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...     

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.     

An individual-based analysis of the dynamics of two coexisting phytoplankton species in the mixed layer

In marine ecosystems ecological and environmental conditions continuously change, possibly supporting the wide range of phytoplankton species coexisting in aquatic environments. Phytoplankton communities are not homogeneously distributed in the water column due to the spatial and temporal variability of turbulent mixing and the concurrent biological response. In this paper an individual-based model (Lagrangian method) simulating the basic physiology of two coexisting phytoplankton species has been developed. The species, sharing the same availability of light and nutrient resource, are characterized by different photo-physiological parameters. The spatial and temporal evolution of turbulent mixing is simulated introducing vertical profiles of measured eddy diffusivity. Three case studies have been examined to analyze the role of environment–individual interactions in determining bloom conditions for both the selected species. The organisms experience recurrent fluctuations of light, temperature, and nutrient concentration gradients, due to the turbulent mixing in the water column, which have significant effects on the growth of the phytoplankton species. In all the numerical experiments, the temporal and spatial variability of different forcings do not support the prevalence of one species over the other over the time scale typical of a phytoplankton bloom.A well mixed water column favours the growth of both the populations while a variable mixing regime limits their growth reducing the photophysiological differences between the species.     

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.     

Estimation of far-field horizontal and vertical turbulent diffusion coefficients from the concentration field of a wastewater plume near the Akashi Strait

We carried out a field study of the plume discharged by a near-shore wastewater outfall near the Akashi Strait, Japan. Using an Acoustic Doppler Current Profiler and a tow-body CTD, we measured the near-surface salinity and temperature fields in the region throughout an M₂ tidal cycle. We filtered the data in T–S space to remove water masses other than the wastewater, and then used the adiabatic mixing assumption to calculate the concentration of wastewater in the far field of this plume. Averaging the T–S fields of repeated surveys over a time period during which the tidal regime did not change substantially, allowed comparison of the time-averaged plume with the analytical solution for a plume diffusing in both the horizontal and vertical dimensions. The resulting vertical turbulent diffusion coefficients agreed well with those resulting from Thorpe scales determined via a vertically-profiling CTD, as well as with the canonical value for open channel flow of D _z = 0.067hu _*. The corresponding horizontal turbulent diffusion coefficients, however, were two orders of magnitude larger than those typically observed in straight channels, and an order of magnitude larger than those observed in meandering rivers. This is likely a result of enhanced horizontal mixing due to barotropic eddies generated by the interaction of strong tidal flow with headlands and levees, as well as due to the time-varying nature of tidal flow, and baroclinic spreading of the buoyant wastewater plume.     

A closure approach with multi-scale mixing length,and its application to wind and shear stress profiles within the atmospheric boundary layer

A method to determine flow specific first-order closure for the turbulent flux of momentum in the atmospheric boundary layer (ABL) is presented. This is based on the premise that eddy viscosity is a flow rather than a fluid property, and the physically more realistic assumption that the transfer of momentum and other scalar quantities in a turbulent flow takes place by a large, but finite number of length scales, than the often used single length scale, the ‘mixing length’. The resulting eddy viscosity is flow specific and when applied to the study of the ABL, yields the vertical profiles of shear stress and mean wind velocity in good agreement with observations. The method may be extended to other types of turbulent flows, however it should be recognized that each type of flow may yield a different eddy viscosity profile. Using the derived eddy viscosity the paper presents simple analytical solutions of the ABL equations to determine observationally consistent wind speed and shear stress profiles in the ABL for a variety of practical applications including air pollution modelling.     

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.     

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.     

LES validation of urban flow,part II: eddy statistics and flow structures

Time-dependent three-dimensional numerical simulations such as large-eddy simulation (LES) play an important role in fundamental research and practical applications in meteorology and wind engineering. Whether these simulations provide a sufficiently accurate picture of the time-dependent structure of the flow, however, is often not determined in enough detail. We propose an application-specific validation procedure for LES that focuses on the time dependent nature of mechanically induced shear-layer turbulence to derive information about strengths and limitations of the model. The validation procedure is tested for LES of turbulent flow in a complex city, for which reference data from wind-tunnel experiments are available. An initial comparison of mean flow statistics and frequency distributions was presented in part I. Part II focuses on comparing eddy statistics and flow structures. Analyses of integral time scales and auto-spectral energy densities show that the tested LES reproduces the temporal characteristics of energy-dominant and flux-carrying eddies accurately. Quadrant analysis of the vertical turbulent momentum flux reveals strong similarities between instantaneous ejection-sweep patterns in the LES and the laboratory flow, also showing comparable occurrence statistics of rare but strong flux events. A further comparison of wavelet-coefficient frequency distributions and associated high-order statistics reveals a strong agreement of location-dependent intermittency patterns induced by resolved eddies in the energy-production range. The validation concept enables wide-ranging conclusions to be drawn about the skill of turbulence-resolving simulations than the traditional approach of comparing only mean flow and turbulence statistics. Based on the accuracy levels determined, it can be stated that the tested LES is sufficiently accurate for its purpose of generating realistic urban wind fields that can be used to drive simpler dispersion models.     

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.     

Dissipation of Tidal Energy and Associated Mixing in a Wide Fjord

This paper sets out to test the hypothesis that vertical mixing due to the dissipation of the internal tide accounts for a significant proportion of the total vertical mixing in a fjordic basin during a period of deep water isolation. During July and August 1999 two locations in the Clyde Sea were instrumented with moored RD Instruments Acoustic Doppler Current Profilers (ADCPs) and conductivity-temperature-pressure chains: Station C2, near the shallow entrance sill (55 m water depth), and station C1 in the deep basin (155 m water depth). A bottom pressure recorder was also deployed at station C3 by the seaward entrance to the Clyde Sea in the North Channel of the Irish Sea. A Free-falling Light Yo-yo shear microstructure profiler (FLY) was used to measure the dissipation rate of turbulent kinetic energy (TKE) throughout the water column over 25 h at both C1 and C2. These were interspersed with two-hourly conductivity-temperature-depth casts at both sites. The observations show agreement between the dissipation rate of TKE estimated by using a microstructure profiler and that estimated from the decay of the internal tide as measured by the two ADCPs. However, to account for all the implied mixing it is necessary to invoke an additional source of buoyancy flux, the most probable candidate mechanism is enhanced internal wave breaking near the sill and at the sloping boundaries of the deep basin. In addition, the vertical eddy diffusivity estimated from the micro-structure profiler (O(0.5 cm² s^–1) indicates that internal tide induced mixing away from any boundaries contributed significantly to the overall level of mixing which is required to account for the observed evolution of the deep basin water properties.     

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.     

Spatial patterns of ichthyoplankton distribution in relation to hydrographic features in the Northern Benguela region

The spatial distribution of the most abundant eggs and larvae of teleost fish species on the continental shelf and slope off the northern Benguela region was studied in April 1986. The horizontal and vertical distribution of eggs and larvae were analysed together with environmental data, in order to determine patterns of ichthyoplankton distribution. Both species composition and relative egg and larval abundance levels exhibited important latitudinal differences during a period of quiescent upwelling with an intense intrusion of Angolan water into the system. Larval diversity was higher in the northern part of the study area, where, because of the intrusion of the warmer Angolan water, the water column was more stratified than in the southern part, where the affect of upwelling of South Atlantic Central Water was continuous and only a few species spawned. The frontal zone appeared to be a nursery ground for the most important pelagic species of the region:Trachurus trachurus capensis, Engraulis capensis, andSardinops ocellatus. Vertical egg and larval distributions showed evidence of stratification, with highest concentrations located in the uppermost 50 m. In comparison, during periods of intense upwelling, longitudinal gradients were responsible for the horizontal distribution of ichthyoplankton, and the vertical distribution of eggs and larvae were much more extensive because of the greater mixing of the water column.     

Embedded large eddy simulation approach for pollutant dispersion around a model building in atmospheric boundary layer

In the present article, the potential of embedded large eddy simulation (ELES) approach to reliably predict pollutant dispersion around a model building in atmospheric boundary layer is assessed. The performance of ELES in comparison with large eddy simulation (LES) is evaluated in several ways. These include a number of qualitative and quantitative comparisons of time-averaged and instantaneous results with wind tunnel measurements supplemented by statistical data analyses using scatter plots and standard evaluation metrics. Results obtained by both LES and ELES approaches show very good agreement with the experiment. However, addition of turbulence to mean flow at Reynolds averaged Navier–Stokes (RANS)–LES interface in ELES approach not only increases the turbulence intensity, it also results in larger values of turbulent kinetic energy (TKE) as well as a shorter reattachment length in the wake region. Accordingly, higher levels of TKE predicted by ELES increase the local intensity of concentration leading to shorter plume shapes as compared with LES. In general, ELES shows better agreement with experiment on the surfaces of model building and also in the downstream wake region. In terms of computational costs, the CPU time required to obtain statistical values in ELES is about 49 % lower than that of LES and the number of iterations per time step is also reduced by 55 % as compared with LES.     

Stratification and Tidal Current Effects on Larval Transport in the Eastern English Channel: Observations and 3D Modeling

We study how the combination of tides and freshwater buoyancy affects the marine organisms accumulation and horizontal transport in the ROFI system of the eastern English Channel. The Princeton Ocean Model coupled with a particle-tracking module is used to study the migration of fish eggs and larvae under different forcing conditions. Results of modeling are validated against observed concentrations of Flounder (Pleuronectes flesus) larvae. Numerical Lagrangian tracking experiments are performed with passive and active particles, representing sea-water organisms. Passive particles are neutrally buoyant whereas active particles are able to exercise light dependent vertical migrations equating to the swimming behavior of larvae. The experiments reveal that the strongest accumulation of particles occurs along the French coast on the margin of the ROFI. This happens because the interaction between the turbulence, the freshwater buoyancy input, and tidal dynamics, produces particle trapping and vertical spreading within the frontal convergence zone. Tides and freshwater input induce net alongshore horizontal transport toward the North. Tidal currents modulate the magnitude of horizontal transport whereas the fresh water input controls more the location of accumulation zones. Tracking experiments with active particles indicate that the vertical migration leads to a significant departure from the passive particle transport pattern. Differences lie in the shape of the particle transport pattern and the rate of the northward migration. In particular, vertically migrating particles travel slower. To find possible Flounder migration pathways, particles are released within the assumed spawning area of Flounder. The model predicts larvae drift routes and demonstrates that throughout the entire particle-tracking period the horizontal structure of the particle distribution is consistent with the larvae concentrations observed during the field experiments.     

Quantifying vertical mixing in estuaries

Estuarine turbulence is notable in that both the dissipation rate and the buoyancy frequency extend to much higher values than in other natural environments. The high dissipation rates lead to a distinct inertial subrange in the velocity and scalar spectra, which can be exploited for quantifying the turbulence quantities. However, high buoyancy frequencies lead to small Ozmidov scales, which require high sampling rates and small spatial aperture to resolve the turbulent fluxes. A set of observations in a highly stratified estuary demonstrate the effectiveness of a vessel-mounted turbulence array for resolving turbulent processes, and for relating the turbulence to the forcing by the Reynolds-averaged flow. The observations focus on the ebb, when most of the buoyancy flux occurs. Three stages of mixing are observed: (1) intermittent and localized but intense shear instability during the early ebb; (2) continuous and relatively homogeneous shear-induced mixing during the mid-ebb, and weakly stratified, boundary-layer mixing during the late ebb. The mixing efficiency as quantified by the flux Richardson number Rf was frequently observed to be higher than the canonical value of 0.15 from Osborn (J Phys Oceanogr 10:83–89, 1980). The high efficiency may be linked to the temporal–spatial evolution of shear instabilities.     

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.     

Similarity theory and parameterization of mixing in the upper ocean

Boundary layers with small thermal and mechanical inertia are close to steady-state conditions. This underlies the Monin-Obukhov similarity theory and explains why the surface values of the fluxes can be chosen as external parameters. For fluids with large thermal inertia, such as the ocean, the thermal time scale is relatively large, and the density flux is a complex function of depth; thus, the external thermal forcing is no longer a governing parameter. However, the mechanical inertia of the upper ocean is about three orders of magnitude smaller than the thermal inertia. Consequently, the upper ocean can be considered as steady-state in the dynamic sense, to any dynamic property depends primarily on the depth, the surface momentum flux, and the vertical density structure. This property allows us to suggest an alternative formulation of the similarity theory for the stratified boundary layers through specification of a new stratification parameter which characterizes the internal density structure instead of the external density flux. The turbulent mixing coefficient is derived as dependent on the stratification parameter. The latter includes the surface stress and the integral density deficit for the entire layer above. The general form and the asymptotic behavior of the nondimensional turbulent mixing coefficient as a function of the stratification parameter are obtained using dimensional considerations. Determination of numerical parameters is based on 8 years of temperature profiles acquired at the Ocean Weather Ship (OWS) PAPA. Finally, a method for calculating the profile of the turbulent mixing coefficient is obtained. This approach reproduces the 8-year evolution of the upper ocean with the maximum rms difference of approximately 1C and the bias of 1C over the depth range 0–150 m. Additional 1-year simulation of the upper ocean at OWS CHARLEY and 9-year simulation at OWS NOVEMBER confirms reasonable applicability of this approach. The proposed simple turbulent mixing scheme reproduces the evolution of the upper ocean with accuracies similar to those obtained using much more complicated models.     

A Large-Eddy Simulation Study of the Convective Boundary Layer over Philadelphia during the 1999 Summer NE-OPS Campaign

This study presents a large-eddy simulation (LES) study of the convective boundary layer on August 1, 1999 over Philadelphia, PA during a summer ozone episode. The study is an evaluation of the Colorado State University's Regional Atmospheric Modeling System Version 4.3 (RAMS4.3) with the LES option using Northeast Oxidant and Particulate Study (NE-OPS) data. Simulations were performed with different imposed sensible heat fluxes at the ground surface. The model was initialized with the atmospheric sounding data collected at Philadelphia at 1230 UTC and model integrations continued till 2130 UTC. The resulting mean profiles of temperature and humidity obtained from the LES model were compared with atmospheric soundings, tethered balloon and aircraft data collected during the NE-OPS 1999 field campaign. Also the model-derived vertical profiles of virtual temperature were compared with NE-OPS Radio Acoustic Sounder System (RASS) data while the humidity profiles were compared with NE-OPS lidar data. The comparison of the radiosonde data with the LES model predictions suggests that the growth of the mixing layer is reasonably well simulated by the model. Overall, the agreement of temperature predictions of the LES model with the radiosonde observations is good. The model appears to underestimate humidity values for the case of higher imposed sensible heat flux. However, the humidity values in the mixing layer agree quite well with radiosonde observations for the case of lower imposed sensible heat flux. The model-predicted temperature and humidity profiles are in reasonable agreement with the tethered balloon data except for some small overestimation of temperature at lower layers and some underestimation of humidity values. However, the humidity profiles as simulated by the model agree quite well with the tethered balloon data for the case of lower imposed sensible heat flux. The model-predicted virtual temperature profile is also in better agreement with RASS data for the case of lower imposed sensible heat flux. The model-predicted temperature profile further agrees quite well with aircraft data for the case of lower imposed heat flux. However, the relative humidity values predicted by the model are lower compared with the aircraft data. The model-predicted humidity profiles are only in partial agreement with the lidar data. The results of this study suggest that the explicitly resolved energetic eddies seem to provide the correct forcing necessary to produce good agreement with observations for the case of an imposed sensible heat flux of 0.1 K m s^–1 at the surface.