Axisymmetric gravity currents at high Reynolds number: On the quality of shallow-water modeling of experimental observations

2007 ◽  
Vol 19 (3) ◽  
pp. 036602 ◽  
Author(s):  
Marius Ungarish
Keyword(s):  
Reynolds Number ◽  
Shallow Water ◽  
High Reynolds Number ◽  
Gravity Currents ◽  
Water Modeling ◽  
High Reynolds

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.

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

High-Reynolds-number gravity currents over a porous boundary: shallow-water solutions and box-model approximations

2000 ◽  
Vol 418 ◽  
pp. 1-23 ◽  
Author(s):  
MARIUS UNGARISH ◽  
HERBERT E. HUPPERT
Keyword(s):  
Shallow Water ◽  
Characteristic Time ◽  
High Reynolds Number ◽  
Gravity Current ◽  
Gravity Currents ◽  
Box Model ◽  
Shallow Water Theory ◽  
Fluid Boundary ◽  
Horizontal Spread ◽  
High Reynolds

The behaviour of an inviscid, lock-released gravity current which propagates over a horizontal porous boundary in either a rectangular or an axisymmetric geometry is analysed by both shallow-water theory and ‘box-model’ approximations. It is shown that the effect of the porous boundary can be incorporated by means of a parameter λ which represents the ratio of the characteristic time of porous drainage, τ, to that of horizontal spread, x0 =(g′h0)1/2, where x0 and h0 are the length and height of the fluid initially behind the lock and g′ is the reduced gravity. The value of τ is assumed to be known for the fluid–boundary combination under simulation. The interesting cases correspond to small values of λ; otherwise the current has drained before any significant propagation can occur. Typical solutions are presented for various values of the parameters, and differences to the classical current (over a non-porous boundary) are pointed out. The results are consistent with the experiments in a rectangular tank reported by Thomas, Marino & Linden (1998), but a detailed verification, in particular for the axisymmetric geometry case, requires additional experimental data.

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