Mixing in a density-driven current flowing down a slope in a rotating fluid

Author Posting. © Cambridge University Press, 2008. 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 604 (2008): 369-388, doi:10.1017/S0022112008001237.We discuss laboratory experiments investigating mixing in a density-driven current flowing down a sloping bottom, in a rotating homogenous fluid. A systematic study spanning a wide range of Froude, 0.8 < Fr < 10, and Reynolds, 10 < Re < 1400, numbers was conducted by varying three parameters: the bottom slope; the flow rate; and the density of the dense fluid. Different flow regimes were observed, i.e. waves (non-breaking and breaking) and turbulent regimes, while changing the above parameters. Mixing in the density-driven current has been quantified within the observed regimes, and at different locations on the slope. The dependence of mixing on the relevant non-dimensional numbers, i.e. slope, Fr and Re, is discussed. The entrainment parameter, E, was found to be dependent not only on Fr, as assumed in previous studies, but also on Re. In particular, mixing increased with increasing Fr and Re. For low Fr and Re, the magnitude of the mixing was comparable to mixing in the ocean. For large Fr and Re, mixing was comparable to that observed in previous laboratory experiments that exhibited the classic turbulent entrainment behaviour.Support was given by the National Science Foundation project number OCE-0350891

An experimental study of a mesoscale vortex colliding with topography of varying geometry in a rotating fluid

Author Posting. © Sears Foundation for Marine Research, 2004. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 62 (2004): 611-638, doi:10.1357/0022240042387583.The interaction of a self-propagating barotropic cyclonic vortex with an obstacle has been investigated and the conditions for a vortex to bifurcate into two vortices determined. As in a previous study, after a self-propagating cyclonic vortex came into contact with the obstacle, fluid peeled off the outer edge of the vortex and a so-called "streamer" went around the obstacle in a counterclockwise direction. Under certain conditions, this fluid formed a new cyclonic vortex in the wake of the obstacle, causing bifurcation of the original vortex into two vortices. In the present study we performed three sets of idealized laboratory experiments with the aim of investigating the importance on the bifurcation mechanism of the obstacle's horizontal cross sectional geometry, the influence of the height of the obstacle, and the importance of the slope of the obstacle sidewalls. The present results suggest that bifurcation occurs only when the obstacle height is equal or larger than 85% of the vortex height and that steep sloping sidewalls do not influence the bifurcation mechanism. In addition, experiments performed using an obstacle with an elliptical horizontal cross section revealed that the relevant parameter governing the occurrence of bifurcation is the length which the "streamer" has to travel around the obstacle, and not the dimension of the obstacle in the direction orthogonal to the motion of the vortex. Collisions of oceanic mesoscale vortices with seamounts often result in major modifications of their structure, having significant impacts on the redistribution of water properties. Observations of a "Meddy" bifurcating after colliding with the Irving Seamount in the Canary Basin show behavior similar to these idealized laboratory experiments. This suggests that these results could be used to explain and predict the outcome of a vortex colliding with seamounts of varying geometry in the ocean.Support was given by the National Science Foundation project number OCE-0081756

Phase Analysis of the Stretching Cycles of the Head of Unsteady Gravity Currents Developing over Smooth and Rough Beds

Gravity currents are buoyancy driven flows occurring spontaneously in nature or resulting from human intervention. Examples of gravity currents in the water are oceanic fronts, resulting from differences in temperature and salinity, and turbidity currents caused by high concentration of suspended particles. The release of pollutant materials into rivers, oil spillage in the ocean and desalination plant outflows are examples of anthropogenic gravity currents in the water, frequently with negative environmental impacts. The present work experimentally investigates the dynamics of unsteady gravity currents produced by lock-release of a saline mixture into a fresh water tank. Seven different experimental runs were performed by varying e density of the saline mixture in the lock and the bed roughness. The experiments were conducted in a 3.0 m long Perspex flume, of horizontal bed and rectangular cross section of 0.20 x 0.30 m2, and recorded with a 25 Hz CCD video camera. An image analysis technique was applied to visualize and characterize the current allowing the detailed analysis of the gravity current dynamics and more specifically of the head dynamics. The temporal evolution of variables assessed at the head of the gravity current i.e. length, surface, volume and mass, per unit width, shows repeated cycles of stretching and break of the head. During the stretching phase, ambient fluid is entrained into the head causing its growth. However this is not unlimited, a limit in which the head becomes unstable and consequently breaks exists. There is a strong similarity in the head aspect ratio, of maximum head height to length, and mass between the cycles and between runs, thus a phase lumped analysis within the periodically well-behaved cycles is presented in terms of head aspect ratio, head mass and mass rate. In the instants of head break, the head aspect ratio shows a consistent limit of 0.2, for all runs, and the mass of the head is of the order of the initial mass in the lock. Regarding the periodicity of the break events, it is seen to increase with bed roughness. Entrainment at the head is evaluated through mass rate and is seen to occur during all the stages of the current development

Experimental study of uni and bi-directional exchange flows in a large scale rotating trapezoidal channel

International audienceA large-scale experimental study has been conducted at the Coriolis Rotating Platform to investigate the dynamics of uni- and bi-directional exchange flows along a channel with a trapezoidal cross section under the influence of background rotation. High-resolution two-dimensional particle image velocimetry and micro-conductivity probes were used to obtain detailed velocity fields and density profiles of the exchange flow generated across the channel under different parametric conditions. Experimental measurements give new insight into the stratified-flow dynamics dependence on the magnitude of Burger number, defined as the ratio of the Rossby radius to the channel width, such that values lower than 0.5 characterize unsteady exchange flows. The measurements highlight the role that both ambient rotation and net-barotropic forcing have on the geostrophic adjustment of the dense outflowing layer and on the corresponding counter-flowing water layer fluxes. The coupled effect of these two parametric conditions largely affects the transverse velocity distribution and, for the largest net-barotropic flow in the upper fresh water layer, leads to the partial blockage of the lower saline outflow. Moreover, an increase in the mixing layer thickness, associated with larger rotation rates, and due the interface dynamics, is observed, with shear-driven interfacial instabilities analyzed to highlight the influence of both ambient rotation and net-barotropic forcin

Axisymmetric three-dimensional gravity currents generated by lock exchange

Unconfined three-dimensional gravity currents generated by lock exchange using a small dividing gate in a sufficiently large tank are investigated by means of large eddy simulations under the Boussinesq approximation, with Grashof numbers varying over five orders of magnitudes. The study shows that, after an initial transient, the flow can be separated into an axisymmetric expansion and a globally translating motion. In particular, the circular frontline spreads like a constant-flow-rate, axially symmetric gravity current about a virtual source translating along the symmetry axis. The flow is characterised by the presence of lobe and cleft instabilities and hydrodynamic shocks. Depending on the Grashof number, the shocks can either be isolated or produced continuously. In the latter case a typical ring structure is visible in the density and velocity fields. The analysis of the frontal spreading of the axisymmetric part of the current indicates the presence of three regimes, namely, a slumping phase, an inertial-buoyancy equilibrium regime and a viscous-buoyancy equilibrium regime. The viscous-buoyancy phase is in good agreement with the model of Huppert (J. Fluid Mech., vol. 121, 1982, pp. 43-58), while the inertial phase is consistent with the experiments of Britter (Atmos. Environ., vol. 13, 1979, pp. 1241-1247), conducted for purely axially symmetric, constant inflow, gravity currents. The adoption of the slumping model of Huppert & Simpson (J. Fluid Mech., vol. 99 (04), 1980, pp. 785-799), which is here extended to the case of constant-flow-rate cylindrical currents, allows reconciling of the different theories about the initial radial spreading in the context of different asymptotic regimes. As expected, the slumping phase is governed by the Froude number at the lock's gate, whereas the transition to the viscous phase depends on both the Froude number at the gate and the Grashof number. The identification of the inertial-buoyancy regime in the presence of hydrodynamic shocks for this class of flows is important, due to the lack of analytical solutions for the similarity problem in the framework of shallow water theory. This fact has considerably slowed the research on variable-flow-rate axisymmetric gravity currents, as opposed to the rapid development of the knowledge about cylindrical constant-volume and planar gravity currents, despite their own environmental relevance

The dynamics of bi-directional exchange flows

The global demand for low carbon electricity requires a variety of energy generation approaches, the choice of which is dependent on multiple criteria. Tidal flows have long been identified as a reliable source of energy, with a high degree of predictability. To this end a novel turbine has been developed that could be well suited to energy generation in both tidal flows, or water courses. In this study a Smoothed Particle Hydrodynamics (SPH) model, namely DualSPHysics, is used to predict the behavior of this novel turbine design. Which will be used to guide the design process. The SPH method was chosen as the design of the turbine uses several connected parts, that requires free movement and interactions to properly represent the prototype and was found to be capable of expressing this behavior

Image analysis technique applied to lock-exchange gravity currents

An image analysis technique is used to estimate the two-dimensional instantaneous density field of unsteady gravity currents produced by full-depth lock-release of saline water. An experiment reproducing a gravity current was performed in a 3.0 m long, 0.20 m wide and 0.30 m deep Perspex flume with horizontal smooth bed and recorded with a 25 Hz CCD video camera under controlled light conditions. Using dye concentration as a tracer, a calibration procedure was established for each pixel in the image relating the amount of dye uniformly distributed in the tank and the greyscale values in the corresponding images. The results are evaluated and corrected by applying the mass conservation principle within the experimental tank. The procedure is a simple way to assess the time-varying density distribution within the gravity current, allowing the investigation of gravity current dynamics and mixing processes

The dynamics of bi-directional exchange flows::implication for morphodynamic change within estuaries and sea straits

Environmental and geophysical flows, including dense bottom gravity currents in the ocean and buoyancy-driven exchange flows in marginal seas, are strongly controlled by topographic features. These are known to exert significant influence on both internal mixing and secondary circulations generated by these flows. In such cases, uni-directional or bi-directional exchange flows develop when horizontal density differences and/or pressure gradients are present between adjacent water bodies connected by a submerged channel. The flow dynamics of the dense lower layer depend primarily on the volumetric flux and channel cross-sectional shape, while the stratified interfacial flow mixing characteristics, leading to fluid entrainment/detrainment, are also dependent on the buoyancy flux and motion within the upper (lower density) water mass. For submerged channels that are relatively wide compared to the internal Rossby radius of deformation, Earth rotation effects introduce geostrophic adjustment of these internal fluid motions, which can suppress turbulent mixing generated at the interface and result in the development of Ekman layers that induce secondary, cross-channel circulations, even within straight channels. Moreover, recent studies of dense, gravity currents generated in rotating and non-rotating systems, respectively, indicated that the V-shaped channel topography had a strong influence on both flow distribution and associated interfacial mixing characteristics along the channel. However, such topographic controls on the interfacial mixing and secondary circulations generated by bi-directional exchange flows are not yet fully understood and remain to be investigated thoroughly in the laboratory. Also the effect of mobile bed for bi-directional exchange flows generated in deformable channels along with the physical interactions between the lower dense water flow and the erodible bed sediments will have a strong influence in (re-)shaping the overall channel bed topography (i.e. bed morphodynamics). Consequently, the resulting temporal changes in cross-sectional channel bathymetry (i.e. through erosion and deposition processes) would also be expected to have associated feedbacks on transverse asymmetries in the bi-directional exchange flow structure, as well as on the internal flow stability