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Visible plumes above wet cooling towers are of great concern due to the associated aesthetic and environmental impacts. The parallel path wet/dry cooling tower is one of the most commonly used approaches for plume abatement, however, the associated capital cost is usually high due to the addition of the dry coils. Recently, passive technologies, which make use of free solar energy or the latent heat of the hot, moist air rising through the cooling tower fill, have been proposed to minimize or abate the visible plume and/or conserve water. In this review, we contrast established versus novel technologies and give a perspective on the relative merits and demerits of each. Of course, no assessment of the severity of a visible plume can be made without first understanding its atmospheric trajectory. To this end, numerous attempts, being either theoretical or numerical or experimental, have been proposed to predict plume behavior in atmospheres that are either uniform versus density-stratified or still versus windy (whether highly-turbulent or not). Problems of particular interests are plume rise/deflection, condensation and drift deposition, the latter consideration being a concern of public health due to the possible transport and spread of Legionella bacteria.

We report upon a series of laboratory experiments and complementary (two-dimensional) direct numerical simulations that explore the lock release of a fixed volume of dense fluid into a two-layer density-stratified ambient. By initial condition, the lock release experiments/simulations fall into one of two categories: full-depth and partial-depth. Our particular focus is on the “tailwaters” limiting case where the lock fluid density matches that of the lower ambient layer. In either case the front speed of the advancing lock fluid is less than that of the excited interfacial disturbances. Consequently, the internal front propagates at constant speed for less time than, say, the downstream-propagating interfacial disturbance, which we term the dense gravity current (or GC1). Complementing GC1, there is an analogue flow of light ambient fluid into the lock, and this we refer to as the light gravity current (or GC2). Measured speeds for GC1, GC2 and the internal front are compared against analogue predictions from shallow water (SW) theory. From this comparison, positive agreement is noted in the case of GC1 and the internal front. Meanwhile, the speed of GC2 post reflection from the lock end wall is under-predicted by 10–20% depending on the initial depth of dense fluid within the lock. This under-prediction is believed to result from a mismatch between where the SW prediction is made (immediately following GC2 reflection from the back of the lock) and where the experimental GC2 speed is measured, usually 0.5–2.5 lock lengths downstream by which point the GC2 height has decreased due to dispersion. Although the GC1 height also undergoes a dispersive decrease in height, generally more positive agreement is noted when comparing measured and predicted gravity current heights. The distance travelled by the internal front prior to being arrested by the reflected GC2 agrees robustly with SW theory. Laboratory and DNS experiments exhibiting a thick ambient interface are also reported upon. We observe that the speed of the internal front and the downstream distance it travels at a constant speed increase with interface thickness. The insights gained from this investigation can be applied to realistic environmental flows such as nocturnal thunderstorm outflows.

International audience; Through laboratory experiments and numerical simulations, we examine the evolution of buoyant plumes as they are influenced by background rotation in a uniform density ambient fluid. The source Rossby number is sufficiently large that rotation does not directly affect the plume at early times. However, on a time scale of the order of half a rotation period, the plume becomes deflected from the vertical axis. For some experiments and simulations, the deflection persists and the flow precesses about the vertical axis. In other cases, shortly after being deflected, the plume laminarizes near the source to form a near-vertical columnar vortex, which we refer to as a ‘tornado’. Tornado formation occurs in some experiments and not in others even if the source and background rotation parameters are identical. However, their formation is more likely if the plumes are ‘lazy’. Simulations reveal that this is a consequence of the competing dynamics that occurs on comparable time scales. As a consequence of entrainment, vertical vorticity builds up within the plume reducing the Rossby number and suppressing vertical motion at distances progressively closer to the source. Meanwhile, the swirl (the ratio of the azimuthal to vertical flow) around the vicinity of the source increases, which tends to suppress three-dimensional turbulence in the near-source flow. Although the former process ultimately acts to deflect the plume off axis, in some instances, the swirl around the source succeeds in laminarizing the flow, resulting in tornado formation.

We investigate experimentally the outflow that occurs when a plume of dense fluid strikes a sloping permeability jump in a saturated two-layered porous medium of finite extent. Contact of the plume with the jump results in a pair of leaky (primary) gravity currents that propagate up- and downdip. Previous studies have considered a thin or thick lower layer; here, we identify the non-trivial dynamics that arises for the intermediate thickness case. For instance, the primary gravity currents become arrested when the volume supplied by the plume matches that lost by basal draining. However, fluid draining into the lower layer will eventually contact the bottom boundary leading to the formation of secondary gravity currents. As these secondary gravity currents propagate left and right, they ‘tug’ upon the primary gravity currents causing remobilization. Of course, the motion of the primary and secondary gravity currents must eventually become impeded by the sidewall boundaries leading, thereafter, to layer filling. We categorize the overall filling process as either simultaneous (upper and lower layers fill concurrently) or sequential (lower layer fills first). Factors influencing the filling mode include the permeability jump angle and the plume source conditions/location. Owing to the asymmetric manner in which the upper layer fills, the plume, originally vertical, must become deflected. We categorize this deflection and identify scenarios where, somewhat counterintuitively, the plume bends towards the lower (lower permeability) layer. The significance of our measurements relative to real geophysical flows is highlighted with particular attention paid to geological sequestration and storage.

Laboratory experiments are conducted to examine a descending plume in a rotating two-layer stratified ambient fluid such that the plume at the interface has moderate to large Rossby number. While the source fluid is more dense than the lower layer, the experiments are designed so that the mean density of the plume fluid impinging upon the interface is less than the lower layer density, as represented by a buoyancy parameter, $$\varLambda $$, being less than unity. In such cases, the discharged plume fluid spreads radially at the interface in the form of an intrusive gravity current at early times. At later times, this intrusion evolves to form an anticyclonic lens due to the influence of the Coriolis force. The measured radial position of the intrusion front, R(t), follows different power law relationships at early and late times during the spread of the intrusion: at early times when rotation does not play a significant role the power law exponent lies between 0.5 and 1.1; at late times when the intrusion acts as a rotationally influenced expanding lens the power law exponent ranges between 0.15 and 0.5, with generally smaller values for larger $$\varLambda $$. The plume fluid reaching the interface progressively increases in density due to re-entraining relatively dense fluid as the plume descends within the thickening lens. Consequently, the plume eventually penetrates through the interface and descends to the bottom of the tank. Faster rotation makes the lens thicker and hence increases the volume of the re-entrained lens-fluid, which decreases the time for the onset of penetration. The penetration time normalized by the rotation rate is found to hold a simple power law relationship with $$\varLambda $$.

We propose theoretical models to describe Boussinesq and non-Boussinesq plume rise in a corner of arbitrary angle. The Boussinesq plume theory is applied to the case of a naturally ventilated room and agrees well with previous experimental/theoretical results. The non-Boussinesq plume theory compares satisfactorily with previous measurements of fire plume mass flux.

Theoretical models are proposed to describe the merging of dual rows of plumes in a quiescent ambient and a single row of plumes in a crosswind. The theory for the dual row case is applied to model the reduced entrainment rate in the case of plumes emitted from back-to-back cooling towers. The theory of plumes in a crosswind predicts satisfactory agreement with the previous water flume measurements in terms of the plume trajectories.

The migration of dense fluid through a saturated, layered porous medium leads to two end-member examples of buoyancy-driven flow, namely plumes and gravity currents. Herein we develop an integrated theoretical model to study this scenario for the special case where the boundary between the permeable layers, in a two-layered porous medium, is inclined at an angle to the horizontal. Far from being a routine detail, the inclination of the permeability jump leads to a symmetry-breaking: up- and downdip flows have different volume fluxes and travel different distances, possibly substantially different distances, before becoming arrested at the point where plume inflow balances basal draining. Our model predicts these associated run-out lengths and the transient approach thereto. Predictions are validated with measurements from similitude laboratory experiments, in which the upper and lower layers are comprised of glass beads of different diameters. Experiments are conducted for a range of inclination angles and also a range of plume source conditions. The experimental data suggest a complicated structure for the gravity currents, whose boundaries are blurred by dispersion in a manner not captured by our (sharp interface) model. This observation has particular significance in predicting the lateral spread of contaminated fluid through real geological formations, particularly in instances where for example groundwater contamination is of particular concern.

The traditional approach of cooling tower plume abatement is supposed to result in an unsaturated, well-mixed plume with a “top-hat” structure in the radial structure, but this is an idealization that is rarely achieved in practice. Meanwhile, previous analyses have shown that there may be an advantage in specifically separating the wet and dry air streams whereby the corresponding plume is of the coaxial variety with dry air enveloping (and thereby shielding) an inner core of wet air. Given that a detailed understanding of the evolution of coaxial plumes is presently lacking, we derive an analytical model of coaxial plumes in the atmosphere, which includes the effects of possible condensation. Of particular concern is to properly parameterize the entrainment (by turbulent engulfment) of fluid from the inner to the outer plume and vice versa. We also present and discuss the two different body force formulations that apply in describing the dynamics of the inner plume. Based on the resulting model predictions, we introduce a so-called resistance factor, which is defined as the ratio of the average non-dimensional velocity to the average relative humidity. In the context of visible plume abatement, the resistance factor so defined specifies the likelihood of fog formation and/or a recirculation of moist air into the plenum chamber. On the basis of this analysis, we can identify the region of the operating-environmental condition parameter space where a coaxial plume might offer advantages over its uniform counterpart.

The dynamics of a fully nonlinear, tree-structured resonator and its response to a broadband forcing of the branches is examined. It is shown that the broadband forcing yields a transfer of energy between the parts of the spectrum so that the spectrum becomes progressively more narrow-band for each level of the tree-like structure in the direction of the stem. We show that this behavior is in contrast to the response of a linear oscillator, which simply filters out the harmonics away from the resonance. We term such behavior “regularization” and examine its significance for two- and three-dimensional motion using a Lagrangian framework. Key to our analysis is to investigate the dependence of the spectrum of motion, and its narrowing, on the parameters of the tree-like structure, for instance the lengths of different branches. Model predictions are obtained for idealized wind forcing characterized by an airflow that is interrupted at random time intervals. Our numerically-derived results are then compared against the data collected from select analogue laboratory experiments, which confirm the robust nature of the vibration regularization.

Boussinesq, turbulent plume flows have been successfully described by the well-established model of Morton et al (1956), however, the more complicated case of a coaxial plume consisting of an inner circular plume and an outer annular plume is more challenging to describe theoretically. The difficulties in question arise because of the turbulent exchange of mass, momentum and buoyancy between the inner plume, the outer plume and the ambient. The present study explores the possibility of using a double plume model for coaxial plumes. Model predictions are compared against analogue experimental measurements where, in the latter case, we employ a planar laser-induced fluorescence technique for purposes of visualizing the flow and for measuring concentrations of coaxial plumes. The plumes in question issued from a specially-designed coaxial nozzle, are of moderate Reynolds number (approximately 500) and are of intermediate flux-balance parameter indicating a plume that is either slightly lazy or slightly forced. A whole-field comparison of the scalar concentration between theory and experiment is conducted to obtain the optimal entrainment coefficients. The advantage and limitation of using coaxial plumes to abate the visible plume discharged by cooling towers is discussed.

We report upon experimental and analytical investigations of filling box flows in non-uniform porous media characterized by a sudden change in permeability. The porous medium consists of two layers separated by a horizontal permeability jump and is initially filled with light ambient fluid. A line source located at the top of the upper layer supplies dense contaminated fluid that falls toward the bottom of the domain. Two configurations are studied, i.e., a low-permeability layer on top of a high-permeability layer and vice versa. In the former scenario, the flow dynamics are qualitatively similar to the case of a uniform porous medium. Thus, the analytical formulation of Sahu and Flynn (J Fluid Mech 782:455–478, 2015) can be adopted to compute the parameters of interest, e.g., the plume volume flux. In the latter scenario, the flow dynamics are significantly different from those of the uniform porous medium case; after reaching the permeability jump, some fraction of the dense plume propagates horizontally as a pair of oppositely directed interfacial gravity currents. Meanwhile, the remaining fraction of the plume flows downward into the lower layer where it accumulates along the bottom boundary in the form of a deepening layer of discharged plume fluid. Depending on the permeability ratio of the upper and lower layers and the source conditions, the gravity currents may become temporarily arrested after traveling some finite horizontal length. An analytical prediction for this so-called run-out length is derived, motivated, in part, by the immiscible analysis of Goda and Sato (J Fluid Mech 673:60–79, 2011). Finally, a prediction of the filling box time, consisting of the time required to fill the control volume up to the point of contaminated fluid overflow, is made. These predictions are compared with analog experimental measurements. Generally positive agreement is found when the higher-permeability layer is located below the lower-permeability layer. In the opposite circumstance, the agreement is conditional. If the run-out length of the gravity current is less than the horizontal dimensions of the control volume (or tank in case of the experiments), the agreement is good. By contrast, when the run-out length is large, comparatively poor agreement may be realized: In spite of the higher density of the contaminated fluid, it may occupy the entirety of the upper layer before filling the lower layer.

We experimentally investigate the behaviour of a line-source plume falling through a finite two-layer stratified ambient where the depth of the upper ambient layer increases in time. Laboratory observations suggest one of two possible flow regimes depending on the value of $\unicode[STIX]{x1D706}$, which represents the relative loss of buoyancy experienced by the plume upon crossing the ambient interface. When $\unicode[STIX]{x1D706}>1$, a classical filling-box-type flow is realized and plume fluid always reaches the bottom boundary. By contrast, when $\unicode[STIX]{x1D706}, we observe a transition by which an increasing fraction of plume fluid discharges along the interface. The approximate start time, $t_{v}$, and end time, $t_{t}$, of the transition process are well determined by $\unicode[STIX]{x1D706}$. After transition, the ambient density evolves to form a three-layer fluid with an intermediate layer that grows in time. Measured densities of the intermediate layer in experiments with $\unicode[STIX]{x1D706} are well predicted using plume theory. We further characterize the horizontal speed of the intrusion that forms along the ambient interface, the mass of solute present in the intermediate layer at time $t_{t}$ and the rate of descent of the intrusion level for $t>t_{t}$. The significance of our findings is discussed in the context of the ventilation of natural and hybrid ventilated buildings and of effluent discharge through marine outfall diffusers.

We examine the transient evolution of a negatively buoyant, laminar plume in an emptying filling box containing a uniform porous medium. In the long time limit, , the box is partitioned into two uniform layers of different densities. However, the approach towards steady state is characterized by a lower contaminated layer that is continuously stratified. The presence of this continuous stratification poses non-trivial analytical challenges; we nonetheless demonstrate that it is possible to derive meaningful bounds on the range of possible solutions, particularly in the limit of large , where represents the ratio of the draining to filling time scales. The validity of our approach is confirmed by drawing comparisons against the free turbulent plume case where, unlike with porous media plumes, an analytical solution that accounts for the time-variable continuous stratification of the lower layer is available (Baines & Turner, J. Fluid Mech., vol. 37, 1969, pp. 51–80; Germeles, J. Fluid Mech., vol. 71, 1975, pp. 601–623). A separate component of our study considers time-variable forcing where the laminar plume source strength changes abruptly with time. When the source is turned on and off with a half-period, , the depth and reduced gravity of the contaminated layer oscillate between two extrema after the first few cycles. Different behaviour is seen when the source is merely turned up or down. For instance, a change of the source reduced gravity leads to a permanent change of interface depth, which is a qualitative point of difference from the free turbulent plume case.

The shape of the liquid-vapor interface along the length of the adiabatic section of a heat pipe - a passive heat transfer device that relies on capillary pumping - is investigated to identify the mechanisms behind both performance enhancement techniques as well as operational failure. In formulating the associated mathematical model, the liquid flow within the (screen type) wick is described using Darcy’s law while Poiseuille’s equation is applied for the vapor phase. The liquid and vapor phases are coupled together using the Young-Laplace equation with additional closure provided by select thermodynamic relations e.g. to relate the temperature and pressure changes experienced by the vapor. Our model thereby predicts the shape of the liquid-vapor interface and its deflection owing to the variations in the heat load, operating temperature and the wick-surface characteristics. Together, these details can prescribe the parameter space over which the liquid-vapor interface remains mechanically-stable meaning that the heat pipe can function effectively. The possibility of employing a wick with non-uniform wetting characteristics is also explored with comparisons drawn against the uniform wettability case. The comparison in question reveals some of the benefits of the former approach. For instance, a wick exhibiting a contact angle that varies as a function of the axial coordinate allows for better control of (i) the depth to which the interface is recessed within the wires comprising the wick, and, therefore (ii) the entrainment of liquid droplets into the counter-flowing vapor stream. As such, the space of acceptable operating parameters can be suitably expanded.

We present an analytical solution for buoyancy-driven “filling box” flows in axisymmetric porous media having closed bottom and side boundaries. The flow consists first and foremost of a descending, point source plume. When plume fluid reaches the (horizontal) bottom boundary, it begins to flow radially outward in the form of an axisymmetric gravity current. The leading edge of the gravity current advances with time as $$t^{1/2}$$ until it reaches the vertical sidewalls. At this point, the flow is characterized by a vertically ascending “first front” that steadily advects towards the plume source. We assume the plume to be in a Darcy regime, i.e. $$\text{ Re }\mathop {\sim }\limits ^{\mathcal {O}(1)$$ , where Re and Pe are, respectively, the Reynolds and Peclet numbers, and derive a similarity solution for the plume by applying a boundary layer approximation. Formulas are therefore obtained for the vertical variation of the plume volume flux and area-averaged concentration. The former result shows important qualitative differences with the analogue equation derived in the limit $$\text{ Pe }

Core annular flow theory is used to model the parallel flow of fluids of different phases and has been used to describe drag reduction in the context of internal flows bounded by superhydrophobic surfaces. The work presented here is an extension of core annular flow theory to the study of the adiabatic section of heat pipes. Our aim is to develop a first-principles estimate of the conditions necessary to maximize the (counter) flow of liquid and vapor and, by extension, the axial flow of heat. The planar and axisymmetric geometries are examined as are heat pipes containing vs being devoid of a wick. In the wick vs no-wick cases, the peripheral return flow of liquid is, respectively, driven by capillarity and by gravity. Our model is used to predict velocity profiles and the flux-maximizing pressure gradient ratio (vapor-to-liquid). We further obtain estimates for the optimum thickness of the liquid layer. Note finally that when the liquid flow occurs via capillary pumping, there is a minimum surface tension below which the wick cannot supply a sufficient flow of liquid. We characterize this critical point in terms of the properties of the working fluid and of the wick.

Internal waves such as those produced by tidal sloshing over seafloor topography play an important role in the energy budget of the oceanic overturning circulation. Understanding their spatial and temporal structure, which depend on both the details of the forcing topography and the forcing frequency, is relevant in predicting how and where wave breaking and mixing may occur. Past work has largely focused on the case of a monochromatic wave field; however, the forcing tides may be composed of multiple frequency constituents. Here we present an approach by which the vertical mode structure of a polychromatic internal wave field may be computed from velocity timeseries data without any a priori knowledge of the details of the forcing topography. We consider wave fields in both uniform and vertically-varying stratification, and show using synthetic data that our approach is able to accurately reconstruct the vertical mode strengths. The sensitivity of our approach to noise and vertical resolution is also examined.

The dynamics, instability, and pattern formation of thermally triggered thin liquid films are investigated numerically under a long-wave limit approximation. To determine the mechanisms responsible for instability growth and pattern formation in confined heated nanofilms, acoustic phonon (AP) and thermocapillary (TC) models are examined using both linear and nonlinear analyses. Under uniform heating conditions, both AP and TC models predict the formation of raised columnar structures (pillars) and bicontinuous structures for very low and high filling ratios defined as the ratio of the initial film thickness to the plate separation distance, ${D}^{\ensuremath{-}1}$. A transition threshold is observed when $D\ensuremath{\approx}2.5$. However, the TC model predicts smaller features for larger $D$, whereas the opposite prediction applies for the AP model. Under spatially variable cooling conditions involving a patterned top plate, both TC and AP models exhibit similar predictions: pillars form under the top plate protrusions. When the heating is spatially variable, the lower plate is patterned; the AP model predicts pillar formation above ridges, whereas the TC model predicts pillar formation above the valleys.

We report upon a theoretical and experimental investigation of a porous medium ‘filling box’ flow by specifically examining the details of the laminar descending plume and its outflow in a control volume having an impermeable bottom boundary and sidewalls. The plume outflow initially comprises a pair of oppositely directed gravity currents. The gravity currents propagate horizontally until they reach the lateral sidewalls at $y=\pm L$. The flow then becomes of filling box type, with a vertically ascending ‘first front’ separating discharged plume fluid below from ambient fluid above. The flow details are described analytically by first deriving a new similarity solution for Darcy plumes with $\mathit{Pe}>O(1)$, where $\mathit{Pe}$ is the Péclet number. From the similarity solution so obtained, we then derive expressions for the plume volume flux and mean reduced gravity as functions of the vertical distance from the source. Regarding the plume outflow, a similarity solution adopted from Huppert & Woods (J. Fluid Mech., vol. 292, 1995, pp. 55–69) describes the height and front speed of the gravity currents, whereas a semi-implicit finite difference scheme is used to predict the first front elevation versus time and horizontal distance. As with high-Reynolds-number filling box flows, that studied here is an example of a coupled problem: the gravity current source conditions are prescribed by the plume volume flux and mean reduced gravity. Conversely, discharged plume fluid may be re-entrained into the plume, be it soon or long after reaching the bottom impermeable boundary. To corroborate our model predictions, analogue laboratory experiments are performed with fresh water and salt water as the working fluids. Our experiments consider as independent variables the porous medium bead diameter and the plume source volume flux and reduced gravity. Predictions for the gravity current front position and height compare favourably against analogue measured data. Good agreement is likewise noted when considering either the mean elevation or the profile of the first front. Results from this study may be adopted in modelling geological plumes. For example, our equations can be used to predict the time required for discharged plume fluid to return to the point of injection in the case of aquifers closed on the sides and below by impermeable boundaries.

We examine the buoyancy driven flow between two adjacent building zones separated by top and bottom vents with and without a source of buoyancy. In the absence of a source, by opening the vents, the pressure difference between the two zones drives the exchange flow. When there is an isolated source of buoyancy, two distinct flow regimes are defined: a ventilation-dominated regime in which the flow that is generated by the initial temperature difference, and a source-dominated regime in which the flow is principally governed by the source. Here, we restrict attention to the former case. Thus in each zone our analytical model assumes a horizontal interface that separates the upper layer, which is comprised of fluid having the initial density of the light zone, from the lower layer, comprised of fluid whose density is larger than that of the light zone. The transient evolution of such interfaces along with the stratification and buoyancy in each zone are predicted. Attention is focused on the influence of the effective area, source buoyancy flux and the time during which the source is switched on. Because the interface elevations change significantly at early times, a non-monotonic behavior is predicted for the evolution of stratification in the light zone. We also find that the terminal stratification and buoyancy in both zones are not impacted by the number of connecting vents; however, this number has a strong influence on how quickly steady state is achieved. Similitude laboratory experiments help to corroborate key predictions.

Numerous studies have considered the flow of a rectilinear, high Reynolds number, Boussinesq gravity current through a two-layer stratified ambient, however, far less is known concerning the analogue axisymmetric problem. Whereas in both instances there is the possibility of a dynamic coupling between the gravity current front and the waves that are excited by its forward advance, axisymmetric gravity currents entail the added complexity of a radially-diverging flow. Because a steady-state formulation cannot then be developed, we instead present a one-layer shallow water model that describes the flow evolution for various initial conditions and ambient stratifications. We also report upon $$>\!\!30$$ full- and partial-depth lock release laboratory experiments that span a densitometric range $$0 \le S < 0.8868$$ where $$S=(\rho _1-\rho _2)/(\rho _c-\rho _2)$$ in which $$\rho _c$$ , $$\rho _1$$ and $$\rho _2$$ denote, respectively, the densities of the gravity current and lower and upper ambient layers. Of principal interest is the initial front speed of the gravity current for which good agreement is observed between laboratory measurement and shallow water numerical simulation, despite the limiting assumptions of the latter. The horizontal distance over which the initial front speed is maintained may span several lock-lengths, however, this depends on whether or not the gravity current is substantially impacted by the interfacial wave(s). For example, when the lower ambient layer is moderate and $$S$$ is large, the transfer of momentum from the gravity current front to the wave may lead to a deceleration so severe that gravity current fluid is swept in the $$-r$$ direction. The connection between our analysis and problems of pollution dispersion is briefly outlined.

The dynamics of coaxial plumes that consist of an inner, humid plume and an outer, less humid plume has been studied analytically, however, only for the case of a stationary ambient. The present study extends the previous theoretical model by incorporating the effect of a windy ambient for both single and multiple cooling tower cell cases. Of particular concern is the choice of an appropriate entrainment assumption associated with wind shear and the modeling of entrainment between the inner and outer plumes. Two entrainment formulations are proposed regarding the entrainment from the inner to the outer plume. Meanwhile, two body force formulations for the inner plume are discussed. In terms of plume abatement, a visible plume length, defined on the basis of the predicted plume trajectory and relative humidity, is used to evaluate the severity of visible plumes under different operating and environmental conditions. By extension, and with fixed wind speed and cooling tower operating conditions, the parameter range of environmental conditions where fog is restricted to the inner plume is determined.

The application of turbulent plume theory in describing the dynamics of emptying filling boxes, control volumes connected to an infinite exterior through a series of openings along the upper and lower boundaries, has yielded novel strategies for the natural ventilation of buildings. Making the plume laminar and having it fall through a porous medium yields a problem of fundamental significance in its own right, insights from which may be applied, for example, in minimizing the contamination of drinking water by geologically sequestered $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathrm{CO}}_2$ or the chemicals leached from waste piles. After reviewing the theory appropriate to rectilinear and axisymmetric plumes in porous media, we demonstrate how the model equations may be adapted to the case of an emptying filling box. In this circumstance, the long-time solution consists of two ambient layers, each of which has a uniform density. The lower and upper layers comprise fluid that is respectively discharged by the plume and advected into the box through the upper opening. Our theory provides an estimate for both the height and thickness of the associated interface in terms of, for example, the source volume and buoyancy fluxes, the outlet area and permeability, and the depth-average solute dispersion coefficient, which is itself a function of the far-field horizontal flow speed. Complementary laboratory experiments are provided for the case of a line source plume and show very good agreement with model predictions. Our measurements also indicate that the permeability, $k_f$, of the lower opening (or fissure) decreases with the density of the fluid being discharged, a fact that has been overlooked in some previous studies, wherein $k_f$ is assumed to depend only on the fissure geometry.

When a common rectangular barrier between two zones with slightly different densities is partially removed mimicking the sudden opening of a door, a two-layer exchange flow develops and two qualitatively different, though highly coupled, kinds of flow are observed to either side of the barrier. In the zone that initially contained the dense fluid, a buoyant plume ascends resulting, over time, in a vertical density stratification through a filling-box process. Depending on the geometric parameters two scenarios are possible. Either the terminal position of the first front lies above the bottom of the barrier, or it lies below. Special attention is devoted to the latter case, which is favored for large doorway heights and when the zone that initially contains the dense fluid is comparatively small in volume. The associated complications are (i) the nature of the exchange flow changes once the downward-propagating first front surpasses the bottom of the barrier, and, (ii) the terminal stratification in the zone that initially contains the light fluid contains an intermediate layer in which the density varies continuously with height. We also present a model that presumes that both zones remain well-mixed. Similitude experiments help to identify the limitations of both categories of analytical models discussed above. The implications of our results on the design of buildings that exploit heat gains by attached solaria are discussed.

An oil spill on solid ice poses unique challenges to that of a spill on water or land. One challenge, which this study has elected to investigate, is the tendency of ice to crack and form channels. These channels are able to transport the oil away from the main mass of the spill making efficient cleanup difficult. Within the context of in situ burning, the oil channels may expedite the critical thickness of the oil spill being reached. A series of bench scale tests using a 100 cm long ice channel were conducted to study the effects of varying ice channel widths on the spread of an oil mixture, to mimic solid sea ice conditions that may be found in higher latitudes. Results suggest that spread rates of oil in ice channels approximately follows a viscous two-dimensional box model. The implication of these results on in situ burning of oil in icy conditions is discussed.

The potential for oil exploration on the Arctic Outer Continental Shelf warrants determination of an efficient method to clean up an oil spill. Traditional spill response equipment may not be practical in an Arctic environment due to the presence of ice, which would act to prevent proper deployment of equipment. Additionally, the areas proposed for oil exploration lack the infrastructure and support networks necessary to stage a response to a large oil spill due to their remoteness. These difficulties make it necessary to explore alternative means of oil spill cleanup. In situ burning is one method that may be particularly well-suited for Arctic and sub-Arctic environments due to the minimal amount of equipment required to achieve an efficient burn, i.e. high mass loss. The Arctic and sub-Arctic environments add an additional level of complexity by introducing a spill medium (ice) that is highly unstable at elevated temperatures. Our experiments sought to calculate the mass loss rates of oil mixtures to determine the efficiency with which they burn within ice channels of varying widths. An average mass loss rate of 0.06 g/s was recorded which translates to efficiencies of 10%. The dominant factor contributing to low mass loss rates was the melting of the channel walls which resulted in the critical thickness of the oil to be reached sooner. Based on the findings, in situ burning would not be a viable means of oil spill cleanup. Instead, it may be preferred to use in situ burning in conjunction with mechanical cleanup techniques.

Fundamental diagrams of vehicular traffic flow are generally multi-valued in the congested flow regime. We show that such set-valued fundamental diagrams can be constructed systematically from simple second order macroscopic traffic models, such as the classical Payne-Whitham model or the inhomogeneous Aw-Rascle-Zhang model. These second order models possess nonlinear traveling wave solutions, called jamitons, and the multi-valued parts in the fundamental diagram correspond precisely to jamiton-dominated solutions. This study shows that transitions from function-valued to set-valued parts in a fundamental diagram arise naturally in well-known second order models. As a particular consequence, these models intrinsically reproduce traffic phases.

Buoyancy driven flow between two finite zones containing fluid of slightly different density is investigated. The two zones are connected through a common rectangular doorway spanning the channel width so that a two-layer exchange flow develops once the barrier is removed. In the zone that initially contained dense fluid, a buoyant plume of light fluid mixes with the dense fluid leading, over time, to the development of non-trivial ambient density stratification. Meanwhile, dense fluid flows as a gravity current into the zone that initially contained light fluid. This gravity current reflects from the end wall and propagates back toward the opening in the form of an internal bore. When the bore reaches the opening the dynamics of the exchange flow (and consequently the source conditions of the buoyant plume) are substantially altered. Such dynamics are modeled using elements of gravity current, internal bore and plume theory. The flow dynamics of the two zones are linked using two-layer exchange flow theory whereby a maximal exchange flow rate is prescribed only before the bore reaches the opening. The velocity and density jump across the first front decrease substantially once the exchange flow becomes sub-maximal. Depending on the geometrical parameters, the terminal elevation of the first front may lie above, at or below the top of the opening; here, we focus on the former scenario. Experiments have been carried out to validate the model. The comparison between theory and experiment plus the application of the research to architectural fluid mechanics is discussed.

This brief communication corrects a minor error in the presentation of the model results described in §2 of Tan et al. [1] (referred to hereafter as T.al.). Previously, we predicted that the solution of Eqs. 2.10 and 2.11 becomes unphysical for g′ 12/g′ 02 ≥ 3/4 irrespective of h′1. Upon closer inspection, we observe that model breakdown occurs at g′ 12/g′ 02 = 3/4 when h′1 0.50 but extends beyond this value when h′1 0.50. This is illustrated in Fig. 2a which shows the surface plot of Fr vs. g′ 12/g′ 02 and h′1 and is identical to Fig. 3a of T. al. with the exception of the aforementioned correction. In like fashion, Figs. 1, 2, 3 and 4 are, respectively, the corrected versions of Figs. 2, 3, 4 and 5 from T. al. (Note, that the geometric variables h′1, h1, h′2 and h2 used here have been non-dimensionalized by H , the channel depth.) As these new figures make clear, the region of parameter space where the model is valid and, by extension, where the gravity current is predicted to be supercritical, is larger than described in the original manuscript. Notwithstanding this correction, the principal conclusions of T. al. remain unchanged. In addition to calculating head loss along streamlines as we do with Eqs. 2.14 and 2.15 of T. al., one can also evaluate the global dissipation by determining the change of D = ∫ u(p + 1 2ρu + ρgz) dz from far upstream to far downstream. The expression for D, written in non-dimensional form reads

An analytical, experimental and numerical study of boundary gravity currents propagating through a two-layer stratified ambient of finite vertical extent is presented. Gravity currents are supposed to originate from a lock-release apparatus; the (heavy) gravity current fluid is assumed to span the entire channel depth, H, at the initial instant. Our theoretical discussion considers slumping, supercritical gravity currents, i.e. those that generate an interfacial disturbance whose speed of propagation matches the front speed, and follows from the classical analysis of Benjamin (J Fluid Mech 31:209–248, 1968). In contrast to previous investigations, we argue that the interfacial disturbance must be parameterized so that its amplitude can be straightforwardly determined from the ambient layer depths. Our parameterization is based on sensible physical arguments; its accuracy is confirmed by comparison against experimental and numerical data. More generally, measured front speeds show positive agreement with analogue model predictions, which remain strictly single-valued. From experimental and numerical observations of supercritical gravity currents, it is noted that this front speed is essentially independent of the interfacial thickness, δ, even in the limiting case where δ = H so that the environment is comprised of a uniformly stratified ambient with no readily discernible upper or lower ambient layer. Conversely, when the gravity current is subcritical, there is a mild increase of front speed with δ. Our experiments also consider the horizontal distance, X, at which the front begins to decelerate. The variation of X with the interface thickness and the depths and densities of the ambient layers is discussed. For subcritical gravity currents, X may be as small as three lock lengths whereas with supercritical gravity currents, the gravity current may travel long distances at constant speed, particularly as the lower layer depth diminishes.

We examine the role of diffusivity, whether molecular or turbulent, on the steady-state stratification in a ventilated filling box. The buoyancy-driven displacement ventilation model of Linden et al. (J. Fluid Mech., vol. 212, 1990, p. 309) predicts the formation of a two-layer stratification when a single plume is introduced into an enclosure with vents at the top and bottom. The model assumes that diffusion plays no role in the development of the ambient buoyancy stratification: diffusion is a slow process and the entrainment of ambient fluid into the plume from the diffuse interface will act to thin the interface resulting in a near discontinuity of density between the upper and lower layers. This prediction has been corroborated by small-scale salt bath experiments; however, full-scale measurements in ventilated rooms and complementary numerical simulations suggest an interface that is not sharp but rather smeared out over a finite thickness. For a given plume buoyancy flux, as the cross-sectional area of the enclosure increases the volume of fluid that must be entrained by the plume to maintain a sharp interface also increases. Therefore the balance between the diffusive thickening of the interface and plume-driven thinning favours a thicker interface. Conversely, the interface thickness decreases with increasing source buoyancy flux, although the dependence is relatively weak. Our analysis presents two models for predicting the interface thickness as a function of the enclosure height, base area, composite vent area, plume buoyancy flux and buoyancy diffusivity. Model results are compared with interface thickness measurements based on previously reported data. Positive qualitative and quantitative agreement is observed.

Gas release in photic-zone microbialites can lead to preservable morphological biosignatures. Here, we investigate the formation and stability of oxygen-rich bubbles enmeshed by filamentous cyanobacteria. Sub-millimetric and millimetric bubbles can be stable for weeks and even months. During this time, lithifying organic-rich laminae surrounding the bubbles can preserve the shape of bubbles. Cm-scale unstable bubbles support the growth of centimetric tubular towers with distinctly laminated mineralized walls. In environments that enable high photosynthetic rates, only small stable bubbles will be enclosed by a dense microbial mesh, while in deep waters extensive microbial mesh will cover even larger photosynthetic bubbles, increasing their preservation potential. Stable photosynthetic bubbles may be preserved as sub-millimeter and millimeter-diameter features with nearly circular cross-sections in the crests of some Proterozoic conical stromatolites, while centrimetric tubes formed around unstable bubbles provide a model for the formation of tubular carbonate microbialites that are not markedly depleted in 13C.

We analyse the low-mode structure of internal tides generated in laboratory experiments and numerical simulations by a two-dimensional ridge in a channel of finite depth. The height of the ridge is approximately half of the channel depth and the regimes considered span sub- to supercritical topography. For small tidal excursions, of the order of 1% of the topographic width, our results agree well with linear theory. For larger tidal excursions, up to 15% of the topographic width, we find that the scaled mode 1 conversion rate decreases by less than 15%, in spite of nonlinear phenomena that break down the familiar wave-beam structure and generate harmonics and inter-harmonics. Modes two and three, however, are more strongly affected. For this topographic configuration, most of the linear baroclinic energy flux is associated with the mode 1 tide, so our experiments reveal that nonlinear behaviour does not significantly affect the barotropic to baroclinic energy conversion in this regime, which is relevant to large-scale ocean ridges. This may not be the case, however, for smaller scale ridges that generate a response dominated by higher modes.

The summer-time cooling efficiency of hybrid buildings depends critically upon exploiting multiple environmental resources to dispose of waste heat. To this end, many previous studies have explored the role of wind, which exerts different static pressures on a building's windward and leeward facades. Here, we consider how this methodology may be extended to the converse problem of winter-time heating wherein hot, buoyant air is purposefully supplied to the interior space using a coupled ventilation scheme. A "blocked" flow regime is desired such that cold air inflow is impeded; to avoid interstitial condensation, the pressure distribution within the building must favor outflow through designated extraction vents. For the idealized geometry considered here, blocked conditions represent a unique solution to the flow equations in well-defined regions of parameter space. The likelihood of blocking may be increased through prudent choice of extraction vent size/orientation depending on the external forcing conditions. A discussion of the inherent tradeoffs associated with multi-season design of hybrid buildings is also presented.

Experiments of intrusive gravity currents generated by lock exchange offer insights into atmospheric and oceanic flows. However, whereas many previous investigations have considered the full‐depth’ lock exchange problem, in which the intermediate density fluid initially spans the entire channel depth, less is known about ‘partial‐depth’ releases, which represent a more appropriate analogue to environmental flows where the inceptive, localized interfacial mixing is relatively weak and/or the upper and lower ambient layers are of significant vertical expanse. Here, we consider this circumstance using a combination of experimental, (two‐dimensional) numerical and analytical techniques with a particular focus on equilibrium flow for which there is no auxiliary concentration or dilution of the active scalar, and the interface ahead of the intrusion remains approximately horizontal. In this case, the initial (steady) speed of propagation, U, can be well‐predicted by adapting a shallow‐water model for g...

The rough, hairy surfaces of many insects and spiders serve to render them water-repellent; consequently, when submerged, many are able to survive by virtue of a thin air layer trapped along their exteriors. The diffusion of dissolved oxygen from the ambient water may allow this layer to function as a respiratory bubble or ‘plastron’, and so enable certain species to remain underwater indefinitely. Maintenance of the plastron requires that the curvature pressure balance the pressure difference between the plastron and ambient. Moreover, viable plastrons must be of sufficient area to accommodate the interfacial exchange of O2and CO2necessary to meet metabolic demands. By coupling the bubble mechanics, surface and gas-phase chemistry, we enumerate criteria for plastron viability and thereby deduce the range of environmental conditions and dive depths over which plastron breathers can survive. The influence of an external flow on plastron breathing is also examined. Dynamic pressure may become significant for respiration in fast-flowing, shallow and well-aerated streams. Moreover, flow effects are generally significant because they sharpen chemical gradients and so enhance mass transfer across the plastron interface. Modelling this process provides a rationale for the ventilation movements documented in the biology literature, whereby arthropods enhance plastron respiration by flapping their limbs or antennae. Biomimetic implications of our results are discussed.

The collapse of a uniform density fluid (a “mixed region”) into a surrounding ambient fluid with complex stratification is examined by way of laboratory experiments and fully nonlinear numerical simulations. The analysis focuses upon the consequent generation of internal gravity waves and their influence upon the evolution of the collapsing mixed region. In experiments and simulations for which the ambient fluid has uniform density over the vertical extent of the mixed region and is stratified below, we find the mixed region collapses to form an intrusive gravity current and internal waves are excited in the underlying stratified fluid. The amplitude of the waves is weak in the sense that the intrusion is not significantly affected by the waves. However, scaling the results to the surface mixed layer of the ocean we find that the momentum flux associated with the waves can be as large as 1 N / m 2 . In simulations for which the ambient fluid is stratified everywhere, including over the vertical extent of the mixed region, we find that internal waves are excited with such large amplitude that the collapsing mixed region is distorted through strong interactions with the waves.

The excitation of internal gravity waves by fluid intrusions that propagate along the interface between a uniform upper layer and a uniformly stratified lower layer is examined by way of laboratory experiments. Intrusions are generated using a simple lock-release apparatus. Experiments are conducted in which the density gradient of the uniformly stratified layer, the density jump across the interface and the density difference between the lock fluid and the uniform upper layer are varied.In all cases, the fluid intrusions travelled at a constant speed. The forcing imparted by the generated internal gravity waves did not deform the intrusion head or significantly retard the intrusion's rate of forward advance. For a limited range of density parameters, good agreement was obtained between the experimental data and the two-layer analytical theory of J. Y. Holyer & H. E. Huppert (J. Fluid Mech. vol. 100 (1980), pp. 739–767) which provides estimates for the intrusion speed and depths of penetration into the upper and lower layers. Internal gravity wave excitation is due to the initial collapse of the lock fluid and the forcing imparted by the head of the intrusion. Waves are visualized and their amplitudes measured using ‘synthetic schlieren’.The vertical flux of horizontal momentum due to internal gravity wave excitation is related to measurable properties of the fluid intrusion. This analysis suggests that outflows produced by tall convective storms that travel along the tropopause may excite non-hydrostatic internal gravity waves in the stratosphere whose momentum flux, at least during the transient generation time, is comparable to that of waves generated by topographic forcing.

We investigate the dynamics of a gravity current that propagates along the interface of a two-layer fluid. The results of the well-studied symmetric case are reproduced in which the upper- and lower-layer depth of the ambient are equal and the density of the intrusion is the average density of the ambient. In addition, we present the first detailed examination of asymmetric circumstances in which the density of the intrusion differs from the mean density of the ambient and in which the upper- and lower-layer fluid depths are unequal. The general equations derived by J. Y. Holyer & H. E. Huppert (J. Fluid Mech.) vol. 100, 1980, pp. 739–767,), which predict the speed and vertical extent of the gravity current head, are re-expressed in a simpler form that employs the Boussinesq approximation. Approximate analytic solutions are determined using perturbation theory. The predictions are compared with the results of laboratory experiments. We find excellent agreement if the density of the gravity current is the average of the upper- and lower-layer densities weighted by the respective depths of the two layers. However, exact theory significantly underpredicts the gravity current speeds if the current density differs from this weighted-mean average. The discrepancy is attributed to the generation of waves that lead and trail the gravity current head. Empirical support for this assertion is provided through an examination of the observed wave characteristics.

The properties of waves generated by a vertically oscillating sphere in a uniformly stratified fluid are examined both theoretically and experimentally. Existing predictions for the wave amplitude and phase structure are modified to account fo rt he effects of viscous attenuation. As with waves generated by an oscillating cylinder, the main effect of attenuation is to broaden the two peaks of the amplitude envelope on either flank of the wave beam so that far from the sphere the wave beam exhibits a single peak with a maximum along the centreline. The transition distance from bimodal to unimodal wave beam structure is shown to occur closer to the source than the corresponding distance calculated for the oscillating circular cylinder. For laboratory experiments, a recently developed ‘synthetic schlieren’ method is adapted so that quantitative measurements may be made of an axisymmetric wave field. This non-intrusive technique allows us to evaluate the amplitude of the waves everywhere in space and time. Experiments are performed to examine the amplitude of waves generated by small and large spheres oscillating with a range of amplitudes and frequencies. The wave amplitude is found to scale linearly with the oscillation amplitude A for A/a as large as 0.27, where a is the radius of the sphere. Generally good agreement between theory and experiment is found for the small sphere experiments. However, the theory overpredicts both the amplitude and the bimodal-to-unimodal transition distance for waves generated by the large sphere.

Synthetic schlieren'', which has been used to measure the amplitude of two-dimensional internal wave beams generated from an oscillating cylinder, is adapted to analyze axisymmetric internal waves generated by an oscillating sphere. This nonintrusive technique uses ele- mentary inverse tomographic methods to measure the amplitude of the conical-structured wave beams every- where in space and time. We compare the results with in situ probe measurements, and we examine the structure of the wave beams generated by a sphere oscillating at dif- ferent amplitudes.

Microstructures on insect wings can promote directional drop shedding, and the local orientation of these structures is expected to facilitate drop removal. However, microstructures may exhibit very different orientations at different locations on the wing. Using the march fly Penthetria heteroptera, we propose that local orientation of small hairs (microtrichia) reflects a balance of three nonexclusive strategies: (1) preventing water from becoming stuck in intervenous grooves (microtrichia point upslope), (2) shedding water off the wing as readily as possible (microtrichia point towards the nearest edge), and, (3) shedding water away from the body (microtrichia point distally). We present evidence for all three and show that local microtrichial orientation is seldom determined by any one factor. We develop a mathematical model that employs factor-specific weighting values determined via optimization. Our predictions are tested against the orientation of microtrichia randomly sampled from a P. heteroptera specimen. Using the best-fit weighting parameters, the model displays a median residual of 20°; no residual is greater than 46°. The model also reproduces qualitative aspects of microtrichial orientation, such as bifurcation midway between veins and convergence toward peaks. This strong correspondence between modelled and observed orientation supports the role of microtrichia as directional antiwetting devices and highlights the importance of considering both function and wing geometry to explain the organization of natural microstructure arrays.

This paper specifies the configuration of a harvester for absorbing energy from ambient oscillation with broadband frequencies. Two major methodologies for broadband harvesting have been developed, one is the use of a nonlinear oscillator, and the other is the use of multiple resonators. We focus on the traditional way of assembling multiple resonators but suggest some nontrivial improvements in the configuration. In order to make a variety of resonant frequencies, resonators can be connected in series, in the form of a tree-like structure. The energy absorption of the tree configuration harvester under broadband frequency excitation is tested, and additionally the placement of multiple resonators is also considered. The numerical results indicate that our proposal of the tree configuration might be useful under broadband frequency excitation.Copyright © 2014 by ASME

Bitumen aeration was studied by flooding samples of medium grade oil sand with de-ionized water under both ambient and high vacuum conditions. The samples were then agitated on a shaker table. Subsequent analysis revealed the presence or absence of an air gap in the sample container was the single most important factor in determining the overall bitumen recovery. Furthermore, samples that were flooded while under high vacuum produced slightly less bitumen compared to samples flooded at atmospheric pressure. This suggests that oil sand that is not under high vacuum when flooded with water contains some amount of indigenous air (see introduction) that would aid in bitumen flotation. On a etudie l'aeration de bitume en inondant des echantillons de sable bitumineux de grade intermediaire avec de l'eau desionisee dans des conditions ambiantes et de vide pousse. Les echantillons ont ensuite ete agites sur une table vibrante. L'analyse a montre que la presence ou l'absence d'un entrefer dans le bac d'echantillons est le facteur le plus important pour determiner la recuperation globale de bitume. En outre, les echantillons qui ont ete inondes alors qu'ils etaient soumis a un vide pousse produisent un peu moins de bitume comparativement aux echantillons inondes a la pression atmospherique. Ceci suggere que le sable bitumineux qui n'est pas soumis a un vide pousse lorsqu'il est inonde avec l'eau contient une certaine quantite d'air indigene qui aiderait a la flottation du bitume.

In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions, termed "jamitons," to the hyperbolic ("inviscid") continuum traffic equations. Generic existence criteria are examined in the context of the Lax entropy conditions. Our analysis naturally precludes traveling wave solutions for which the shocks travel downstream more rapidly than individual vehicles. Consistent with recent experimental observations from a periodic roadway (Sugiyama et al., New Journal of Physics, 10, 2008), our numerical calculations show that, under appropriate road conditions, jamitons are attracting solutions, with the time evolution of the system converging towards a jamiton-dominated configuration. Jamitons are characterized by a sharp increase in density over a relatively compact section of the roadway. Applications of our analysis to traffic modeling and control are examined by way of a detailed example., 27 pages, 4 figures

We report upon a laboratory experimental study of dense full- and partial-depth locks released gravity currents propagating through a two-layer ambient and over sinusoidal topography of amplitude A and wavelength λ. Attention is restricted to a Boussinesq flow regime and the initial (or slumping) stage of motion. Because of the presence of the topography, the lower layer depth and channel depth vary in the downstream direction by as much as ±52% and ±40%, respectively. Despite such large variations, the instantaneous gravity current front speed typically changes by only a small amount from its average value, U. We conclude that the reason for this unexpected observation is a counterbalancing between the contraction/expansion of the channel on one hand and along-slope variations of the buoyancy force on the other hand. Compared to the case of gravity current flow over a horizontal surface, the topography has a retarding effect on U; we characterize the variation of U with the following parameters: A, A/...

Gravity currents produced by partial-depth lock-release and travelling along the base of a two-layer stratified ambient are investigated as they propagate along a rising slope. The initial gravity current front speed is found to be consistent with a theory adapted from Shin et al. [“Gravity currents produced by lock exchange,” J. Fluid Mech. 521, 1-34 (2004)] to the case of partial-depth currents in two-layer ambients. The subsequent evolution depends on the gravity current speed relative to the speed of the interfacial disturbance it creates. The deceleration of supercritical gravity currents, which travel faster than the interfacial disturbance, is gradual and agrees well with the relationship developed by Marleau et al. [“Gravity currents propagating up a slope,” Phys. Fluids 26, 046605 (2014)] for upslope gravity currents in uniform density ambients. In several subcritical cases, the gravity current suddenly came to rest as a consequence of interactions with the interfacial disturbance. The disturbance amplitude, speed, and width are found to be nearly constant during its evolution. In cases for which the ambient interface intersected the bottom slope, the amplitude, speed, and width were nearly constant up to the point where the lower layer shallowed and the disturbance transformed into an upslope-propagating gravity current.

Synthetic schlieren is a new technique that al- lows one easily and inexpensively to visualise density vari- ations, such as those caused by internal waves propagat- ing in a density stratified fluid. In the special case of two- dimensional internal waves (for example, those created by an oscillating cylinder), synthetic schlieren allows one to measure non-intrusively the wave amplitudes everywhere in space and time. The technique works by measuring the ap- parent displacement of points in a digitised image (such as a grid of horizontal lines), which is observed by a CCD camera through the experimental test section. Synthetic schlieren is sufficiently sensitive that it can measure sub-pixel-scale dis- turbances. In this work, we report on the first step toward measuring fully three-dimensional disturbances. We perform laboratory experiments in which internal waves are generated in a uni- formly salt-stratified fluid by a vertically oscillating sphere. Theory predicts that the resulting wave-field is in the form of two cones emanating above and below the sphere. Using inverse tomographic techniques, we exploit the axisymmetry of the wave-field to relate the apparent displacement of pix- els in an image to the wave amplitudes. tioning of the mirrors, and the sensitivity to optical imper- fections on the mirror surface and test section of the exper- iment. Furthermore, because mirrors are prone to damage traditional schlieren is prohibitively difficult to employ out- side controlled laboratory conditions. In contrast, "synthetic schlieren" is much less expensive and easier to implement: the field of view can be as large as required to visualise the

Bottom propagating gravity currents resulting from full- and partial-depth lock-release experiments are investigated as they approach and then propagate up a rising slope. Consistent with the prediction of a WKB-like theory, the gravity current front decelerates in a nearly uniform manner along the slope as 0.112g′s(D/H)(2 − D/H), in which g′ is the reduced gravity, s is the slope, D is the initial lock-fluid height, and H is the ambient fluid height. The shape of the gravity current as it decelerates over relatively steep slopes is found to be self similar with a nearly linear decrease of the head height between the start of the slope and up to 80% of the distance to the nose. Some deviation from self-similar behaviour is found in cases with small s because of the comparatively large volume of fluid in the gravity current tail that flows downslope while the front continues to advance upwards.