Mixing in continuous gravity currents

2017 ◽  
Vol 818 ◽  
Author(s):  
Diana Sher ◽  
Andrew W. Woods
Keyword(s):  
Light Attenuation ◽  
Vertical Gradient ◽  
Gravity Currents ◽  
Mixing Zone ◽  
Ambient Fluid ◽  
Unit Width ◽  
A Value ◽  
Dense Fluid ◽  
Catch Up ◽  
High Reynolds

We present measurements of the entrainment of ambient fluid into high-Reynolds-number gravity currents produced by a steady flux of buoyancy. The currents propagate along a horizontal channel and the mixing is measured using a light attenuation technique to obtain the cross-channel average of the density throughout the current. The total volume of the current increases linearly with time, at a rate in the range $(1.8{-}2.1)Q_{o}$ for source Froude numbers, $Fr_{o}$, in the range $0.1{-}3.7$, where $Q_{o}$ is the source volume flux per unit width. Most mixing occurs either immediately downstream of the inflow or near the head of the flow, with an increasing proportion of the entrainment occurring in a mixing zone near the inflow as $Fr_{o}$ increases. A vertical gradient in the density and horizontal velocity develops in this mixing zone. This enables relatively dense fluid at the base of the current to catch up with the head, where it rises and mixes with the ambient fluid which is displaced over the head. The mixed fluid continues forward more slowly than the head, forming the relatively dilute fluid in the upper part of the current. Our data show that the depth and the depth-averaged buoyancy are primarily dependent on the position relative to the front, with the speed of the front being $\unicode[STIX]{x1D706}(Fr_{o})B_{o}^{1/3}$, where $B_{o}$ is the source buoyancy flux per unit width. Here, $\unicode[STIX]{x1D706}(Fr_{o})$ increases from 0.9 to 1.1 as $Fr_{o}$ increases from 0.1 to 3.7, while the Froude number at the head of the flow has a value of $1.1\pm 0.05$.

scholarly journals Mixing in axisymmetric gravity currents

2015 ◽  
Vol 782 ◽  
Author(s):  
Peeradon Samasiri ◽  
Andrew W. Woods
Keyword(s):  
Light Attenuation ◽  
Gravity Current ◽  
Finite Depth ◽  
Aqueous Salt Solution ◽  
Vertical Shear ◽  
Ambient Fluid ◽  
Averaged Equations ◽  
Self Similar Solution ◽  
Diverging Channel ◽  
High Reynolds

We present new experiments to measure the rate of entrainment of ambient fluid into a high Reynolds number, axisymmetric, turbulent gravity current. The current is produced by the rapid release of a finite volume of aqueous salt solution from a lock of length $r_{o}$ into a diverging channel, $r>0$, of angle $9.5^{\circ }$, filled with a finite depth, $H$, of fresh water. Using light attenuation we measure the evolving density of the flow, and using dye studies we illustrate the process of mixing between the current and ambient fluid. After an initial adjustment, a circulation develops in the head of the flow: current fluid reaches the nose of the flow, rises up and moves backwards relative to the nose. We find that, owing to the mixing, the volume of the current increases as $V\sim 0.2r_{n}^{7/4}r_{o}^{1/4}H$ while the maximum depth of the head decreases as $h_{n}\sim 0.5H(r_{o}/r_{n})^{1/4}$, where $r_{n}$ is the location of the front of the current. Combining these results, we estimate that the recirculating current fluid mixes with a fraction $E=0.33\pm 0.09$ of the ambient fluid that is directly ahead of the current and displaced upwards by it. Some of the mixed fluid supplies the tail of the flow, while the remainder recirculates into the head, which becomes progressively more dilute. In accord with Huppert & Simpson (J. Fluid Mech., vol. 99, 1980, pp. 785–799), we find that the position of the front increases with time as $r_{n}\approx (1.28\pm 0.05)B^{1/4}t^{1/2}$, where $B$ is the total buoyancy of the flow. We also find that the maximum value of the vertical integral of the buoyancy $(\overline{g^{\prime }}h)_{n}$ decreases with the position of the nose according to the relation $(\overline{g^{\prime }}h)_{n}\approx (0.89\pm 0.12)Br_{n}^{-2}$, consistent with a Froude number $0.86\pm 0.07$. We compare our measurements with a new idealised self-similar solution of the depth-averaged equations that accounts for the mixing at the nose, the vertical shear in the velocity and the lateral stratification of the buoyancy within the current.

On the formation and propagation of nonlinear internal boluses across a shelf break

2007 ◽  
Vol 577 ◽  
pp. 137-159 ◽  
Author(s):  
SUBHAS K. VENAYAGAMOORTHY ◽  
OLIVER B. FRINGER
Keyword(s):  
High Resolution ◽  
Gravity Waves ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Gravity Currents ◽  
Interaction Process ◽  
Shelf Break ◽  
Ambient Fluid ◽  
Dense Fluid ◽  
Incident Waves

High-resolution two- and three-dimensional numerical simulations are performed of first-mode internal gravity waves interacting with a shelf break in a linearly stratified fluid. The interaction of nonlinear incident waves with the shelf break results in the formation of upslope-surging vortex cores of dense fluid (referred to here as internal boluses) that propagate onto the shelf. This paper primarily focuses on understanding the dynamics of the interaction process with particular emphasis on the formation, structure and propagation of internal boluses onshelf. A possible mechanism is identified for the excitation of vortex cores that are lifted over the shelf break, from where (from the simplest viewpoint) they essentially propagate as gravity currents into a linearly stratified ambient fluid.

A flow-front instability in viscous gravity currents

1998 ◽  
Vol 369 ◽  
pp. 1-21 ◽  
Author(s):  
DON SNYDER ◽  
STEPHEN TAIT
Keyword(s):  
Gravitational Instability ◽  
Gravity Current ◽  
High Viscosity ◽  
Gravity Currents ◽  
Ambient Fluid ◽  
Cell Width ◽  
Dense Fluid ◽  
Unstable Layer ◽  
Gravitational Mechanism ◽  
Hele Shaw Cell

We describe an instability that appears at the front of laminar gravity currents as they intrude into a viscous, miscible ambient fluid. The instability causes a current to segment into fingers aligned with its direction of flow. In the case of currents flowing along a rigid floor into a less dense fluid, the case of primary interest here, two mechanisms can produce this instability. The first is gravitational and arises because the nose of the gravity current is elevated above the floor and overrides a buoyantly unstable layer of ambient liquid. The second is a form of viscous fingering analogous to a Saffman–Taylor instability in a Hele-Shaw cell. Whereas the ambient fluid must be more viscous than the current in order for the latter instability to occur, the gravitational instability can occur even if the ambient fluid is less viscous, as long as it is viscous enough to elevate the nose of the current and trap a layer of ambient fluid. For the gravitational mechanism, which is most important when the current and ambient fluids have comparable viscosities, the wavelength when the instability first appears is proportional to a length scale constructed with the viscosity, the flux and the buoyancy. The Saffman–Taylor-type mechanism is most important when the ambient liquid is much more viscous than the current. We have carried out experiments with miscible fluids in a Hele-Shaw cell that show that, at the onset of instability, the ratio of the finger wavelength to the cell width is a constant approximately equal to 2. This result is explained by using the principle that the flow tends to minimize the dissipation associated with the finger perturbation. For the gravity currents with high viscosity ratios, the ratio of the wavelength to the current thickness is also a constant of about 2, apparently consistent with the same mechanism. But, further analysis of this instability mechanism is required in order to assess its role in wavelength selection for gravity currents.

Gravity induced vertical motion of dense fluids into saturated granular beds

2021 ◽  
Author(s):  
Rui M L Ferreira ◽  
Gabriel Solis ◽  
Claudia Adduce ◽  
Ana Margarida Ricardo
Keyword(s):  
Porous Layer ◽  
High Speed ◽  
Rectangular Cross Section ◽  
Gravity Current ◽  
Gravity Currents ◽  
Frame Rate ◽  
Ambient Fluid ◽  
Porous Bed ◽  
Loose Packing ◽  
Dense Fluid

<p>Gravity currents propagating over and within porous layers occurs in natural environments and in industrial processes. The particular modes by which the dense fluid flows into the porous layer is a subject that is not sufficiently understood. To overcome this research gap, we conducted laboratory experiments aimed at describing experimentally the dynamics of the drainage flow.</p><p>The experiments were conducted in a horizontal channel with a rectangular cross-section. The channel is 3.0 m long, 0.05 m wide. The porous bottom was composed of 5 cm and 10 cm layers of 3 mm borosilicate spheres – unimodal bed – and of a mixture of 3 mm (50% in weight) and 5 mm spheres (50%) – bi-modal bed. The porosity of the unimodal bed ranged between 0.60 and 0.64 (compatible with loose packing). The porosity of the bi-modal bed ranged between 0.61 and 0.65. All gravity currents were generated by releasing suddenly denser fluid locked by a thin vertical barrier placed at 0.2 m from the channel end. The dense fluid consists in a mixture of freshwater and salt (coloured with Rhodamine) while the ambient fluid is a solution of freshwater and ethanol. The density difference between the ambient fluid and the current, and the need to maintain the same refractive index, determine the amount of salt and alcohol added in each mixture. Here we report the findings of currents with a reduced gravity of 0.06 ms<sup>-2</sup>.</p><p>Each experiment was recorded by an high-speed camera with a frame-rate of 386 Hz and a resolution of 2320 x 1726 pxxpx. Measurements were based on light absorption techniques: a LED light panel 0.3 m high and 0.61 m long was used as back illumination. All images were calibrated to ascribe, pixel by pixel, a concentration value from a 8 bit gray level. Different calibrations were performed for the porous layer and for the surface current.</p><p>Results show that, in the slumping phase, the gravity current flows with velocities compatible with those over rough beds. As the current progresses further attenuation of momentum is noticed owing to mass loss to the porous bed.</p><p>The flow in the porous bed reveals plume instability akin to a Saffman-Taylor instability. The growth of the plumes seems independent from the initial fluid height in both types of porous beds. The wavelength and the growth rate of the plumes depends on the bed material. Plumes grow faster in the case of the bi-modal bed and the wavelength of the bi-modal bed is about 1.5 as that of the unimodal bed. It is hypothesised that the gravity-induced porous flow is best parameterized by a Péclet number defined as a ratio of dispersive (mechanical diffusion) and advective modes of transport. Smaller wavelengths and slower growths are attained for stronger dispersion, characterisitic of the unimodal bed. For bimodal beds, permeability is larger, and thus also advection. This causes the flow to concentrate in faster growing but farther apart plumes.</p><p> </p><p>This research was funded by national funds through Portuguese Foundation for Science and Technology (FCT) project PTDC/CTA-OHR/30561/2017 (WinTherface).</p>

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.

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.

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.

scholarly journals On the dynamics of starting plumes

2017 ◽  
Vol 833 ◽  
Author(s):  
N. Bhamidipati ◽  
Andrew W. Woods
Keyword(s):  
Laboratory Experiments ◽  
Added Mass ◽  
Rate Of Change ◽  
Small Scale ◽  
Maximum Height ◽  
Ambient Fluid ◽  
A Value ◽  
Proposed Model ◽  
The Difference ◽  
Reasonable Description

We explore the dynamics of starting plumes by analysis of a series of new small-scale laboratory experiments combined with a theoretical model for mass, momentum, and buoyancy conservation. We find that the head of the plume ascends with a speed which is approximately 0.6 times the characteristic speed of the fluid in the following steady plume, in accord with Turner (J. Fluid Mech., vol. 13 (03), 1962, pp. 356–368), and so the fluid released from the source eventually catches the head of the flow. On reaching the top of the plume it recirculates and mixes in the plume head. We estimate that approximately $0.61\pm 0.04$ of the total buoyancy released from the source accumulates in the plume head, with the remainder in the following steady plume. Using measurements of the volume of the head, we estimate that a fraction $0.16\pm 0.08$ of the volume of the head is entrained directly from the ambient, with the remainder of the fluid in the head being supplied by the following steady plume. These results imply that the buoyancy force exerted on the plume head plus the momentum flux supplied by the following plume exceeds the rate of change of momentum of the plume head even including the added mass of the plume head. We propose that the difference is associated with a drag force resulting from the displacement of ambient fluid around the plume head. Using our experimental data, we estimate that the drag coefficient $C_{d}$ has a value $4.2\pm 1.4$, with the range in values associated with the uncertainty in our estimate of entrainment of fluid directly into the plume head. As a test, the proposed model is shown to provide a reasonable description of a starting plume rising through a stratified environment in the region below the maximum height of rise of the associated steady plume, although, above this point, the shape of the plume head changes and the model breaks down.

scholarly journals Tyrosine requirement during the rapid catch-up growth phase of recovery from severe childhood undernutrition

2010 ◽  
Vol 104 (8) ◽  
pp. 1174-1180 ◽  
Author(s):  
Asha Badaloo ◽  
Jean W.-C. Hsu ◽  
Carolyn Taylor-Bryan ◽  
Marvin Reid ◽  
Terrence Forrester ◽  
...  
Keyword(s):  
Amino Acids ◽  
Growth Phase ◽  
Aromatic Amino Acids ◽  
Nutritional Rehabilitation ◽  
Two Phase ◽  
A Value ◽  
The Mean ◽  
Catch Up ◽  
Breakpoint Analysis ◽  
Childhood Undernutrition

The requirement for aromatic amino acids during the rapid catch-up in weight phase of recovery from severe childhood undernutrition (SCU) is not clearly established. As a first step, the present study aimed to estimate the tyrosine requirement of children with SCU during the catch-up growth phase of nutritional rehabilitation using a diet enriched in energy and proteins. Tyrosine requirement was calculated from the rate of excretion of 13CO2 (F 13CO2) during [13C]phenylalanine infusion in thirteen children with SCU, five females and eight males, at about 19 d after admission when the subjects were considered to have entered their rapid catch-up growth phase and were consuming 627·3 kJ and about 3·5 g protein/kg per d. Measurements of F 13CO2 during [13C]phenylalanine infusion were made on two separate days with a 1 d interval. Three measurements at tyrosine intakes of 48, 71 and 95 mg/kg per d were performed on experimental day 1 and measurements at tyrosine intakes of 148, 195 and 241 mg/kg per d were performed on experimental day 2. An estimate of the mean requirement was derived by breakpoint analysis with a two-phase linear regression cross-over model. The breakpoint, which represents an estimate of the mean tyrosine requirement, is a value of 99 mg/kg per d when the children were growing at about 15 g/kg per d. The result indicates that the mean requirement for tyrosine during the catch-up growth phase of SCU is about 99 mg/kg per d under similar conditions to the present study.

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