ALBERT

Description: Author Posting. © Cambridge University Press, 2014. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 752 (2014): R2, doi:10.1017/jfm.2014.389.

Description: A model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an ‘effective’ entrainment constant, αeff, as the value of α needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of αeff allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions.

Description: The authors gratefully acknowledge the National Science Foundation (grant OCE-0824636) and the Office of Naval Research (grant N00014-09-1-0844) for their support of the 2013 WHOI Geophysical Fluid Dynamics Summer School where this project was initiated. Support to C.C. was given by the National Science Foundation project OCE-1130008.

Description: 2015-07-11

Description: Air curtains are used to reduce the heat and mass exchange across open doorways. Their sealing ability is assessed in terms of the effectiveness E, the fraction of the exchange flow prevented by the air curtain compared to an unobstructed open door. Previous work has studied air-curtain effectiveness when the doorway is the only means of ventilating a space. In this paper, we examine the effects of additional displacement ventilation on the dynamics of the air curtain and the resulting changes in its effectiveness. The main controlling parameter is the deflection modulus Dm, which is the ratio between the momentum flux of the air curtain and the transverse forces due to the displacement ventilation. For a relatively warm interior, we find that, for small values of Dm, the air curtain is drawn inside the space by the ventilation flow. For large values of Dm, the flow through the doorway is controlled by the air curtain. A smooth transition occurs between these two regimes, and we estimate the Dm value for the onset of this transition. Our model provides a quantitative prediction of E.Dm/ in the ventilation-driven regime, and gives a qualitative description of the other two regimes. Laboratory experiments were conducted to test the proposed model. The experimental data were compared to theoretical predictions, and good agreement was found. © 2014 Cambridge University Press.

Description: We present an experimental and numerical study of the upstream internal wavefield in a channel generated by constant density intrusions propagating into a linearly stratified ambient fluid during the initial phase of translation. Using synthetic schlieren imaging and two-dimensional direct numerical simulations, we quantify this wave motion within the ambient stratified fluid ahead of the advancing front. We show that the height of the neutral buoyancy surface in the ambient fluid determines the vertical modal response with the predominant waves being mode 2 for intrusions near the mid-depth of the channel and mode 1 waves being produced by intrusions nearer the top or bottom of the domain. All higher vertical modes travel slower than the intrusion and so do not appear upstream ahead of the intrusion front. We find the energy flux into this upstream wavefield to be approximately constant, and to be between 10 and 30 % of the rate of available potential energy transfer into the flow. © 2014 Cambridge University Press.

Description: Nature is often an inspiration for scientists and especially so in fluid dynamics. We observe and admire the beauty of birds and fish as they move through the air and water, and wonder how these forms of locomotion evolved and whether they are optimised for efficiency. A common feature of this locomotion is that the thrust is generated by the flapping of a wing or fin, creating an unsteady flow. Other less readily observed animals such as salps or squid eject a pulsed jet, raising the question of whether there is an advantage of this unsteady forcing over a steady jet. This is the question addressed by Ruiz, Whittlesey & Dabiri (J. Fluid Mech., this issue, vol. 668, 2011, pp. 5-32) who have carried out detailed flow and power-consumption measurements with a self-propelled vehicle in water. The vehicle has a novel propulsion mechanism that allows a comparison of the efficiency of a pulsed and steady jet to be compared. They show that significant increases in efficiency are possible with the pulsed jet, even allowing for the additional power needed to create the pulsed flow. They also show that vortex rings are produced by the unsteady jet and that the additional entrainment of ambient fluid into the ring and the higher pressure at the front of the ring are the cause of this increased efficiency. © 2011 Cambridge University Press.

Description: In this paper, results of laboratory experiments simulating buoyancy-driven coastal currents produced by estuarine discharges into the ocean, are discussed. The responses of the propagation speeds of the currents to increases and decreases of the volumetric discharge rate at the source are investigated. For increasing discharge rate, we find that the mean speed of the current head displays a sharp rise some time after the source discharge condition has changed. In contrast, a decrease of the current speed following a decreasing discharge rate proceeds gradually. The current speed after acceleration or deceleration is found to be equal to the speed that would be expected had the discharge been at the higher or lower rate from the start of the experiment. The relative speed at which the information of the changed discharge condition at the source approaches the advancing current head from upstream, for both increasing and decreasing discharge rates, is found to be approximately one to three times the mean speed of the current. Further, we find that this transmission speed is 0.82+0.20 times the propagation speed of a linear, long interfacial Kelvin wave. © 2010 Cambridge University Press.

Description: The advance of the front of a dense gravity current propagating in a rectangular channel and V-shaped valley both horizontally and up a shallow slope is examined through theory, full-depth lock–release laboratory experiments and hydrostatic numerical simulations. Consistent with theory, experiments and simulations show that the front speed is relatively faster in the valley than in the channel. The front speed measured shortly after release from the lock is 5–22 % smaller than theory, with greater discrepancy found in upsloping V-shaped valleys. By contrast, the simulated speed is approximately 6 % larger than theory, showing no dependence on slope for rise angles up to ${itheta}=8^{circ }$. Unlike gravity currents in a channel, the current head is observed in experiments to be more turbulent when propagating in a V-shaped valley. The turbulence is presumably enhanced due to the lateral flows down the sloping sides of the valley. As a consequence, lateral momentum transport contributes to the observed lower initial speeds. A Wentzel–Kramers–Brillouin like theory predicting the deceleration of the current as it runs upslope agrees remarkably well with simulations and with most experiments, within errors.

Description: A model of the total volume flux and entrainment occurring in two coalescing axisymmetric turbulent plumes is developed and compared with laboratory experiments. The dynamical evolution of the two plumes is divided into three regions. In region 1, where the plumes are separate, the entrainment in each plume is unaffected by the other plume, although the two plumes are drawn together due to the entrainment of ambient fluid between them. In region 2 the two plumes touch each other but are not yet merged. In this region the total entrainment is a function of both the dynamics of the touching plumes and the reduced surface area through which entrainment occurs. In region 3 the two plumes are merged and the entrainment is equivalent to that in a single plume. We find that the total volume flux after the two plumes touch and before they merge increases linearly with distance from the sources, and can be expressed as a function of the known total volume fluxes at the touching and merging heights. Finally, we define an 'effective' entrainment constant, αeff, as the value of α needed to obtain the same total volume flux in two independent plumes as that occurring in two coalescing plumes. The definition of αeff allows us to find a single expression for the development of the total volume flux in the three different dynamical regions. This single expression will simplify the representation of coalescing plumes in more complex models, such as in large-scale geophysical convection, in which plume dynamics are not resolved. Experiments show that the model provides an accurate measure of the total volume flux in the two coalescing plumes as they evolve through the three regions. © 2014 Cambridge University Press.

Description: We present results of experiments on stratified shear flow in an inclined duct. The duct connects two reservoirs of fluid with different densities, and contains a counterflow with a dense layer flowing beneath a less dense layer moving in the opposite direction. We identify four flow states in this experiment, depending on the fractional density differences, characterised by the dimensionless Atwood number, and the angle of inclination θ, which is defined to be positive (negative) when the along-duct component of gravity reinforces (opposes) the buoyancy-induced pressure differences across the ends of the duct. For sufficiently negative angles and small fractional density differences, the flow is observed to be laminar (L state), with an undisturbed density interface separating the two layers. For positive angles and/or high fractional density differences, three other states are observed. For small angles of inclination, the flow is wave-dominated and exhibits Holmboe modes (H state) on the interface, with characteristic cusp-like wave breaking. At the highest positive angles and density differences, there is a turbulent (T state) high-dissipation interfacial region typically containing Kelvin-Helmholtz (KH)-like structures sheared in the direction of the mean shear and connecting both layers. For intermediate angles and density differences, an intermittent state (I state) is found, which exhibits a rich range of spatio-temporal behaviour and an interfacial region that contains features of KH-like structures and of the other two lower-dissipation states: thin interfaces and Holmboe-like structures. We map the state diagram of these flows in the Atwood number-θ plane and examine the force balances that determine each of these states. We find that the L and H states are hydraulically controlled at the ends of the duct and the flow is determined by the pressure difference associated with the density difference between the reservoirs. As the inclination increases, the along-slope component of the buoyancy force becomes more significant and the I and T states are associated with increasing dissipation within the duct. We replot the state space in the Grashof number-θ phase plane and find the transition to the T state is governed by a critical Grashof number. We find that the corresponding buoyancy Reynolds number of the transition to the T state is of the order of 100, and that this state is also found to be hydraulically controlled at the ends of the duct. In this state the dissipation balances the force associated with the along-slope component of buoyancy and the counterflow has a critical composite Froude number. © 2014 Cambridge University Press.

Description: We present an experimental and numerical study of one stratified fluid propagating into another. The two fluids are initially at rest in a horizontal channel and are separated by a vertical gate which is removed to start the flow. We consider the case in which the two fluids have the same mean densities but have different, constant, non-zero buoyancy frequencies. In this case the fluid with the smaller buoyancy frequency flows into the other fluid along the mid-depth of the channel in the form of an intrusion and two counter-flowing gravity currents of the fluid with the larger buoyancy frequency flow along the top and bottom boundaries of the channel. Working from the available potential energy of the system and measurements of the intrusion thickness, we develop an energy model to describe the speed of the intrusion in terms of the ratio of the two buoyancy frequencies. We examine the role of the stratification within the intrusion and the two gravity currents, and show that this stratification plays an important role in the internal structure of the flow, but has only a secondary effect on the speeds of the exchange flows. © 2010 Cambridge University Press.