Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.     

Visualization of the internal flow properties and the material exchange interface in an entraining viscous Newtonian gravity current

In order to simulate a simple entraining geophysical flow, a viscous Newtonian gravity current is released from a reservoir by a dam-break and flows along a rigid horizontal bed until it meets a layer of entrainable material of finite depth, identical to the current. The goal is to examine the entrainment mechanisms by observing the interaction between the incoming flow and the loose bed. The sole parameter varied is the initial volume of the gravity current, thus altering its height and velocity. The gravity current plunges or spills into the entrainable bed and the velocity of the flow front becomes linear with time. The bed material is directly affected: motion is generated in the fluid far downstream of, and in that lying beneath the encroaching front. Shear bands are identified, separating horizontal flow downstream from flow with a strong vertical component close to the step. Downstream of the step the flow is horizontal and stratified, with no slip on the bottom boundary and very low shear near the surface. Between these two regions may lie transitional zones with linear velocity profiles, separated by horizontal bands of high shear; the number of transitional zones in the cross-section varies with the initial volume of the dam-break.     

Flow and transport characteristics at an Epinephelus guttatus (red hind grouper) spawning aggregation site in St. Thomas (US Virgin Islands)

This study characterizes the flow field at a spawning site located at the shelf break of a Caribbean island for the Epinephelus guttatus (red hind grouper) in relation to this species spawning events. In order to understand the oceanographic dynamics targeted by the fishes, current measurements were profiled throughout the water column for almost a year at the spawning site. The characteristics of the flow field and its evolution after spawning were investigated by using a numerical ocean model that resolved the observed tide and simulated the island scale flow where passive, neutrally buoyant virtual particles were released for 10 days to trace the flow pathways.Observed currents during the spawning period revealed that the flow was vertically sheared, to the south and weakest at the bottom, and to the west or east at the surface. The tidal analysis revealed that the flow at the time of spawning was directed across and on-shelf, although weaker close to the bottom. The model showed that the initial on-shelf transport was counteracted by the bottom flow directed to the shelf break, where virtual particles were entrained by the downwelling flow. A significant percent of particles resided less than two hundred meters deep, in the vicinity of the chlorophyll maximum and returned to the shelf break, close to the release location within 8-10 days. This journey was largely controlled by the timing between downwelling at the spawning site and upwelling further east at the shelf break, which was driven by the coupling between wind and tide induced vertical movements at the shelf break and deeper. The release location, vertical rotation of its flow field, and its transport properties were shown to be relatively resilient to the passage of transient sub-mesoscale eddies as well as to acute mesoscale flow reversals, suggesting that physical retention is maximized in the area surrounding the spawning site.     

The flow of high-Reynolds axisymmetric gravity currents of a stratified fluid into a stratified ambient: shallow-water and box model solutions

We consider the axisymmetric flow (in a full cylinder or a wedge) of high-Reynolds-number Boussinesq gravity currents and intrusions systems in which both the ambient and the propagating “current” are linearly stratified. The main focus is on a current of fixed volume released from a cylinder lock; the height ratio of the fluids H, and the stratification parameter of the ambient S, are quite general. We develop a one-layer shallow-water model. The internal stratification enters as a new dimensionless parameter, ${\sigma \in [0, 1]}$ . In general, the time-dependent motion is obtained by standard finite-difference solutions; a self-similar analytical solution exists for S?= 0. We show that, in general, the speed of propagation decreases when the internal stratification becomes more pronounced (σ increases). We also developed a box-model approximation, and show that the resulting radius of propagation is in good agreement with the more rigorous shallow-water prediction.     

Streamwise velocity profiles in coastal currents

The ability to model marine currents can be a powerful device for many planning activities, for which the knowledge of the velocity field is of pivotal importance, such as the evaluation of current-induced loading on maritime structures or the diffusion and dispersion of polluted flow discharges. Observations of time-averaged velocity profiles, taken with a vessel mounted acoustic Doppler current profiler during a monitoring survey program in the seas of Southern Italy, are analysed in this paper. The measurements were taken under non-breaking conditions, offshore the surf zone, with the aim of reproducing the vertical trends of the streamwise velocity by means of standard theoretical laws. To evaluate also the possible influence of stratification on the current velocity profile shape, together with velocity measurements water temperature and salinity were also measured at the same time and locations, by means of a CTD recorder. The examined surveys referred to different time periods and sites, to guarantee a general validity of deductions. On the basis of the experiments, we verified the actual existence of a log-layer and concluded that the upper limit of the region in which the log law is applicable extends well beyond the inner region. Moreover, the deviations of the measured velocity from the logarithmic profiles above the height of the log layer is consistent with the effects of stratification. The parameters of the log law were estimated, depending on both flow dynamics and stratification in the target area. As a second step, in the most superficial and stratified layer, the velocity profiles were modelled by means of a power law, which fitted the measured data well. According to previous studies, the power law parameters result Reynolds number dependent by means of a new proposed formulation. Finally, the bottom stress and the bottom drag coefficient were investigated.     

Lock-exchange gravity currents over rough bottoms

In nature, density driven currents often flow over or within a bottom roughness: a sea breeze encountering tall buildings, a shallow flow encountering aquatic vegetation, or a dense oceanic current flowing over a rough bottom. Laboratory experiments investigating the mechanisms by which bottom roughness enhances or inhibits entrainment and dilution in a lock-exchange dense gravity current have been conducted. The bottom roughness has been idealized by an array of vertical, rigid cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Two-dimensional density fields have been obtained. Experimental results suggest that enhancement of the entrainment/dilution of the current can occur due to two different mechanisms. For a sparse configuration, the dense current propagates between the cylinders and the entrainment is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration, the dense current rides on top of the cylinders and the dilution is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. For low values of the ratio of the cylinder to lock height \(\lambda \) the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of \(\lambda \).     

A numerical (LES) investigation of a shallow-water, mid-latitude, tidally-driven boundary layer

We investigate turbulent mixing in a tidally driven, mid-latitude, shallow-water basin. The study is carried out numerically at a laboratory-scale, using large-eddy simulation. We compared the results of the simulation with those of a correspondent purely oscillatory flow (Stokes boundary layer). The effect of rotation on the flow dynamics is twofold. First, rotation gives rise to a mean spanwise flow that concurs to redistribute the turbulent energy among the Reynolds stresses, in particular between the horizontal directions, thus increasing the mixing across the water column and thickening the layer where developed turbulence is observable. Second, the presence of the horizontal component of the background vorticity (latitude effect) breaks the symmetry between the two semi-cycles of the oscillation, since turbulence results suppressed/enhanced during the first/second semi-cycle. These two effects significantly modify the turbulent characteristics with respect to the purely oscillating flow, although the mechanisms that generates turbulence present similar features. The qualitative agreement between our results and some measurements carried out in two sites with characteristics similar to the case analyzed suggests that the outcomes here provided may be of general use for the analysis of mid-latitude, neutrally stratified, shallow-water basins mainly driven by semi-diurnal tidal currents.     

A mesoscale vortex in a small stratified lake

A mesoscale vortex structure in the small stratified Lake Stechlin has been revealed by field experiments with satellite-tracked quasi-lagrangian drifters. The vortex with a radius of about 200 m drifted at 300 m/day along the western bight of the lake with nearly constant rotation speed of 3 cpd. Analysis of kinematical properties of the vortex motion demonstrates solid body character of rotation. Extrapolation of the vortex drift trajectory over the period preceding the observations combined with data on local winds and seiche dynamics has allowed tracing the vortex fate from its generation point. The normal modes analysis of the internal seiching in the lake reveals the vortex generation mechanism to be the interaction of certain seiche modes with local bottom topography and suggests generation of the mesoscale vortices to be the a regular feature of the lake circulation. Analysis of vorticity suggests additional energy supply to rotational flow, possibly from inverse cascading of small-scale turbulent motions—a feature typical for quasi-2D turbulence. The vortices can play an important role in the energy transport from basin-scale motions to small-scale boundary mixing. They can also contribute significantly to the horizontal heterogeneity of phyto- and zooplankton distribution as well as to the transport of dissolved matter such as nutrients between littoral and profundal areas. The topographically generated traveling vortices represent an analog of the synoptic eddies in the Ocean and in the Atmosphere, whereas their role in the lake hydrodynamics is practically unknown.     

A Model of the Thermal Bar in the Rotating Frame Including Vertically Non-Uniform Heating

Small bottom slope, inviscid solutions are found for a model of the temperature and circulation structure of the thermal bar system. This model includes Coriolis effects, a vertically non-uniform heat input and is axisymmetric. The model also includes general topography and time dependent heating. These solutions include inertial oscillations that have a significant effect on the circulation, especially for the case when the heating is instantaneously applied.     

3D numerical modelling of turbidity currents

During floods, the density of river water usually increases due to a subsequent increase in the concentration of the suspended sediment that the river carries, causing the river to plunge underneath the free surface of a receiving water basin and form a turbidity current that continues to flow along the bottom. The study and understanding of such complex phenomena is of great importance, as they constitute one of the major mechanisms for suspended sediment transport from rivers into oceans, lakes or reservoirs. Unlike most of the previous numerical investigations on turbidity currents, in this paper, a 3D numerical model that simulates the dynamics and flow structure of turbidity currents, through a multiphase flow approach is proposed, using the commercial CFD code FLUENT. A series of numerical simulations that reproduce particular published laboratory flows are presented. The detailed qualitative and quantitative comparison of numerical with laboratory results indicates that apart from the global flow structure, the proposed numerical approach efficiently predicts various important aspects of turbidity current flows, such as the effect of suspended sediment mixture composition in the temporal and spatial evolution of the simulated currents, the interaction of turbidity currents with loose sediment bottom layers and the formation of internal hydraulic jumps. Furthermore, various extreme cases among the numerical runs considered are further analyzed, in order to identify the importance of various controlling flow parameters.     

Modelling hydraulic jump using the bubbly two-phase flow method

Hydraulic jumps have complex flow structures, characterised by strong turbulence and large air contents. It is difficult to numerically predict the flows. It is necessary to bolster the existing computer models to emphasise the gas phase in hydraulic jumps, and avoid the pitfall of treating the phenomenon as a single-phase water flow. This paper aims to improve predictions of hydraulic jumps as bubbly two-phase flow. We allow for airflow above the free surface and air mass entrained across it. We use the Reynolds-averaged Navier–Stokes equations to describe fluid motion, the volume of fluid method to track the interface, and the k–ε model for turbulence closure. A shear layer is shown to form between the bottom jet flow and the upper recirculation flow. The key to success in predicting the jet flow lies in formulating appropriate bottom boundary conditions. The majority of entrained air bubbles are advected downstream through the shear layer. Predictions of the recirculation region’s length and air volume fraction within the layer are validated by available measurements. The predictions show a linear growth of the shear layer. There is strong turbulence at the impingement, and the bulk of the turbulence kinetic energy is advected to the recirculation region via the shear layer. The predicted bottom-shear-stress distribution, with a peak value upstream of the toe of the jump and a decaying trend downstream, is realistic. This paper reveals a significant transient bottom shear stress associated with temporal fluctuations of mainly flow velocity in the jump. The prediction method discussed is useful for modelling hydraulic jumps and advancing the understanding of the complex flow phenomenon.     

A simplified approach to address turbulence modulation in turbidity currents as a response to slope breaks and loss of lateral confinement

Turbidity currents traversing canyon-fan systems flow over bed slopes that decrease in the downstream direction. This slope decrease eventually causes turbidity currents to decelerate and enter a net-depositional mode. When the slope decrease is relatively rapid in the downstream direction, the turbidity current undergoes a concomitantly rapid and substantial transition. Similar conditions are found when turbidity currents debouch to fan systems with loss of lateral confinement. In this work a simplified approach to perform direct numerical simulation of continuous turbidity currents undergoing slope breaks and loss of lateral confinement is presented and applied to study turbulence modulation in the flow. The presence of settling sediment particles breaks the top–bottom symmetry of the flow, with a tendency to self-stratify. This self-stratification damps turbulence, particularly near the bottom wall, affecting substantially the flow’s ability to transport sediment in suspension. This work reports results on two different situations: turbidity currents driven by fine and coarser sediment flowing through a decreasing slope. In the case of fine sediment, after the reduction in the slope of the channel, the flow remains turbulent with only a modest influence on turbulence statistics. In the case of coarse sediments, after the change in slope, turbulence is totally suppressed.     

Oil spreading in instantaneous and continuous spills on rotating earth

The effect of the Coriolis force on the oil spill spreading in the gravity-viscous regime is examined. A new shallow water model for the transport and spreading of oil slick of arbitrary shape is described in which the Coriolis force is included in the momentum equations and the oil–water friction is parameterized in a frame of the boundary layer theory including the Ekman friction. The numerical Lagrangian method based on smoothed particle dynamics is described. New similarity solutions of the model equations are obtained for unidirectional and axisymmetric spreading in gravity-viscous, gravity-turbulent and gravity-viscous-rotational regimes for instantaneous as well as continuous releases. The numerical simulation extends these results for the case of continuous release in the presence of currents. It was shown that Coriolis term in the momentum equation can be omitted if slick thickness is much less of the laminar Ekman layer thickness. However, the Ekman friction should be retained for slicks of any thickness for larger times. The Ekman friction results in the essential slowdown of the spreading as well as in the deflection of the oil spreading velocity at 45° from the direction of velocity in the non-rotation case. Numerical simulations of large-scale spills showed that after the 2?days the slick area with the Coriolis effect was approximately less than half of that without rotation. Therefore, the earth rotation can be also important in the oil weathering.     

Genetic variation among populations of Mytilus spp. in eastern Newfoundland

Small-scale population densities of tidal creek eastern mudsnails, Ilyanassa obsoleta Say (studied in 1986 and in 1992 at West Meadow Creek, Stony Brook, New York) corresponded more to variation in water flow velocity than to surface sediment chlorophyll a. Higher densities were found at low flow sites. Short-term behavioral responses are likely to be responsible for density variation. Experiments using laboratory flumes and field observations both demonstrated that the snails responded to strong flow by burrowing into the substratum. Burrowing may prevent dislodgment from the sediment surface, but it also appears to be disadvantageous since burrowed mudsnails have smaller amounts of food in their guts. Snails released in sites of periodic high flow conditions moved greater distances and were soon found near the quiet-water periphery of the creek, whereas snails released at the quiet-water periphery moved far less. It is not clear whether movement from the high flow site was through crawling or through hydrodynamic transport. Laboratory flume experiments demonstrated an active crawling movement towards areas of lower current velocity. This evidence suggests that strong bottom flow in the creek center results in a combined response of burial to avoid dislodgment and a net movement towards quiet water, which reduces exposure to the high velocity conditions of the creek center.     

Stratified flow interactions with a suspended canopy

Field observations of the interactions between a stratified flow and a canopy suspended from the free surface above a solid boundary are described and analysed. Data were recorded in and around the canopy formed by a large long-line mussel farm. The canopy causes a partial blockage of the water flow, reducing velocities in the upper water column. Deceleration of the approaching flow results in a deepening of isopycnals upstream of the canopy. Energy considerations show that the potential for an approaching stratified flow to be diverted beneath a porous canopy is indicated by a densimetric Froude number. Strong stratification or low-velocities inhibit vertical diversion beneath the canopy, instead favouring a horizontal diversion around the sides. The effect on vertical mixing is also considered with a shear layer generated beneath the canopy and turbulence generated from drag within the canopy. In the observations, stratification is shown to be of sufficient strength to limit the effectiveness of the first mixing process, while the turbulence within the canopy is likely to enhance vertical exchange. Velocity and temperature microstructure measurements are used to investigate the effect of the canopy on turbulent dissipation and show that dissipation is enhanced within the canopy.     

Flow Dynamics in Eccentrically Rotating Flasks Used for Dispersant Effectiveness Testing

The evaluation of dispersant effectiveness used for oil spills is commonly done using tests conducted in laboratory flasks. We used a Hot Wire Anemometer (HWA) to characterize mixing dynamics in the Swirling Flask (SF) and the Baffled Flask (BF), the latter is being considered by the EPA to replace the prior to test dispersant effectiveness in the laboratory. Five rotation speeds of the orbital shaker carrying the flasks were considered, Ω = 50, 100, 150, 175 and 200 rpm. The radial and azimuthal water speeds were measured for each Ω. It was found that the flow in the SF is, in general, two-dimensional changing from horizontal at low Ω to axi-symmetric at high Ω. The flow in the BF appeared to be three-dimensional at all rotation speeds. This indicates that the BF is more suitable for representing the (inherently) 3-D flow at sea. In the SF, the speeds and energy dissipation rates ɛ increased gradually as the rotation speed increased. Those in the BF increased sharply at rotation speeds greater than 150 rpm. At 200 rpm, the Kolmogorov scale (i.e., size of smallest eddies) was about 250 and 50 μm in the SF and BF, respectively. Noting that the observed droplet sizes of dispersed oils range from 50 to 400 μm (hence most of it is less than 250 μm), one concludes that the mixing in the SF (even at 200 rpm) is not representative of the vigorous mixing occurring at sea.     

Removing the boundary influence on negatively buoyant jets

A comprehensive laboratory study of negatively buoyant discharges is presented. Unlike previous studies, here the focus is on generating data sets where influences of the bottom boundary have been eliminated. There are significant discrepancies in the published dilution data for these flows and a contributing factor is the large variation in the bottom boundary condition. A Laser-induced Fluorescence system is employed to gather flow spread, peak concentration (minimum dilution) and trajectory data for a wide range of densimetric Froude numbers and initial discharge angles. Data from these experiments are compared with previously published data, along with predictions from integral models and a revised form of the previously published semi-analytical solutions. The new data sets are not distorted by mixing processes associated with the bottom boundary and therefore provide the basis for more meaningful assessments of the predictive capabilities of existing models, given that the influences of the bottom boundary on contaminant mixing are not incorporated into these models. In general the models assessed are able to predict key geometric quantities with reasonable accuracy, but their minimum dilution predictions are conservative. Importantly dilution at the return point shows a strong dependence on the initial discharge angle and this could have important implications for the design of discharge systems.     

A review of gravity currents formed by submerged single-port discharges in inland and coastal waters

In this paper, the authors review the current state of the science on the dynamics of gravity currents generated by positively and negatively buoyant jet discharges from submerged round outfalls (i.e., a point source) in inland and coastal waters. Specifically, this article focuses on describing gravity currents occurring at both the bottom boundary and the free surface of the receiving fluid. The manmade discharge operations generating both types of gravity currents and their significance to sustainability of the surrounding hydro-environment are first described. The authors then summarize the flow regimes characteristics of these discharges before becoming gravity currents and how those flow regimes influence the dynamics of the gravity currents. The gravity current dynamics in the calm receiving waters are then analyzed. This analysis is followed by an analysis of the influence of the hydrodynamic forces (e.g., currents, turbulence, waves) on the dynamics of gravity currents. Finally, the authors review quantitative modeling approaches for different forms of gravity current, and identify the current knowledge gaps and research needs.