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

2012 ◽  
Vol 24 (2) ◽  
pp. 026601 ◽  
Author(s):  
M. R. Flynn ◽  
M. Ungarish ◽  
A. W. Tan
Keyword(s):  
Steady State ◽  
Gravity Currents ◽  
Front Condition

The front condition for intrusive gravity currents

2008 ◽  
Vol 46 (6) ◽  
pp. 788-801 ◽  
Author(s):  
Roger I. Nokes ◽  
Mark J. Davidson ◽  
Charlotte A. Stepien ◽  
William B. Veale ◽  
Rowan L. Oliver
Keyword(s):  
Gravity Currents ◽  
Front Condition ◽  
Intrusive Gravity Currents

scholarly journals Axisymmetric viscous gravity currents flowing over a porous medium

2009 ◽  
Vol 622 ◽  
pp. 135-144 ◽  
Author(s):  
MELISSA J. SPANNUTH ◽  
JEROME A. NEUFELD ◽  
J. S. WETTLAUFER ◽  
M. GRAE WORSTER
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Gravity Current ◽  
Gravity Currents ◽  
Constant Input ◽  
Radial Extent ◽  
Vertically Aligned ◽  
Analytical Expressions ◽  
Permeability Structure ◽  
Good Agreement

We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant input from a point source. In this case, a steady state is possible in which drainage balances the input, and we present analytical expressions for the resulting steady profile and radial extent. We demonstrate good agreement between our experiments, which use a bed of vertically aligned tubes as the porous medium, and the theoretically predicted evolution and steady state. However, analogous experiments using glass beads as the porous medium exhibit a variety of unexpected behaviours, including overshoot of the steady-state radius and subsequent retreat, thus highlighting the importance of the porous medium geometry and permeability structure in these systems.

A new front condition for non-Boussinesq gravity currents

2018 ◽  
Vol 56 (4) ◽  
pp. 517-525 ◽  
Author(s):  
G. Sciortino ◽  
C. Adduce ◽  
V. Lombardi
Keyword(s):  
Gravity Currents ◽  
Front Condition

Gravity currents over fractured substrates in a porous medium

2007 ◽  
Vol 584 ◽  
pp. 415-431 ◽  
Author(s):  
DAVID PRITCHARD
Keyword(s):  
Porous Medium ◽  
Steady State ◽  
Gravity Current ◽  
Gravity Currents ◽  
Limited Extent ◽  
Form Part ◽  
Long Time ◽  
Self Similar ◽  
Steady State Solutions ◽  
A Current

We consider the behaviour of a gravity current in a porous medium when the horizontal surface along which it spreads is punctuated either by narrow fractures or by permeable regions of limited extent. We derive steady-state solutions for the current, and show that these form part of a long-time asymptotic description which may also include a self-similar ‘leakage current’ propagating beyond the fractured region with a length proportional to t1/2. We discuss the conditions under which a current can be completely trapped by a permeable region or a series of fractures.

The front condition for gravity currents

2005 ◽  
Vol 536 ◽  
pp. 49-78 ◽  
Author(s):  
B. M. MARINO ◽  
L. P. THOMAS ◽  
P. F. LINDEN
Keyword(s):  
Gravity Currents ◽  
Front Condition

scholarly journals Modelling gravity currents without an energy closure

2016 ◽  
Vol 789 ◽  
pp. 806-829 ◽  
Author(s):  
N. A. Konopliv ◽  
Stefan G. Llewellyn Smith ◽  
J. N. McElwaine ◽  
E. Meiburg
Keyword(s):  
Steady State ◽  
Froude Number ◽  
Inviscid Flow ◽  
Gravity Currents ◽  
Current Approach ◽  
Steady State Flow ◽  
Simulation Data ◽  
Correct Form ◽  
Simulation Results ◽  
Modelling Approach

We extend the vorticity-based modelling approach of Borden & Meiburg (Phys. Fluids, vol. 25 (10), 2013, 101301) to non-Boussinesq gravity currents and derive an analytical expression for the Froude number without the need for an energy closure or any assumptions about the pressure. The Froude-number expression we obtain reduces to the correct form in the Boussinesq limit and agrees closely with simulation data. Via detailed comparisons with simulation results, we furthermore assess the validity of three key assumptions underlying both our as well as earlier models: (i) steady-state flow in the moving reference frame; (ii) inviscid flow; and (iii) horizontal flow sufficiently far in front of and behind the current. The current approach does not require an assumption of zero velocity in the current.

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.

Gravity currents in rotating channels. Part 1. Steady-state theory

2002 ◽  
Vol 457 ◽  
pp. 295-324 ◽  
Author(s):  
J. N. HACKER ◽  
P. F. LINDEN
Keyword(s):  
Steady State ◽  
Perfect Fluid ◽  
Control Point ◽  
Gravity Current ◽  
Propagation Speed ◽  
Gravity Currents ◽  
Force Balance ◽  
Fluid Approximation ◽  
Left Hand ◽  
Layer Solution

A theory is developed for the speed and structure of steady-state non-dissipative gravity currents in rotating channels. The theory is an extension of that of Benjamin (1968) for non-rotating gravity currents, and in a similar way makes use of the steady-state and perfect-fluid (incompressible, inviscid and immiscible) approximations, and supposes the existence of a hydrostatic ‘control point’ in the current some distance away from the nose. The model allows for fully non-hydrostatic and ageostrophic motion in a control volume V ahead of the control point, with the solution being determined by the requirements, consistent with the perfect-fluid approximation, of energy and momentum conservation in V, as expressed by Bernoulli's theorem and a generalized flow-force balance. The governing parameter in the problem, which expresses the strength of the background rotation, is the ratio W = B/R, where B is the channel width and R = (g′H)1/2/f is the internal Rossby radius of deformation based on the total depth of the ambient fluid H. Analytic solutions are determined for the particular case of zero front-relative flow within the gravity current. For each value of W there is a unique non-dissipative two-layer solution, and a non-dissipative one-layer solution which is specified by the value of the wall-depth h0. In the two-layer case, the non-dimensional propagation speed c = cf(g′H)−1/2 increases smoothly from the non-rotating value of 0.5 as W increases, asymptoting to unity for W → ∞. The gravity current separates from the left-hand wall of the channel at W = 0.67 and thereafter has decreasing width. The depth of the current at the right-hand wall, h0, increases, reaching the full depth at W = 1.90, after which point the interface outcrops on both the upper and lower boundaries, with the distance over which the interface slopes being 0.881R. In the one-layer case, the wall-depth based propagation speed Froude number c0 = cf(g′h0)−1/2 = 21/2, as in the non-rotating one-layer case. The current separates from the left-hand wall of the channel at W0 ≡ B/R0 = 2−1/2, and thereafter has width 2−1/2R0, where R0 = (g′h0)1/2/f is the wall-depth based deformation radius.

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