ALBERT

Description: When a gravity current meets an obstacle a proportion of the flow may continue over the obstacle while the rest is reflected back as a hydraulic jump. There are many examples of this type of flow, both in the natural and man-made environment (e.g. sea breezes meeting hills, dense gas and liquid releases meeting containment walls). Two-dimensional currents and obstacles, where the reflected jump is in the opposite direction to the incoming current, are examined by laboratory experiment and theoretical analysis. The investigation concentrates on the case of no net flow, so that there is a return flow in the (finite depth) upper layer. The theoretical analysis is based on shallow-water theory. Both a rigid lid and a free surface condition for the top of the upper layer are considered. The flow may be divided into several regions: the inflow conditions, the region around the hydraulic jump, the flow at the obstacle and the flow downstream of the obstacle. Both theoretical and empirical inflow conditions are examined; the jump conditions are based on assuming that the energy dissipation is confined to the lower layer; and the flow over the obstacle is described by hydraulic control theory. The predictions for the proportion of the flow that continues over the obstacle, the speed of the reflected jump and the depth of the reflected flow are compared with the laboratory experiments, and give reasonable agreement. A shallower upper layer (which must result in a faster return velocity in the upper layer) is found to have a significant effect, both on the initial incoming gravity current and on the proportion of the flow that continues over the obstacle. © 1995, Cambridge University Press. All rights reserved.

Description: Flows between ocean basins are often controlled by narrow channels and shallow sills. A multi-layer hydraulic control theory is developed for exchange flow through such constrictions. The theory is based on the inviscid shallow-water equations and extends the functional approach introduced by Gill (1977) and developed by Dalziel (1991). The flows considered are those in rectangular-cross-section channels connecting two large reservoirs, with a single constriction (sill and/or narrows). The exchange flow depends on the stratification in the two reservoirs, represented as a finite number of immiscible layers of (different) uniform density. For most cases the flow is 'controlled' at the constriction and often at other points along the channel (virtual controls) too. As with one- and two-layer hydraulics, controls are locations at which the flow passes from one solution branch to another, and at which (at least) one internal wave mode is stationary. The theory is applied to three-layer flows, which have two internal wave modes, predicting interface heights and layer fluxes from the given reservoir conditions. The theoretical results for three-layer flows are compared to a comprehensive set of laboratory experiments and found to give good agreement. The laboratory experiments also show other features of the flow, such as the formation of waves on the interfaces. The implications of the results for oceanographic flows and ocean modelling are discussed.

Description: A comprehensive energy loss theory for gravity currents in rotating rectangular channels is presented. The model is an extension of the non-rotating energy loss theory of Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) and the steady-state dissipationless theory of rotating gravity currents of Hacker (PhD thesis, 1996). The theory assumes the fluid is inviscid, there is no shear within the current, and the Boussinesq approximation is made. Dissipation is introduced using a simple method. A head loss term is introduced into the Bernoulli equation and it is assumed that the energy loss is uniform across the stream. Conservation of momentum, volume flux and potential vorticity between upstream and downstream locations is then considered. By allowing for energy dissipation, results are obtained for channels of arbitrary depth and width (relative to the current). The results match those from earlier workers in the two limits of (i) zero rotation (but including dissipation) and (ii) zero dissipation (but including rotation). Three types of flow are identified as the effect of rotation increases, characterized in terms of the location of the outcropping interface between the gravity current and the ambient fluid on the channel boundaries. The parameters for transitions between these cases are quantified, as is the detailed behaviour of the flow in all cases. In particular, the speed of the current can be predicted for any given channel depth and width. As the channel depth increases, the predicted Froude number tends to √2, as for non-rotating flows. © 2005 Cambridge University Press.

Description: This paper is a description of an experimental study of round, turbulent jets and plumes, investigating the effects of buoyancy on the fractal structure. The jets and plumes are formed by injecting fluid from a small source, with diameter, d, of 0.508 mm, into a stationary body of water contained in a tall tank of dimensions 1.75 m high by 0.6 m by 0.6 m. For both jets and plumes the Reynolds number at the source was in the range 800 to 1800, and the flow was observed in the far field at distances 250d to 550d. In the case of the plumes momentum still dominated near the source so that the flow was fully turbulent before buoyancy forces had a significant effect. The source fluid was dyed with fluorescein, and the flow was illuminated by a thick’ sheet of light (thick in the sense of many Kolmogorov scales) effectively giving a projection rather than a true two-dimensional slice. The fractal dimensions of contours of concentration on this projection were measured, with care taken to normalize with respect to the local intensity and lengthscales. There were no significant differences in the results for jets and plumes, so the smaller scales of motion seem unaffected by the presence of buoyancy forces. The fractal dimension was found to be a function of threshold intensity, with an apparent minimum of 1.23. This may be an artefact of the noise level, however, and an estimated value for the zero-intensity threshold of 1.16 may be important, though the use of a single value for the fractal dimension is questionable. The implications of the results for measurements where no account has been taken of local scales is discussed. © 1993, Cambridge University Press

Description: An extension to the energy-conserving theory of gravity currents in rectangular rotating channels is presented, in which an upstream potential vorticity boundary condition in the current is applied. It is assumed that the fluid is inviscid; that the Boussinesq approximation applies; that the fundamental properties of momentum, energy, volume flux and potential vorticity are conserved between upstream and downstream locations; and that the flow is dissipationless. The upstream potential vorticity in the current is set through the introduction of a new parameter δ, that defines the ratio of the reference depth of the current to the ambient fluid. Flow types are established as a function δ and the rotation rate, and a fourth flow geometry is identified in addition to the three previously identified for rotating gravity currents. Detailed solutions are obtained for three cases δ = 0.5, 1.0 and 1.5, where δ 〈 1 is relevant to currents originating from a shallow source and δ 〉 1 to currents where the source region is deeper than the downstream depth, for example where a deep ocean flow encounters a plateau. The governing equations and solutions for each case are derived, quantifying the flow in terms of the depth, width and front speed. Cross-stream velocity profiles are provided for both the ambient fluid and the current. These predict the evolution of a complex circulation within the current as the rotation rate is varied. The ambient fluid exhibits similar trends to those predicted by the energy-conserving theory, with the Froude number tending to √2 at the right-hand wall at high rotation rates. The introduction of the potential vorticity boundary condition into the energy-conserving theory does not appear to have a substantial effect on the main flow parameters (such as current speed and width); however it does provide an insight into the complex dynamics of the flow within the current. © 2005 Cambridge University Press.

Description: This paper describes the fluid mechanics of the natural ventilation of a space connected to a large body of stationary ambient fluid. The flows are driven by buoyancy differences between the interior and exterior fluids. Connections with the ambient fluid are high level and low level openings. Two main forms of ventilation are identified mixing ventilation and displacement ventilation. Mixing ventilation occurs when the incoming ambient fluid mixes with the fluid within the space, as is the case if dense fluid enters through a high level inlet. In this case vertical stratification is weak. Displacement ventilation occurs when dense fluid enters at low levels and displaces the lighter fluid within the space out through high level openings. A strong stable stratification develops in this case, and there is little mixing between the incoming fluid and that in the interior. Both of these modes of ventilation are studied theoretically and the results are compared with laboratory experiments. Transient draining flows which occur when a space initially contains fluid of a density different from the ambient are examined. The presence of internal sources of buoyancy allows steady states to be established, and the effects of point, line and vertically distributed sources are studied. These steady states are extensions of filling box models, with the addition of continuous exchange of fluid with the environment outside the space. A major result of this work is that the form of the stratification within the space depends on the entrainment caused by the convective elements (plumes) produced by the buoyancy sourcesfbut is independent of the strength of the sources. The strength of the stratification and the magnitudes of the velocities do, however, depend on the source strength. The effects of opening size(s) and configurations are determined, and criteria for producing a particular stratification within the space are established. Applications of this work to the ventilation of buildings are presented. © 1990, Cambridge University Press. All rights reserved.

Description: A model for steady flow in a ventilated space containing a heat source is developed, taking account of the main heat transfers at the upper and lower boundaries. The space has an opening at low level, allowing cool ambient air to enter the space, and an opening near the ceiling, allowing warm air to leave the space. The flow is driven by the temperature contrast between the air inside and outside the space (natural ventilation). Conductive heat transfer through the ceiling and radiant heat transfer from the ceiling to the floor are incorporated into the model, to investigate how these heat transports affect the flow and temperature distribution within the space. In the steady state, a layer of warm air occupies the upper part of the space, with the lower part of the space filled with cooler air (although this is warmer than the ambient air when the radiant transfer from ceiling to floor is included). Suitable scales are derived for the heat transfers, so that their relative importance can be characterized. Explicit relationships are found between the height of the interface, the opening area and the relative size of the heat transfers. Increasing heat conduction leads to a lowering of the interface height, while the inclusion of the radiant transfer tends to increase the interface height. Both of these effects are relatively small, but the effect on the temperatures of the layers is significant. Conductive heat transfer through the upper boundary leads to a significant lowering of the temperature in the space as a proportion of the injected heat flux is taken out of the space by conduction rather than advection. Radiative transfer from the ceiling to floor results in the lower layer becoming warmer than the ambient air. The results of the model are compared with full-scale laboratory results and a more complex unsteady model, and are shown to give results that are much more accurate than models which ignore the heat transfers. © 2012 Cambridge University Press.

Description: Particle loading affects the dynamics of buoyant plumes, since the difference between particle and fluid densities is much greater than that in the fluid alone. In stratified environments, plume rise is density limited; after initial overshoot, the plume reaches a terminal level and spreads radially. Particles dropping from this horizontal intrusion may be re-entrained. This recycling of dense matter reduces plume buoyancy and intrusion height and, for sufficient load, can lead to plume collapse. Entrainment-based formulae yield a steady-state plume rise. We identify a new conserved quantity for such plumes. Integrating paths of particles dropping from the intrusion yields the fraction re-entrained. A simple mathematical model predicts from buoyancy ratio at source (negative particle buoyancy divided by positive fluid buoyancy) whether a particle-laden plume will collapse. Under this model, for small settling velocity, a particle-laden plume will not collapse if 〈CDATAP. Above this, collapse depends also on the amount of particle-free ambient fluid entrained in the overshoot region. For pure plumes, experimental evidence suggests that this is small. For forced plumes, more substantial overshoot and entrainment is shown to increase the critical ratio. An extension, based on successive recycling, estimates time to collapse. To investigate further we develop a simple computational model, coupling a 'top-hat' plume model, an analytical formula for radially decaying concentrations in the intrusion and an axisymmetric finite-volume solution for time-dependent settling and entrainment. The model can predict the impact of particle load on final rise, as well as the occurrence and time scales of plume collapse. © 2019 Cambridge University Press This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited..