The flow of high-Reynolds axisymmetric gravity currents of a stratified fluid into a stratified ambient: shallow-water and box model solutions

2012 ◽  
Vol 12 (4) ◽  
pp. 347-359 ◽  
Author(s):  
T. Zemach ◽  
M. Ungarish
Keyword(s):  
Shallow Water ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Box Model ◽  
Model Solutions ◽  
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.

Particle-driven gravity currents: asymptotic and box model solutions

2000 ◽  
Vol 19 (1) ◽  
pp. 139-165 ◽  
Author(s):  
Andrew J. Hogg ◽  
Marius Ungarish ◽  
Herbert E. Huppert
Keyword(s):  
Gravity Currents ◽  
Box Model ◽  
Model Solutions

Sedimentation from binary suspensions in a turbulent gravity current along a V-shaped valley

2012 ◽  
Vol 712 ◽  
pp. 624-645 ◽  
Author(s):  
Catherine A. Mériaux ◽  
Cathy B. Kurz-Besson
Keyword(s):  
Silicon Carbide ◽  
Settling Velocity ◽  
Velocity Ratio ◽  
Reynolds Numbers ◽  
Gravity Currents ◽  
Glass Beads ◽  
Box Model ◽  
Complete Agreement ◽  
High Reynolds Numbers ◽  
High Reynolds

AbstractWe present a study of bidispersed particulate gravity currents at high Reynolds numbers flowing along a V-shaped valley. The speed and width of the currents, the mass deposited by the currents and the density of the deposits were examined by both a box model and lock-exchange experiments in a 5 m long tank. Silicon carbide and glass beads were used for the bidispersed suspension models. The initial conditions of the currents were similar, except that the grain size of the glass beads was successively chosen to be 2, 2.5 and 4 times that of the silicon carbide. For all experiments a Stokes’ settling velocity model, assuming that both particles are spherical, gives a settling rate of the glass beads that is greater than that of the silicon carbide by a factor ranging from 1.6 to 16.5. When the ratio of the Stokes’ settling velocity of the glass beads to that of the silicon carbide is greater than ∼6, we find a complete agreement between the box model and the experiment. In particular, the deposit shows a substantial decline in the mass of the coarser glass beads in the first metre, so that it only contains the finer silicon carbide further downstream. By contrast, when the Stokes’ settling velocity ratio is less than ∼4, only the speed of the current and the total sedimented mass can be well described by the box model. The experimental deposit is otherwise characterized by a slightly increasing density, which the box model fails to match. There is no difference in the deposit density across the valley. For all experiments in the V-shaped valley, the width of the currents decreases with time $t$ according to ${t}^{\ensuremath{-} 2/ 7} $. Analogue experiments in a flat-bottom tank were also performed to assess the influence of the valley on the sedimentation dynamics described above. A similar behaviour with settling velocity ratios was found. This study eventually shows the need for considering particle interactions in even dilute gravity currents at high Reynolds numbers.

scholarly journals Particulate gravity currents along V-shaped valleys

2009 ◽  
Vol 631 ◽  
pp. 419-440 ◽  
Author(s):  
JOE J. MONAGHAN ◽  
CATHERINE MÉRIEUX ◽  
HERBERT E. HUPPERT ◽  
JOHN MANSOUR
Keyword(s):  
Unit Area ◽  
Flow Direction ◽  
Pure Water ◽  
Gravity Current ◽  
Gravity Currents ◽  
Turbulent Medium ◽  
Box Model ◽  
Axis Parallel ◽  
High Reynolds ◽  
Silicon Carbide Particles

This paper extends previous studies of saline gravity currents at high Reynolds number flowing along a tank with a V-shaped valley. We use experiments and a box model to determine the primary features of the flow. The particulate gravity currents were initiated by releasing a fixed volume of fluid consisting of pure water mixed with silicon carbide particles from a lock at one end of the tank. The resulting motion and deposit pattern differ significantly from those for the propagation of a particulate gravity current along a flat-bottomed tank. The front of the current, seen from above, is approximately parabolic (with axis parallel to the flow direction) in contrast to the current in a flat-bottomed tank where it is nearly a straight line perpendicular to the flow. This feature mimics the results for pure saline currents. When seen in profile the currents do not have a clearly defined raised head, which is a feature of the flat-bottomed currents. The mass deposited per unit area varies nearly monotonically with respect to distance down the tank, again in contrast to the case of the flat-bottomed tank. The exceptions to this are the two experiments which have the highest ratio of lock height to length. The mass deposited per unit area across the V-shaped valley is much larger in the central part of the valley than it is on the flanks for any position along the valley. We find that the results can be described with remarkable accuracy by a box model using a generalization of the equation for sedimentation from a turbulent medium due to Martin and Nokes. Our results further show that the factor used in the deposition rate equation which is commonly assumed to be 1 should be smaller, typically 0.7.

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.

Assessing the Numerical Accuracy of Complex Spherical Shallow-Water Flows

2007 ◽  
Vol 135 (11) ◽  
pp. 3876-3894 ◽  
Author(s):  
Ali R. Mohebalhojeh ◽  
David G. Dritschel
Keyword(s):  
Shallow Water ◽  
Fourth Order ◽  
Large Scale ◽  
Numerical Accuracy ◽  
Conservation Of Energy ◽  
Water Flows ◽  
Shallow Water Flows ◽  
Low Froude Number ◽  
Contour Advection ◽  
High Reynolds

Abstract The representation of nonlinear shallow-water flows poses severe challenges for numerical modeling. The use of contour advection with contour surgery for potential vorticity (PV) within the contour-advective semi-Lagrangian (CASL) algorithm makes it possible to handle near-discontinuous distributions of PV with an accuracy beyond what is accessible to conventional algorithms used in numerical weather and climate prediction. The emergence of complex distributions of the materially conserved quantity PV, in the absence of forcing and dissipation, results from large-scale shearing and deformation and is a common feature of high Reynolds number flows in the atmosphere and oceans away from boundary layers. The near-discontinuous PV in CASL sets a limit on the actual numerical accuracy of the Eulerian, grid-based part of CASL. For the spherical shallow-water equations, the limit is studied by comparing the accuracy of CASL algorithms with second-order-centered, fourth-order-compact, and sixth-order-supercompact finite differencing in latitude in conjunction with a spectral treatment in longitude. The comparison is carried out on an unstable midlatitude jet at order one Rossby number and low Froude number that evolves into complex vortical structures with sharp gradients of PV. Quantitative measures of global conservation of energy and angular momentum, and of imbalance as diagnosed using PV inversion by means of Bolin–Charney balance, indicate that fourth-order differencing attains the highest numerical accuracy achievable for such nonlinear, advectively dominated flows.

scholarly journals Gravity currents and internal waves in a stratified fluid

2008 ◽  
Vol 616 ◽  
pp. 327-356 ◽  
Author(s):  
BRIAN L. WHITE ◽  
KARL R. HELFRICH
Keyword(s):  
Internal Waves ◽  
Wave Speed ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Gravity Currents ◽  
Stratified Fluid ◽  
Front Speed ◽  
Long Wave ◽  
Conjugate State ◽  
Energy Conserving

A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.

Laboratory experiments and shallow water simulations of gravity currents moving on flat and up-sloping beds

2014 ◽  
pp. 89-95
Author(s):  
C Adduce ◽  
V Lombardi ◽  
G Sciortino ◽  
M La Rocca ◽  
M Morganti
Keyword(s):  
Shallow Water ◽  
Laboratory Experiments ◽  
Gravity Currents
Sign in / Sign up

Export Citation Format

Share Document