Front velocity and structure of bottom gravity currents with a low volume of release propagating in a porous medium

The paper reports results of large eddy simulations of lock exchange compositional gravity currents with a low volume of release advancing in a horizontal, long channel. The channel contains an array of spanwise-oriented square cylinders. The cylinders are uniformly distributed within the whole channel. The flow past the individual cylinders is resolved by the numerical simulation. The paper discusses how the structure and evolution of the current change with the main geometrical parameters of the flow (e.g., solid volume fraction, ratio between the initial height of the region containing lock fluid and the channel depth, ratio between the initial length and height of the region containing lock fluid) and the Reynolds number. Though in all cases with a sufficiently large solid volume fraction the current transitions to a drag-dominated regime, the value of the power law coefficient, α, describing the front position’s variation with time (x _f  ~ t ^α , where t is the time measured from the removal of the lock gate) is different between full depth cases and partial depth cases. The paper also discusses how large eddy simulation (LES) results compare with findings based on shallow-water equations. In particular, LES results show that the values of α are not always equal to values predicted by shallow water theory for the limiting cases where the current height is comparable, or much smaller, than the channel depth.     

Numerical simulation of water mixing and renewals in the Barcelona harbour area: the winter season

In the present paper, we use numerical simulation to investigate currents, mixing and water renewal in Barcelona harbour under typical conditions of wind forcing for the winter season. This site is of particular importance due to the interplay between touristic and commercial activities, requiring detailed and high-definition studies of water quality within the harbour. We use Large Eddy Simulation (LES) which directly resolves the anisotropic and energetic large scales of motion and parametrizes the small, dissipative, ones. Small-scale turbulence is modelled by the anisotropic Smagorinsky model (ASM) to be employed in presence of large cell anisotropy. The complexity of the harbour is modelled using a combination of curvilinear, structured, non-staggered grid and the immersed boundary method. Boundary conditions for wind and currents at the inlets of the port are obtained from in-situ measurements. Analysis of the numerical results is carried out based on both instantaneous and time-averaged velocity fields. First- and second-order statistics, such as turbulent kinetic energy and horizontal and vertical eddy viscosities, are calculated and their spatial distribution is discussed. The study shows the presence of intense current in the narrow and elongated part of the harbour together with sub-surface along-shore elongated rolling structures (with a time scale of a few hours), and they contribute to the vertical water mixing. Time-averaged velocity field reveals intense upwelling and downwelling zones along the walls of the harbour. The analysis of second-order statistics shows strong inhomogeneity of turbulent kinetic energy and horizontal and vertical eddy viscosities in the horizontal plane, with larger values in the regions characterized by stronger currents. The water renewal within the port is quantified for particular sub-domain regions, showing that the complexity of the harbour is such that certain in-harbour basins have a water renewal of over five days, including the yacht marina area. The LES solution compares favourably with available current-meter data. The LES solution is also compared with a RANS solution obtained in literature for the same site under the same forcing conditions, the comparison demonstrating a large sensitivity of properties to model resolution and frictional parametrization.     

LES validation of lock-exchange density currents interacting with an emergent bluff obstacle

Environmental Fluid Mechanics - We address the capability of large eddy simulation (LES) to predict the physics of density currents interacting with bluff obstacles. Most density currents of...     

Compound channel flow with a longitudinal transition in hydraulic roughness over the floodplains

Flows in a compound open-channel (two-stage geometry with a main channel and adjacent floodplains) with a longitudinal transition in roughness over the floodplains are experimentally investigated in an 18 m long and 3 m wide flume. Transitions from submerged dense vegetation (meadow) to emergent rigid vegetation (wood) and vice versa are modelled using plastic grass and vertical wooden cylinders. For a given roughness transition, the upstream discharge distribution between main channel and floodplain (called subsections) is also varied, keeping the total flow rate constant. The flows with a roughness transition are compared to flows with a uniformly distributed roughness over the whole length of the flume. Besides the influence of the downstream boundary condition, the longitudinal profiles of water depth are controlled by the upstream discharge distribution. The latter also strongly influences the magnitude of the lateral net mass exchanges between subsections, especially upstream from the roughness transition. Irrespective of flow conditions, the inflection point in the mean velocity profile across the mixing layer is always observed at the interface between subsections. The longitudinal velocity at the main channel/floodplain interface, denoted \(U_{int}\), appeared to be a key parameter for characterising the flows. First, the mean velocity profiles across the mixing layer, normalised using \(U_{int}\), are superimposed irrespective of downstream position, flow depth, floodplain roughness type and lateral mass transfers. However, the profiles of turbulence quantities do not coincide, indicating that the flows are not fully self-similar and that the eddy viscosity assumption is not valid in this case. Second, the depth-averaged turbulent intensities and Reynolds stresses, when scaled by the depth-averaged velocity \(U_{d,int}\) exhibit two plateau values, each related to a roughness type, meadow or wood. Lastly, the same results hold when scaling by \(U_{d,int}\) the depth-averaged lateral flux of momentum due to secondary currents. Turbulence production and magnitude of secondary currents are increased by the presence of emergent rigid elements over the floodplains. The autocorrelation functions show that the length of the coherent structures scales with the mixing layer width for all flow cases. It is suggested that coherent structures tend to a state where the magnitude of velocity fluctuations (of both horizontal vortices and secondary currents) and the spatial extension of the structures are in equilibrium.     

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.     

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (\(\partial \overline{u}/\partial z < 0\)) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (\(- \overline{{u^{\prime}w^{\prime}}} < 0\)) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.     

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.     

Mass-based depth and velocity scales for gravity currents and related flows

Gravity driven flows on inclines can be caused by cold, saline or turbid inflows into water bodies. Another example are cold downslope winds, which are caused by cooling of the atmosphere at the lower boundary. In a well-known contribution, Ellison and Turner (ET) investigated such flows by making use of earlier work on free shear flows by Morton, Taylor and Turner (MTT). Their entrainment relation is compared here with a spread relation based on a diffusion model for jets by Prandtl. This diffusion approach is suitable for forced plumes on an incline, but only when the channel topography is uniform, and the flow remains supercritical. A second aspect considered here is that the structure of ET’s entrainment relation, and their shallow water equations, agrees with the one for open channel flows, but their depth and velocity scales are those for free shear flows, and derived from the velocity field. Conversely, the depth of an open channel flow is the vertical extent of the excess mass of the liquid phase, and the average velocity is the (known) discharge divided by the depth. As an alternative to ET’s parameterization, two sets of flow scales similar to those of open channel flows are outlined for gravity currents in unstratified environments. The common feature of the two sets is that the velocity scale is derived by dividing the buoyancy flux by the excess pressure at the bottom. The difference between them is the way the volume flux is accounted for, which—unlike in open channel flows—generally increases in the streamwise direction. The relations between the three sets of scales are established here for gravity currents by allowing for a constant co-flow in the upper layer. The actual ratios of the three width, velocity, and buoyancy scales are evaluated from available experimental data on gravity currents, and from field data on katabatic winds. A corresponding study for free shear flows is referred to. Finally, a comparison of mass-based scales with a number of other flow scales is carried out for available data on a two-layer flow over an obstacle. Mass-based flow scales can also be used for other types of flows, such as self-aerated flows on spillways, water jets in air, or bubble plumes.     

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.     

A numerical model of wave- and current-driven nutrient uptake by coral reef communities

We developed a numerical model capable of simulating the spatial zonation of nutrient uptake in coral reef systems driven by hydrodynamic forcing (both from waves and currents). Relationships between nutrient uptake and bed stress derived from flume and field studies were added to a four-component biogeochemical model embedded within a three-dimensional (3-D) hydrodynamic ocean model coupled to a numerical wave model. The performance of the resulting coupled physical-biogeochemical model was first evaluated in an idealized one-dimensional (1-D) channel for both a pure current and a combined wave-current flow. Waves in the channel were represented by an oscillatory flow with constant amplitude and frequency. The simulated nutrient concentrations were in good agreement with the analytical solution for nutrient depletion along a uniform channel, as well as with existing observations of phosphate uptake across a real reef flat. We then applied this integrated model to investigate more complex two-dimensional (2-D) nutrient dynamics, firstly to an idealized coral reef-lagoon morphology, and secondly to a realistic section of Ningaloo Reef in Western Australia, where nutrients were advected into the domain via alongshore coastal currents. Both the idealized reef and Ningaloo Reef simulations showed similar patterns of maximum uptake rates on the shallow forereef and reef crest, and with nutrient concentration decreasing as water flowed over the reef flat. As a result of the cumulative outflow of nutrient-depleted water exiting the reef channels and then being advected down the coast by alongshore currents, both reef simulations exhibited substantial alongshore variation in nutrient concentrations. The coupled models successfully reproduced the observed spatial-variability in nitrate concentration across the Ningaloo Reef system.     

Large eddy simulation of flow and scalar transport in a vegetated channel

Predicting flow and mass transport in vegetated regions has a broad range of applications in ecology and engineering practice. This paper presents large eddy simulation (LES) of turbulent flow and scalar transport within a fully developed open-channel with submerged vegetation. To properly represent the scalar transport, an additional diffusivity was introduced within the canopy to account for the contribution of stem wakes, which were not resolved by the LES, to turbulent diffusion. The LES produced good agreement with the velocity and concentration fields measured in a flume experiment. The simulation revealed a secondary flow distributed symmetrically about the channel centerline, which differed significantly from the circulation in a bare channel. The secondary circulation accelerated the vertical spread of the plume both within and above the canopy layer. Quadrant analysis was used to identify the form and shape of canopy-scale turbulent structures within and above the vegetation canopy. Within the canopy, sweep events contributed more to momentum transfer than ejection events, whereas the opposite occurred above the canopy. The coherent structures were similar to those observed in terrestrial canopies, but smaller in scale due to the constraint of the water surface.     

Steady Shallow-Water Current and Solute Transport around a Semi-Conical Headland

Laboratory experiments have been carried out to investigate the effects of a sloping wall headland on the flow characteristics and the associated concentration distributions from a point source around the headland. A semi-conical headland with a slope of 1:2 was set up in a flow basin, 4.8 m long and 3.8 m wide. In this paper, the experimental results of a steady shallow-water current are reported. Three dimensional flow velocities in the basin were measured using Sontek-ADV instrument. The dye concentration levels in the basin were measured by two fluorometers. The experimental results showed a large-scale re-circulation region behind the semi-conical headland. The peak turbulence energy, at about 53% of the local kinetic flow energy, coincides with the region of high velocity gradient. Significant vertical flows were observed around the area near the downhill slope of the headland, with a maximum ratio of vertical to horizontal velocities being about 22%. Such relatively significant vertical scouring velocities, coupled with strong turbulence energy and high horizontal velocity gradients in the same region, could cause severe bed erosion. The experimental results have also been compared with the predicted results of a depth-averaged numerical model. The predicted eddy structure and the concentration distribution in the re-circulation area were found to compare favourably with the experimental results. However, the discrepancies in the flow velocities and the concentration levels near the headland were apparent. It was observed that the dye concentration continued to spread in the cross-stream direction after passing the headland, whereas only a limited extent of the lateral spreading was predicted by the numerical model further downstream of the headland.     

Simulation of Ekman Boundary Layers by Large Eddy Model with Dynamic Mixed Subfilter Closure

Theoretical analysis of boundary layer turbulence has suggested a feasibility of sufficiently accurate turbulence resolving simulations at relatively coarse meshes. However, large eddy simulation (LES) codes, which employ traditional eddy-viscosity turbulence closures, fail to provide adequate turbulence statistics at coarse meshes especially within a surface layer. Manual tuning of parameters in these turbulence closures may correct low order turbulence statistics but severely harms spectra of turbulence kinetic energy (TKE). For more than decade, engineering LES codes successfully employ dynamic turbulence closures. A dynamic Smagorinsky turbulence closure (DSM) has been already tried in environmental LES. The DSM is able to provide adequate turbulence statistics at coarse meshes but it is not completely consistent with the LES equations. This paper investigates applicability of an advanced dynamic mixed turbulence closure (DMM) to simulations of Ekman boundary layers of high Reynolds number flows. The DMM differs from the DSM by explicit calculation of the Leonard term in the turbulence stress tensor. The Horizontal Array Turbulence Study (HATS) field program has revealed that the Leonard term is indeed an important component of the real turbulence stress tensor. This paper presents validation of a new LES code LESNIC. The study shows that the LES code with the DMM provides rather accurate low order turbulence statistics and the TKE spectra at very coarse meshes. These coarse LES maintain more energetic small scale fluctuations of velocity especially within the surface layer. This is critically important for success of simulations. Accurate representation of higher order turbulence statistics, however, requires essentially better LES resolution. The study also shows that LES of the Ekman boundary layer cannot be directly compared with conventionally neutral atmospheric boundary layers. The depth of the boundary layer is an important scaling parameter for turbulence statistics.     

Mass exchange in a shallow channel flow with a series of groynes: LES study and comparison with laboratory and field experiments

The exchange of dissolved matter between a straight open channel and a series of shallow embayments present at one of its sides is investigated using large eddy simulation (LES). The direct link between the mechanism of mass exchange and the dynamics of coherent structures is demonstrated. It is shown that for the geometrical configuration considered in the present study, the mass exchange process is very non-uniform over the depth in the vicinity of the channel–embayment interface. Most of the contaminant is ejected from the embayments close to the free surface. The amount of contaminant re-entrained into the embayments situated downstream of the one in which contaminant was introduced is quantified. The mass exchange coefficient predicted by LES does not vary significantly with the embayment rank and is in very good agreement with the one predicted by the model proposed by Weitbrecht et al. (J Hydraul Eng 134(2):173–183, 2008) based on the value of a dimensionless morphometric groyne-field parameter. Field experiments were purposely performed in a natural stream with embayments whose length over width ratios were close to the ratio in the LES study. The concentration fields predicted by LES are compared with video-records of colored dye used to visualize the mass exchange in the field experiment. It is shown that, for both LES and the field experiment, the dominant passage frequency of the eddies inside the interfacial mixing layer is well predicted by the analytical model of Sukhodolov and Sukhodolova (in: Cowen et al (eds) Hydraulic measurements & experimental methods. Proceedings of international conference, Lake Placid, USA, pp 172–177, 2007). The model is then used to scale the time in the LES animations and field video-records showing the temporal evolution of the concentration field. The results of the comparison indicate several similarities in the mixing process, despite the differences in the bathymetry and the large difference in the Reynolds number between LES and the field experiment. This proves the usefulness of performing detailed LES and laboratory studies in well-controlled environments to understand mass-exchange processes around river groyne fields.     

Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model

We present a method for estimating the upper bound of the horizontal eddy diffusivity using a non-stationary Lagrangian stochastic model. First, we identify a mixing barrier using a priori evidence (e.g., aerial photographs or satellite imagery) and using a Lagrangian diagnostic calculated from observed or modeled spatially non-trivial, time-dependent velocities [for instance, the relative dispersion (RD) or finite time Lyapunov exponent (FDLE)]. Second, we add a stochastic component to the observed (or modeled) velocity field. The stochastic component represents sub-grid stochastic diffusion and its mean magnitude is related to the eddy diffusivity. The RD of Lagrangian trajectories is computed for increasing values of the eddy diffusivity until the mixing barrier is no longer present. The value at which the mixing barrier disappears provides a dynamical estimate of the upper bound of the eddy diffusivity. The erosion of the mixing barrier is visually observed in numerical simulations, and is quantified by computing the kurtosis of the RD at each value of the eddy diffusivity. We demonstrate our method using the double gyre circulation model and apply it to high frequency (HF) radar observations of surface currents in the Gulf of Eilat.     

LE of shallow mixing interfaces: A review

Eddy-resolving techniques have become a powerful tool to investigate shallow flows at both laboratory and field scale. In this paper several examples are given where high-resolution 3D numerical simulation are used to investigate the spatial development of mixing interfaces (MIs) forming in shallow environments like open channels with idealized and natural bathymetry where the bed friction plays a major role in the spatial development of the MI and associated large-scale turbulence. The focus is on the coherent structures forming within the MI and in its vicinity that control the momentum and mass exchange and heat transfer between the two sides of the MI. Examples include: (1) a MI developing in a flat-bed open channel downstream of a splitter wall separating two parallel fully-turbulent streams of different velocities, (2) a MI developing in a flat-bed open channel downstream of a 60 \(^{\circ }\) wedge separating two non-parallel fully turbulent streams of different velocities, (3) a MI developing downstream of a river confluence for cases with a large and, respectively, a small difference between the mean velocities of the two streams. Stratification effects due to unequal densities of the two incoming streams are also discussed, (4) a MI developing between a main rectangular straight channel and a series of shallow embayments present at one of the channel banks. Besides using available experimental data to demonstrate that eddy resolving techniques can accurately predict the structure of the MI and its development, the paper discusses new insights into the physics of these flows obtained based on the simulations. The paper also provides an overview of the main numerical approaches that can be used to simulate the unsteady dynamics of the large scale turbulence in flows containing shallow MIs.     

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.     

Advection and resulting CO2 exchange uncertainty in a tall forest in central Germany

Potential losses by advection were estimated at Hainich Forest, Thuringia, Germany, where the tower is located at a gentle slope. Three approaches were used: (1) comparing nighttime eddy covariance fluxes to an independent value of total ecosystem respiration by bottom-up modeling of the underlying processes, (2) direct measurements of a horizontal CO2 gradient and horizontal wind speed at 2 m height in order to calculate horizontal advection, and (3) direct measurements of a vertical CO2 gradient and a three-dimensional wind profile in order to calculate vertical advection. In the first approach, nighttime eddy covariance measurements were compared to independent values of total ecosystem respiration by means of bottom-up modeling of the underlying biological processes. Turbulent fluxes and storage term were normalized to the fluxes calculated by the bottom-up model. Below a u(*) threshold of 0.6 m/s the normalized turbulent fluxes decreased with decreasing u(*), but the flux to the storage increased only up to values less than 20% of the modeled flux at low turbulence. Horizontal advection was measured by a horizontal CO2 gradient over a distance of 130 m combined with horizontal wind speed measurements. Horizontal advection occurred at most of the evenings independently of friction velocity above the canopy. Nevertheless, horizontal advection was higher when u(*) was low. The peaks of horizontal advection correlated with changes in temperature. A full mass balance including turbulent fluxes, storage, and horizontal and vertical advection resulted in an increase of spikes and scatter but seemed to generally improve the results from the flux measurements. The comparison of flux data with independent bottom-up modeling results as well as the direct measurements resulted in strong indications that katabatic flows along the hill slope during evening and night reduces the measured apparent ecosystem respiration rate. In addition, anabatic flows may occur during the morning. We conclude that direct measurements of horizontal and vertical advection are highly necessary at sites located even on gentle hill slopes.     

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.