Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow

The analysis of two-layer exchange flow through contractions with a barotropic component treated by Armi & Farmer (1986) is extended to include exchange flows over sills and through a combination of a sill and contraction. It is shown that exchange over a sill is fundamentally different from exchange through a contraction. Control at the sill crest acts primarily through the deeper layer into which the sill projects and only indirectly controls the surface layer. This asymmetry in the control results in asymmetrical flows. The interface depth above the crest is not one half the total depth, as assumed in other studies by analogy with flow through contractions, but is somewhat deeper; the maximal exchange rate is less than for flow through a contraction of equal depth. When both a sill and a contraction are present, the contraction influences control at the sill crest only if it lies between the sill and the source of denser water. The response to barotropic flow is also asymmetrical: the transition to single-layer flow occurs at much lower speeds for a barotropic component in one direction than the other.Results of the analysis are applied to exchange flow through the Strait of Gibraltar, which includes both a sill and a contraction. It is shown that maximal exchange conditions apply throughout part of the tidal cycle, and observations illustrate several of the analytical predictions for barotropic flows, including the formation of fronts, single-layer flow, submaximal exchange and reverse flow.

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Two-Layer Rotating Exchange Flow between Two Deep Basins: Theory and Application to the Strait of Gibraltar

Journal of Physical Oceanography ◽

10.1175/jpo2775.1 ◽

2005 ◽

Vol 35 (9) ◽

pp. 1568-1592 ◽

Cited By ~ 10

Author(s):

M-L. E. Timmermans ◽

L. J. Pratt

Keyword(s):

Exchange Rate ◽

Space Shuttle ◽

Lower Layer ◽

Exchange Flow ◽

Boundary Current ◽

Strait Of Gibraltar ◽

Flow Through ◽

Upstream Flow ◽

Key Parameter

Abstract Rotating two-layer exchange flow over a sill in a strait separating two relatively deep and wide basins is analyzed. Upstream of the sill in the deep upstream basin, the infinitely deep dense lower layer is assumed to be inactive, while the relatively thin upper layer flowing away from the sill forms a detached boundary current in the upstream basin. This analysis emphasizes the importance of this upstream boundary current, incorporating its width as a key parameter in a formalism for deducing the volume exchange rate and discriminating between maximal and submaximal states. Hence, even for narrow straits in which rotation does not dominate the dynamics within the strait, the importance of rotation in the wide upstream basin can be exploited. It is shown that the maximal allowable exchange transport through straits wider than 1½ Rossby deformation radii increases as rotation increases, unlike for smaller rotations, where the exchange decreases as rotation increases. The theory is applied to the exchange flow through the Strait of Gibraltar. This application illustrates how images of the oceans taken from space showing the width of the upstream flow, in this case a space shuttle photograph, might be used to determine the exchange transport through a strait. Maximal exchange conditions in the Strait of Gibraltar are predicted to apply at the time the space shuttle photograph was taken.

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A lock exchange flow

Journal of Fluid Mechanics ◽

10.1017/s0022112070001544 ◽

1970 ◽

Vol 42 (4) ◽

pp. 671-687 ◽

Cited By ~ 34

Author(s):

I. R. Wood

Keyword(s):

Boundary Layers ◽

Single Layer ◽

Flow Regimes ◽

Major Elements ◽

The Other ◽

Exchange Flow ◽

Minimum Width ◽

Stationary Layer ◽

Virtual Point ◽

Point Of Intersection

In this paper the interchange flow between two reservoirs connected by a contraction and containing fluid of different densities is considered. The effect of the boundary layers on the floor and walls of the contraction on the depth of flow in the contraction is discussed for the case of single layer flowing from one reservoir to the other. Next the theory for a denser layer plunging under a stationary layer is developed. In this case there is a discontinuity at the point of intersection of the surfaces of the flowing and the stationary fluids and there are three possible flow régimes depending on whether this discontinuity occurs at, downstream of, or upstream of the contraction.Finally, the case where there is an interchange flow with fluid flowing from each reservoir into the other is introduced. This latter theory parallels that developed by Wood (1968) for the case of two layers flowing from one reservoir through a contraction into another reservoir and as in this case there are two points of control, one at the position of minimum width and one (the virtual point of control) away from this position of minimum width.Experiments are described for a single layer flowing through the contraction and the results of these are used to obtain an indication of the accuracy that could be expected from the experiments with the more complicated exchange flow. The experiments with the exchange flow verified the major elements of the theory.

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Combined Natural Convection and Forced Flow Through Small Openings in a Horizontal Partition, With Special Reference to Flows in Multicompartment Enclosures

Journal of Heat Transfer ◽

10.1115/1.3250814 ◽

1989 ◽

Vol 111 (4) ◽

pp. 980-987 ◽

Cited By ~ 24

Author(s):

M. Epstein ◽

M. A. Kenton

Keyword(s):

Direct Application ◽

Forced Flow ◽

Theoretical Treatment ◽

Exchange Flow ◽

Exchange Flows ◽

Toxic Gases ◽

Buoyancy Driven Flows ◽

Single Opening ◽

Flow Through ◽

Horizontal Partition

Estimates of the magnitude of buoyancy-driven exchange flows through openings in partitions that separate compartments are needed to assess the movement of toxic gases and smoke through buildings. An experiment using water and brine as a substitute for a light gas moving in a dense gas was designed to measure combined forced and buoyancy-driven exchange flow through a single opening in a horizontal partition. No theoretical treatment exists for this configuration. The same apparatus was used to determine the magnitude of the forced flow required to purge the opening of the oppositely directed buoyant component (i.e., the “flooding” limit). Finally, combined forced and buoyancy-driven flows in a multicompartment enclosure were measured. It has been demonstrated that the combined forced and buoyancy-generated flows in the multicompartment structure can be predicted by a direct application of the results of the study of exchange flow through a single opening.

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Western Mediterranean sea-level rise: Changing exchange flow through the Strait of Gibraltar

Geophysical Research Letters ◽

10.1029/2000gl011653 ◽

2000 ◽

Vol 27 (18) ◽

pp. 2949-2952 ◽

Cited By ~ 34

Author(s):

Tetjana Ross ◽

Chris Garrett ◽

Pierre-Yves Le Traon

Keyword(s):

Sea Level Rise ◽

Mediterranean Sea ◽

Sea Level ◽

Western Mediterranean ◽

Exchange Flow ◽

Strait Of Gibraltar ◽

Western Mediterranean Sea ◽

Flow Through

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Enhancing the capture efficiency and homogeneity of single-layer flow-through trapping microfluidic devices using oblique hydrodynamic streams

Microfluidics and Nanofluidics ◽

10.1007/s10404-021-02492-1 ◽

2021 ◽

Vol 25 (11) ◽

Author(s):

O. Mesdjian ◽

N. Ruyssen ◽

M.-C. Jullien ◽

R. Allena ◽

J. Fattaccioli

Keyword(s):

Single Layer ◽

Microfluidic Devices ◽

Capture Efficiency ◽

Flow Through ◽

Layer Flow

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Natural Convection of Air through an Asymmetrically Heated Vertical Channel with a Baffle

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.846.7 ◽

2016 ◽

Vol 846 ◽

pp. 7-11

Author(s):

Cheng Wang Lei ◽

Tuo Tian Wang

Keyword(s):

Natural Convection ◽

Reverse Flow ◽

Air Flow ◽

Vertical Channel ◽

The Other ◽

Heated Wall ◽

Two Dimensional ◽

Flow Through ◽

Vertical Ventilation ◽

Ventilation Performance

The buoyancy-induced air flow through a two-dimensional vertical ventilation channel is calculated. One of the channel walls is heated uniformly, and the other wall is adiabatic. A thin baffle is placed on the heated wall to manipulate the air flow through the channel. Numerical results are obtained for baffles of different lengths and placed at various heights along the heated wall. It is found that the baffle is effective in weakening a reverse flow at the exit of the channel, and significant enhancement of ventilation performance may be achieved with the presence of the baffle.

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Unsteady two-layer hydraulic exchange flows with friction

Journal of Fluid Mechanics ◽

10.1017/s0022112009007459 ◽

2009 ◽

Vol 633 ◽

pp. 99-114 ◽

Cited By ~ 5

Author(s):

S. S. LI ◽

G. A. LAWRENCE

Keyword(s):

Exchange Rate ◽

Flow Rate ◽

Laboratory Experiments ◽

Time Dependent ◽

Forced Flow ◽

Exchange Flow ◽

Interface Position ◽

Exchange Flows ◽

Sea Straits ◽

Flow Through

Two-layer exchange flow through a contraction with both friction and barotropic forcing is modelled in terms of three parameters reflecting the friction and the strength and period of the barotropic forcing. In the appropriate limits, the results for steady flow with and without friction, and inviscid barotropically forced flow are recovered. The predicted time-dependent interface position compares well with laboratory experiments, improving on the inviscid formulation. The concurrent effects of friction and barotropic forcing on average exchange flow rate are determined. When friction is weak barotropic forcing increases the exchange rate. However, when friction is high, tidal forcing can result in a reduced exchange rate, a phenomena that we call tidal inhibition. When friction is weak maximal exchange occurs throughout the tidal cycle, but as friction is increased submaximal flow develops for longer and longer periods. As friction is increased even further the flow becomes hydraulically uncontrolled. The parameter range for major sea straits includes tidally enhanced and tidally inhibited flows, as well as maximal, submaximal and uncontrolled flows.

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A unified description of two-layer flow over topography

Journal of Fluid Mechanics ◽

10.1017/s0022112084001798 ◽

1984 ◽

Vol 146 ◽

pp. 127-167 ◽

Cited By ~ 105

Author(s):

Peter G. Baines

Keyword(s):

Multiple Equilibria ◽

Single Layer ◽

Nonlinear Effects ◽

Wave Dispersion ◽

Interfacial Stress ◽

The Other ◽

Two Dimensional ◽

Wide Range ◽

Flow Over Topography ◽

Layer Flow

Observations of the flow of a two-layer fluid resulting from the motion of a towed streamlined two-dimensional obstacle are described in some detail. The experiments were designed to further our understanding of the factors governing the nature and magnitude of upstream disturbances in the general flow of stratified fluid over two-dimensional topography, and predictions for arbitrary two-dimensional flows are made from the results of these experiments. In particular, the relationship between uniformly stratified flow and single-layer flow over topography is suggested. Most of the observed features of interest in these experiments are nonlinear in character. Relatively complete descriptions of the observed flows are presented over a wide range of parameter values, and the phenomena observed include upstream undular and turbulent bores, bores with zero energy loss, ‘rarefactions’ (in which the interface height changes monotonically over a transition region of continuously increasing length), and downstream hydraulic drops and jumps. Their properties are shown to be broadly consistent with predictions from a two-layer hydrostatic model based on continuity and momentum considerations, which employs jump criteria and rarefaction equations where appropriate. Bores occur because of nonlinear steepening when the layer containing the obstacle is thinner than the other, and rarefactions occur when this layer thickness is comparable with or greater than that of the other layer. The speed and amplitude of the upstream bores are governed by nonlinear effects, but their character is determined by a balance between nonlinear steepening, wave dispersion and interfacial friction when the bore is non-turbulent.Experimental evidence is presented for two types of hysteresis or ‘multiple equilibria’ - situations where two different flow states may exist for the same external steady conditions. In the first of these hysteresis types, the upstream flow may be supercritical or consist of an upstream bore state. It is analogous to the type anticipated for single-layer flow by Baines & Davies (1980) and described numerically by Pratt (1983), but it is only found experimentally for part of the expected parameter range, apparently because of interfacial stress effects. The second hysteresis type is new, and involves the presence or absence of a downstream hydraulic drop and following jump.

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