Froude scaling limitations in modeling of turbidity currents

The scaling problem associated with the modeling of turbidity currents has been recognized but is yet to be explored systematically. This paper presents an analysis of the dimensionless governing equations of turbidity currents to investigate the scale effect. Three types of flow conditions are considered: (i) conservative density current; (ii) purely depositional turbidity current; and (iii) mixed erosional/depositional turbidity current. Two controlling dimensionless numbers, the Froude number and the Reynolds number, appear in the non-dimensional governing equations. When densimetric Froude similarity is satisfied, the analysis shows that the results would be scale-invariant for conservative density current under the rough turbulent condition. In the case of purely depositional flows, truly scale-invariant results cannot be obtained, as the Reynolds-mediated scale effects appear in the bottom boundary conditions of the flow velocity and sediment fall velocity. However, the scale effect would be relatively modest. The Reynolds effect becomes more significant for erosional or mixed erosional/depositional turbidity currents as Reynolds-mediated scale effects also appear in the sediment entrainment relation. Numerical simulations have been conducted at three different scales by considering densimetric Froude scaling alone as well as combined densimetric Froude and Reynolds similarity. Simulation results confirm that although the scaling of densimetric Froude number alone can produce scale-invariable results for conservative density currents, variations occur in the case of turbidity currents. The results become scale invariant when densimetric Froude and Reynolds similarities are satisfied simultaneously.     

Mixing dynamics of turbidity currents interacting with complex seafloor topography

Direct Numerical Simulations are employed to investigate the mixing dynamics of turbidity currents interacting with seamounts of various heights. The mixing properties are found to be governed by the competing effects of turbulence amplification and enhanced dissipation due to the three-dimensional topography. In addition, particle settling is seen to play an important role as well, as it affects the local density stratification, and hence the stability, of the current. The interplay of these different mechanisms results in the non-monotonic dependence of the mixing behavior on the height of the seamount. Regions of dilute lock fluid concentration generally mix more intensely as a result of the seafloor topography, while concentrated lock fluid remains relatively unaffected. For long times, the strongest mixing occurs for intermediate bump heights. Particle settling is seen to cause turbidity currents to mix more intensely with the ambient than gravity currents.     

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.     

Structure of a dense release produced by varying initial conditions

Buoyancy driven flows such as gravity currents, present in nature and human made applications, are conveyors of particles or dissolved substances for long distances with clear implications for the environment. This transport depends on the triggering conditions of the current. Gravity currents are experimentally simulated under varying initial conditions by combining three different initial buoyancies and five volumes of dense fluid released. The horizontal and vertical structures of the gravity currents are analysed and it is shown that the variation on the initial configuration is conditioning for these. Vertical transport through the gravity current is influenced at the bottom by the solid wall over which the current flows, and at the upper interface by the contact with the ambient water. The relative contribution of shear stress at the bottom and at the upper interfaces are estimated and analysed in terms of the initial triggering conditions of the current; these two compete with the buoyancy, the driver of the current, determining mixing and entrainment. By using a proper parametrization, which accounts for both initial volume of release and location of the observation position relative to the lock, a relation between the resistance at the bottom and at the upper interfaces with the initial conditions of release (i.e. the lock-length) has been found; this is found to be independent of the initial density in the lock. The present study shows that the variation of the initial conditions have consequences on (1) the configuration of the currents and on (2) the hydrodynamics of the currents, including mass and momentum exchanges, which are in addition mutually dependent.     

Flow structure of unconfined turbidity currents interacting with an obstacle

Driven by a growing importance to engineered structures, investigating the flow characteristics of turbidity currents interacting with a basal obstruction has become popular over the last three decades. However, research has focused on confined studies or numerical simulations, whereas in situ turbidity currents are typically unconfined. The present study investigates experimentally the velocity and turbulence structure of an unconfined turbidity current, in the immediate regions surrounding a rectangular obstacle. Initial density of the current, and substrate condition is varied. Through a novel technique of installing ultrasonic probes within the obstacle, the presence of a velocity recirculation region immediately upstream and downstream of the obstacle is revealed and confirmed with high-resolution imagery. This was found to be comparable to previous confined studies, suggesting that stream-wise velocity profile structure is somewhat independent of confinement. The obstacle was found to reduce velocity and turbulence intensity maxima downstream of the obstacle when compared with unobstructed tests.     

A multidimensional continuum model of fish behavior

A numerical model for the simulation and study of fish behavior is presented. The model, based on continuous representations in both biological and spatial dimensions, has been developed as part of a large Norwegian arctic ecosystems modeling project directed by Professor Jens G. Balchen of the University of Trondheim, Norway. The model describes the migratory behavior of fish, and is capable of incorporating a variety of hypothesized driving forces, such as food density, temperature, light, direction and magnitude of ocean currents, and local fish density. The model relies on standard finite difference numerical methods for solution of the continuum transport equations, and a gradient search conceptualization to determine fish taxis. Two driving forces, food and temperature fields, are used to provide a demonstration of the potentials of the proposed modeling methodology.     

Numerical simulation of particle-driven gravity currents

Particle-driven gravity currents frequently occur in nature, for instance as turbidity currents in reservoirs. They are produced by the buoyant forces between fluids of different density and can introduce sediments and pollutants into water bodies. In this study, the propagation dynamics of gravity currents is investigated using the FLOW-3D computational fluid dynamics code. The performance of the numerical model using two different turbulence closure schemes namely the renormalization group (RNG) ${k-\epsilon}$ scheme in a Reynold-averaged Navier-Stokes framework (RANS) and the large-eddy simulation (LES) technique using the Smagorinsky scheme, were compared with laboratory experiments. The numerical simulations focus on two different types of density flows from laboratory experiments namely: Intrusive Gravity Currents (IGC) and Particle-Driven Gravity Currents (PDGC). The simulated evolution profiles and propagation speeds are compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting the temporal and spatial evolution of intrusive gravity currents. In particular, the simulated propagation speeds are in excellent agreement with experimental results. The simulation results do not show any considerable discrepancies between RNG ${k-\epsilon}$ and LES closure schemes. The FLOW-3D model coupled with a particle dynamics algorithm successfully captured the decreasing propagation speeds of PDGC due to settling of sediment particles. The simulation results show that the ratio of transported to initial concentration C _o /C _i by the gravity current varies as a function of the particle diameter d _s . We classify the transport pattern by PDGC into three regimes: (1) a suspended regime (d _s is less than about 16 μm) where the effect of particle deposition rate on the propagation dynamics of gravity currents is negligible i.e. such flows behave like homogeneous fluids (IGC); (2) a mixed regime (16 μm < d _s <40 μm) where deposition rates significantly change the flow dynamics; and (3) a deposition regime (d _s ?> 40 μm) where the PDGC rapidly loses its forward momentum due to fast deposition. The present work highlights the potential of the RANS simulation technique using the RNG ${k-\epsilon}$ turbulence closure scheme for field scale investigation of particle-driven gravity currents.     

Gravity currents in rotating,wedge-shaped,adverse channels

Results are presented from a series of parametric experimental and analytical studies of the behaviour of dense gravity currents along rotating, up-sloping, wedge-shaped channels. High resolution density profile measurements at fixed cross- and along-channel locations reveal the outflowing bottom gravity currents to adjust to quasi-steady, geostrophically-balanced conditions along the channels, with the outflow layer thickness and cross-channel interface slope shown to scale with the inlet Burger number for all experimental conditions tested. A general analytical solution to the classic rotating hydraulics problem has been developed under the assumption of inviscid, zero-potential-vorticity conditions to model dense water flow through a triangular constriction and thus simulate the vee-channel configurations under consideration. Predictions from this zero-PV model are shown to provide good overall quantitative agreement with experimental measurements obtained both under hydraulically-controlled conditions at the channel exit and for subcritical conditions generated along the channel length. Quantitative discrepancies between measurements and analytical predictions are attributed primarily to assumptions and limitations associated with the zero-PV modelling approach adopted, as well as the to the rapid adjustment in outflow characteristics as the channel exit is approached, as characterised by the along-channel variation in densimetric Froude number for the outflows.     

Turbulent entrainment into fluid mud gravity currents

The entrainment of ambient water into non-Newtonian fluid mud gravity currents was investigated in this study. Constant volume release gravity currents were generated in a lock-exchange tank for a wide range of experimental conditions. A technique similar to the so-called light attenuation technique was used to find the boundary of the current, allowing for the calculation of both temporal and bulk entrainment parameters (in terms of the temporal and bulk entrainment velocities, respectively). It was found that the temporal entrainment velocity is dependent on different parameters in the different propagation phases. The slumping phase begins with an adjustment zone (henceforth, non-established zone) in which the temporal entrainment velocity is not a function of the current front velocity, followed by the established zone in which the temporal entrainment velocity is a function of the current front velocity. This dependence of the temporal entrainment velocity on the current front velocity carries through to the inertia-buoyancy phase. As expected, temporal entrainment velocity in the viscous-buoyancy phase was negligible in comparison to average entrainment velocity in the other phases. It is observed that the temporal entrainment characteristics in the non-established zone is governed by the competition between the entrainment-inhibiting density stratification effects and the entrainment-favouring effects of the Kelvin–Helmholtz billows that are quantified by the Richardson number and the Reynolds number of the gravity current, respectively. In the established zone, Reynolds number effects were observed to dominate over Richardson number effects in dictating temporal entrainment characteristics. A parameterization for the temporal entrainment velocity for non-Newtonian fluid mud gravity currents is developed based upon the experimental observations. This study also found that the bulk entrainment characteristics for the non-Newtonian fluid mud gravity currents can be parameterized by the Newtonian bulk entrainment parameterizations that rely solely on a bulk Richardson number. Interestingly, it was found that the non-Newtonian characteristics of the gravity current have little to no effect on the entrainment of the Newtonian ambient fluid.     

On the role of physical modelling in atmospheric and oceanic forecast

We discuss how physical modelling can be used to reproduce atmospheric or oceanic flows in the laboratory. The similarity conditions for the effects of density stratification and Earth rotation are first presented. Then examples of results obtained on the large ‘Coriolis’ platform in Grenoble are described. These include topographic wakes in a stratified fluid and gravity currents. Physical modelling is not used to get direct results of practical relevance, but rather to test numerical models on specific processes of environmental flows. Therefore it must be performed in close relationship with theory and numerical modelling, using advanced measurement and data assimilation techniques.     

A numerical model of periodically forced circulation near the shore of a lake

Numerical calculations for a model of the near-shore circulation in a lake subject to two diurnal forcing mechanisms are presented. The first mechanism is a heating/cooling term in the heat equation representing the daytime heating and nighttime cooling of the diurnal cycle. The second is a periodic surface stress modelling a sea-breeze/gully wind system typical of some coastal regions. The two forcing mechanisms can either act together or against each other depending on their relative phase. The numerical solutions are compared with previously published analytical solutions and used to explore the extra dynamics associated with non-linear effects (specifically advection). The latter dynamics include the formation of gravity currents and unstable density profiles leading to secondary circulation.     

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.     

Experimental and numerical investigation of density current over macro-roughness

The dynamics of density current over a bottom covered by macro-roughness elements were investigated by laboratory experiments and a computational model using large eddy simulations. The macro-roughness considered had significant size in comparison with the scale of density current. Five different roughness conditions were considered, namely flat bottom (for reference), half spheres, fine gravels, medium gravels, and large gravels. These bottom conditions had variations in roughness element size, shape, angularity, and spatial configuration. The density current was a lock-exchange type with a density difference of 1% between the two fluids initially separated by a gate in the middle. In the computational model, the roughness was captured using two different methods depending on the size of the roughness elements. For the large roughness elements, i.e., the half spheres and the medium and large gravels, an immersed boundary method was used to resolve the surface of each gravel, which was obtained through 3D laser scanning. The realistic and physically correct placement of these scanned objects in the simulation domain was achieved using a computer tool which can detect the collision of rigid bodies and simulate their dynamics. For the fine gravels, a rough wall function was used. The computational model was validated with the data measured in the experiments, including front position and velocity, and point velocity measurement within the current. The results show that density currents over macro-roughness have distinct behavior from those over a smooth boundary. The characteristics (size, angularity, and pavement pattern) of the macro-roughness play a key role in the current development. Macro-roughness significantly retards the front propagation and enhances entrainment.     

Fluid mechanics of the mussel gill: The lateral cilia

Quantitative data on the water currents produced by the ciliary tracts of the gill filaments are needed to understand the fluid mechanics of suspension feeding in bivalves, as well as in other ciliary suspension feeders. This paper investigates the water currents produced by the bands of lateral cilia, as studied on isolated gill filaments, gill fragments, and intact gills of the mussel Mytilus edulis L with severed adductor muscles. The metachronally beating cilia produce oscillatory currents near the oscillating enveloping surface of the ciliary bands and rectilinear currents, the interfilamentary through-currents, farther from the surface. It is suggested that the oscillatory currents play an important role in the fluid mechanical capture of suspended particles. In the intact gill the interfilamentary currents pass the bands of lateral cilia at velocities that are two or more times higher than those generated by the bands of isolated filaments. The mussel gill is compared with an optimized peristaltic pump.     

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.     

Animal-sediment relations in Cape Cod Bay,Massachusetts I. A transect study

Benthic macrofauna and bottom sediments were sampled at 7 stations along a 24 km long onshore-offshore transect ranging in depth from 12 to 42 m in Cape Cod Bay, Massachusetts, USA. High faunal density, biomass and species diversity were recorded at stations densely populated by tubicolous polychaetes. These tube mats bind and stabilize the substratum, providing solid surfaces for attachment of epizoans. Three suspension-feeding species, Euchone incolor (polychaete), Thyasira gouldi (bivalve) and Aeginina longicornis (amphipod), co-occur with deposit-feeding species on muds resuspended by tidal currents. Hydrographic profiles of temperature, salinity and turbidity indicate that resuspended silt-clay particles are entrapped in dense water below the summer thermocline, which persists from mid-April to mid-October. The zone of intersection of the thermocline with the sea floor in about 22 m of water defines a major biofacies-lithofacies transition. This ecotone is characterized by high faunal density, biomass, and species diversity. Benthic populations of macrofauna from Cape Cod Bay are larger than those from Buzzards Bay, Massachusetts, and have a widely different taxonomic and trophic composition.Contribution No. 235 of the Systematics-Ecology Program, Marine Biological Laboratory, Woods Hole, Massachusetts, USA.     

Influence of oceanic factors on long-distance movements of loggerhead sea turtles displaced in the southwest Indian Ocean

The routes of five satellite-tracked loggerhead turtles (Caretta caretta), subjected to an experimental translocation away from their usual migratory routes, have been analysed in relation to the concurrent oceanographic conditions. Remote sensing data on sea surface temperature and height anomalies, as well as trajectories of surface drifters were used, to get simultaneous information on the currents encountered by the turtles during their long-range oceanic movements. Turtles mostly turned out to move in the same direction as the main currents, and their routes were often influenced by circulation features they encountered. A comparison between turtle ground speeds with that of drifters shows that in several instances, the turtles did not drift passively with the currents but contributed actively to the overall movement. Two turtles embarked on an oceanic crossing, probably induced by seasonal changes in surface temperatures, a crossing that was largely determined by the main currents existing in the area.     

Courtship in fast water currents by a male stream goby ( Rhinogobius brunneus) communicates the parental quality honestly

The stream goby Rhinogobius sp. DA (dark color type) shows exclusive paternal care of the eggs. Males court females in the stream current and previous field observations suggest that females favor males that perform their courtship display in faster water currents, and that such males may have high parental ability because of good physical condition. To validate these observations we examined female choice under controlled laboratory conditions. Mate choice experiments indicated clearly that females preferred males that courted in the faster currents, whereas neither sexually different morphological traits, such as body size, nor the water current alone were important. The experiments with food supply treatments indicated that only males of high physical condition are able to court in the fast currents. Furthermore, males that courted in the fast currents achieved good egg survival, whereas males that were unable to court in the currents did not, due to cannibalism of their egg clutch. Thus, the maximum speed of the water current in which a male courts should be indicative of his quality and of the subsequent survival of eggs under his care. We conclude that Rhinogobius sp. DA females utilize the male courtship display in the water current as an honest indicator of parental quality.Communicated by K. LindströmAn erratum to this article can be found at     

Colonisation process of vegetative fragments of <Emphasis Type="Italic">Posidonia oceanica</Emphasis> (L.) Delile on rubble mounds

Seagrass colonise new areas via the dispersion of seeds or vegetative fragments. Independent of the manner of colonization, habitat requirements need to be met for the successful establishment of seagrasses. Here we report on the colonization process of Posidonia oceanica in a highly disturbed area: a gas pipeline trench at Capo Feto (SW Sicily, Italy). A trench dredged through a P. oceanica bed was back-filled with rubble added from dump barges leading to the formation of a series of rubble mounds on the seabed. Over time, these mounds became colonised with P. oceanica. I>. In order to understand the pattern of P. oceanica colonization, shoot density was quantified over 3 years (2001–2003) on different mound locations (crests, sides, valleys). Seagrass coalescence was observed only in valleys between mounds where shoot density averaged 133±50 shoots m⁻², while values for sides and crests were significantly lower (30.5±14 and 5.8±2.6 shoots m⁻², respectively). Although sediment accumulated on both crests and valleys, a significantly thicker sediment layer was recorded in the valleys (9.8±0.4 cm) than on crests (1.1±0.2). Plaster dissolution rate (an indicator of the hydrodynamic regime) tended to decrease from crests to valleys but even in the valleys, the currents were still higher than in the adjacent vegetated control location. This pattern was constant over time and depths. This is the first study to report on P. oceanica vegetative recruitment on artificial rubble after a disturbance event. It appears that the valleys between the rubble mounds are suitable for seagrass recruitment as sediment deposited between the rubble provides the necessary resources for plant settlement and growth. Once the seagrass patches are established, they may start a positive feedback of attenuation of currents, sediment accumulation and seagrass patch expansion.     

Some observations of sea turtle nesting activity in Costa Rica

Low level aerial observations were used to obtain synoptic records of the distribution of sea turtle nesting activity along both coasts of Costa Rica. Pertinent environmental information was simultaneously recorded including beach characteristics, river effluents, and evidence of coastal currents. Other correlative information was obtained from detailed maps, current charts, and climatological data. On the Caribbean coast, as expected, green turtle (Chelonia mydas) nesting was concentrated on the beaches between the Tortuguero and Parismina Rivers. On the Pacific coast, two major nesting beaches for the Pacific ridley Lepidochelys olivacea were found, each having over 100 thousand turtles aggregated offshore during the peak period between September and November. Aggregations were present at least from July through December. Massed nesting occurs each year on these same beaches and the event is known as the salida de flota by the natives of Guanacaste Province. Numerous less important nesting beaches were also found. Nesting density did not correlate well with beach quality but, instead, appeared to be related to the proximity of the beach to offshore currents. Oceanic current systems apparently facilitate the transport of sea turtles to the general vicinity of the important nesting beaches on both coasts of Coata Rica.Contribution No. 1557 from the Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA.