-area source of mass and radial momentum in a deep, quiescent ambient. We describe the gravity currents using a shallow-water model with a Froude number closure condition to incorporate ambient form drag at the front and present numerical and asymptotic solutions. The predicted profile consists of an expanding, radially decaying, steady interior that connects via a shock to a deeper, self-similar frontal boundary layer. Controlled by the balance of interior momentum flux and frontal buoyancy across the shock, the front advances as (g′sQ/r1/4s)4/154/5, where g′s is the reduced gravity of the source fluid, Q is the total volume flux, rs is the source radius and is time. A radial momentum source has no effect on this solution below a non-zero threshold value. Above this value, the (virtual) radius over which the flow becomes critical can be used to collapse the solution onto the subthreshold one. We also use a simple parameterization to incorporate the effect of interfacial entrainment, and show that the profile can be substantially modified, although the buoyancy profile and radial extent are less significantly impacted. Our predicted profiles and extents are in reasonable agreement with existing experiments.

The propagation of gravity currents in a V-shaped triangular cross-section channel: experiments and theory

2014 ◽  
Vol 754 ◽  
pp. 232-249 ◽  
Author(s):  
Marius Ungarish ◽  
Catherine A. Mériaux ◽  
Cathy B. Kurz-Besson
Keyword(s):  
Reynolds Number ◽  
Cross Section ◽  
Viscosity Coefficient ◽  
Gravity Currents ◽  
Quantitative Agreement ◽  
Flat Bottom ◽  
Special Configuration ◽  
Theoretical Predictions ◽  
Speed Of Propagation ◽  
High Reynolds

AbstractWe investigate the motion of high-Reynolds-number gravity currents (GCs) in a horizontal channel of V-shaped cross-section combining lock-exchange experiments and a theoretical model. While all previously published experiments in V-shaped channels were performed with the special configuration of the full-depth lock, we present the first part-depth experiment results. A fixed volume of saline, that was initially of length $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}x_0$ and height $h_0$ in a lock and embedded in water of height $H_0$ in a long tank, was released from rest and the propagation was recorded over a distance of typically $ 30 x_0$. In all of the tested cases the current displays a slumping stage of constant speed $u_N$ over a significant distance $x_S$, followed by a self-similar stage up to the distance $x_V$, where transition to the viscous regime occurs. The new data and insights of this study elucidate the influence of the height ratio $H = H_0/h_0$ and of the initial Reynolds number ${\mathit{Re}}_0 = (g^{\prime }h_0)^{{{1/2}}} h_0/ \nu $, on the motion of the triangular GC; $g^{\prime }$ and $\nu $ are the reduced gravity and kinematic viscosity coefficient, respectively. We demonstrate that the speed of propagation $u_N$ scaled with $(g^{\prime } h_0)^{{{1/2}}}$ increases with $H$, while $x_S$ decreases with $H$, and $x_V \sim [{\mathit{Re}}_0(h_0/x_0)]^{{4/9}}$. The initial propagation in the triangle is 50 % more rapid than in a standard flat-bottom channel under similar conditions. Comparisons with theoretical predictions show good qualitative agreements and fair quantitative agreement; the major discrepancy is an overpredicted $u_N$, similar to that observed in the standard flat bottom case.

Energy balances for axisymmetric gravity currents in homogeneous and linearly stratified ambients

2008 ◽  
Vol 616 ◽  
pp. 303-326 ◽  
Author(s):  
MARIUS UNGARISH ◽  
HERBERT E. HUPPERT
Keyword(s):  
High Reynolds Number ◽  
Gravity Current ◽  
Water Model ◽  
Navier Stokes ◽  
Shallow Water Model ◽  
Fluid System ◽  
Dense Fluid ◽  
High Reynolds ◽  
Energy Balances ◽  
Two Fluid

We analyse the exchange of energy for an axisymmetric gravity current, released instantaneously from a lock, propagating over a horizontal boundary at high Reynolds number. The study is relevant to flow in either a wedge or a full circular geometry. Attention is focused on effects due to a linear stratification in the ambient. The investigation uses both a one-layer shallow-water model and Navier–Stokes finite-difference simulations. There is fair agreement between these two approaches for the energy changes of the dense fluid (the current). The stratification enhances the accumulation of potential energy in the ambient and reduces the energy decay (dissipation) of the two-fluid system. The total energy of the axisymmetric current decays considerably faster with distance of propagation than for the two-dimensional counterpart.

High Reynolds number gravity currents along V-shaped valleys

2009 ◽  
Vol 28 (5) ◽  
pp. 651-659 ◽  
Author(s):  
J.J. Monaghan ◽  
C.A. Mériaux ◽  
H.E. Huppert ◽  
J.M. Monaghan
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Gravity Currents ◽  
High Reynolds

Gravity currents propagating into shear

2015 ◽  
Vol 778 ◽  
pp. 552-585 ◽  
Author(s):  
M. M. Nasr-Azadani ◽  
E. Meiburg
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Steady State ◽  
High Reynolds Number ◽  
Gravity Current ◽  
Gravity Currents ◽  
Maximum Energy ◽  
Channel Height ◽  
High Reynolds ◽  
The Given

An analytical vorticity-based model is introduced for steady-state inviscid Boussinesq gravity currents in sheared ambients. The model enforces the conservation of mass and horizontal and vertical momentum, and it does not require any empirical closure assumptions. As a function of the given gravity current height, upstream ambient shear and upstream ambient layer thicknesses, the model predicts the current velocity as well as the downstream ambient layer thicknesses and velocities. In particular, it predicts the existence of gravity currents with a thickness greater than half the channel height, which is confirmed by direct numerical simulation (DNS) results and by an analysis of the energy loss in the flow. For high-Reynolds-number gravity currents exhibiting Kelvin–Helmholtz instabilities along the current/ambient interface, the DNS simulations suggest that for a given shear magnitude, the current height adjusts itself such as to allow for maximum energy dissipation.

On inwardly propagating high-Reynolds-number axisymmetric gravity currents

2003 ◽  
Vol 494 ◽  
pp. 255-274 ◽  
Author(s):  
MARK HALLWORTH ◽  
HERBERT E. HUPPERT ◽  
MARIUS UNGARISH
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Gravity Currents ◽  
High Reynolds
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