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.     

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.     

Single-column model and large eddy simulation of the evening transition in the planetary boundary layer

In the present study, the well-known case of day 33 of the Wangara experiment is resimulated using the Weather Research and Forecasting (WRF) model in an idealized single-column mode to assess the performance of a frequently used planetary boundary layer (PBL) scheme, the Yonsei University PBL scheme. These results are compared with two large eddy simulations for the same case study imposing different surface fluxes: one using previous surface fluxes calculated for the Wangara experiment and a second one using output from the WRF model. Finally, an alternative set of eddy diffusivity equations was tested to represent the transition characteristics of a sunset period, which led to a gradual decrease of the eddy diffusivity, and replaces the instantaneous collapse of traditional diagnostics for eddy diffusivities. More appreciable changes were observed in air temperature and wind speed (up to 0.5 K, and 0.6 m s^?1, respectively), whereas the changes in specific humidity were modest (up to 0.003 g kg^?1). Although the representation of the convective decay in the standard parameterization did not show noticeable improvements in the simulation of state variables for the selected Wangara case study day, small changes in the eddy diffusivity over consecutive hours throughout the night can impact the simulation of distribution of trace gases in air quality models. So, this work points out the relevance of simulating the turbulent decay during sunset, which could help air quality forecast models to better represent the distribution of pollutants storage in the residual layer during the entire night.     

Suspended particulate matter dynamics in a particle framework

Suspended particulate matter (SPM) dynamics in ocean models are usually treated with an advection–diffusion equation for one or more sediment size classes coupled to the hydrodynamical part of the model. Numerical solution of these additional partial differential equations unavoidably introduces numerical diffusion, i.e. in the case of sharp gradients the possible occurrence of artificial oscillations and non-positivity. A Lagrangian particle-tracking model has been developed to simulate short-term SPM dynamics. Modelling individual sediment particles allows a straightforward physical interpretation of the processes. The tracking of large numbers of individual and independent particles (up to 25 million in total in a single sediment class) can be achieved on high performance computer clusters, due to efficient parallelisation of particle tracking. The movement of the particles is described by a stochastic differential equation, which is consistent with the advection–diffusion equation. Here, the concentration profile is represented by a set of independent moving particles, which are advected according to the 3D velocity field, while the diffusive displacements of the particles are sampled from a random distribution, which is related to the eddy diffusivity field. To account for erosion a new parameterisation is proposed. Three numerical particle tracking schemes (EULER, MILSTEIN and HEUN) are presented and validated in idealised test cases. Finally, the particle tracking algorithms are applied to a realistic scenario, a severe winter storm in the East Frisian Wadden Sea (southern North Sea). The comparison with observations and an Eulerian SPM transport model seems to indicate a somewhat better fidelity of the Lagrangian approach.     

Sensitivity of air quality model prediction to parameterization of vertical eddy diffusivity

This paper investigates the effects of vertical eddy diffusivities derived from the 3 different planetary boundary layer (PBL) schemes on predictions of chemical components in the troposphere of East Asia. Three PBL schemes were incorporated into a regional air quality model (RAQM) to represent vertical mixing process and sensitivity simulations were conducted with the three schemes while other options are identical. At altitudes <2km, all schemes exhibit similar skill for predicting SO₂ and O₃, but more difference in the predicted NO_x concentration. The Gayno–Seaman scheme produces the smallest vertical eddy diffusivity (Kz) among all schemes, leading to higher SO₂ and NO_x concentrations near the surface than that from the other 2 schemes. However, the effect of vertical mixing on O₃ concentration is complex and varies spatially due to chemistry. The Gayno–Seaman scheme predicts lower O₃ concentrations than the other two schemes in the parts of northern China (generally VOC-limited) and higher ones in most parts of southern China (NO_x-limited). The Byun and Dennis scheme produces the largest mixing depth in the daytime, which bring more NO_x into upper levels, and the mixing depth predicted by the Gayno–Seaman scheme is the smallest, leading to higher NO_x and lower O₃ concentrations near the surface over intensive emission regions.     

The Residence Time of Settling Particles in the Surface Mixed Layer

The transport from the upper mixed layer into the pycnocline of particles with negative buoyancy is considered. Assuming the hydrodynamic parameters to be time- independent, an adjoint model is resorted to that provides a general expression of the residence time in the mixed layer of the constituent under study. It is seen that the residence time decreases as the settling velocity increases or the diffusivity decreases. Furthermore, it is demonstrated that the residence time must be larger than z/w and smaller than h/w, where z, h and w denote the distance to the pycnocline, the thickness of the mixed layer and the sinking velocity. In the vicinity of the pycnocline, the residence time is not necessarily zero; its behaviour critically depends on the eddy diffusivity profile in this region. Closed-form solutions are obtained for constant and quadratic diffusivity profiles, which allows for an analysis of the sensitivity of the residence time to the Peclet number. Finally, an approximate value is suggested of the depth-averaged value of the residence time.     

Diapycnal Mixing in the Thermocline of Lakes: Estimations by Different Methods

In order to evaluate the performance of different methods for estimation of the vertical eddy diffusivity in thermally stratified lakes, two field studies were conducted in Lake Biwa, Japan and Lake Kinneret, Israel. Lake Biwa experienced three typhoons during the campaign while Lake Kinneret experienced high winds in the afternoons. Microstructure profiles were collected by a portable flux profiler (PFP) during calm and disturbed periods. Then, the vertical eddy diffusivity was estimated by three indirect methods. The estimated vertical eddy diffusivities varied more than one order of magnitude, from 4.7× 10⁻⁷ to 7.7× 10⁻⁶ m² s⁻¹. The comparison of results with previous buoyancy flux measurements and scaling arguments showed that the Dillon–Park’s method is not appropriate and Osborn–Cox method performs better than Osborn method in the studied case. Furthermore, the low value of vertical eddy diffusivity within the thermocline suggests that within the thermocline of these lakes, diffusive vertical transport can be neglected.     

Impact of consistent boundary layer mixing approaches between NAM and CMAQ

Discrepancies in grid structure, dynamics and physics packages in the offline coupled NWS/NCEP NAM meteorological model with the U.S. Environmental Protection Agency Community Multiscale Air Quality (CMAQ) model can give rise to inconsistencies. This study investigates the use of three vertical mixing schemes to drive chemistry tracers in the National Air Quality Forecast Capability (NAQFC). The three schemes evaluated in this study represent various degrees of coupling to improve the commonality in turbulence parameterization between the meteorological and chemistry models. The methods tested include: (1) using NAM predicted TKE-based planetary boundary height, h, as the prime parameter to derive CMAQ vertical diffusivity; (2) using the NAM mixed layer depth to determine h and then proceeding as in (1); and (3) using NAM predicted vertical diffusivity directly to parameterize turbulence mixing within CMAQ. A two week period with elevated surface O₃ concentrations during the summer 2006 has been selected to test these schemes in a sensitivity study. The study results are verified and evaluated using the EPA AIRNow monitoring network and other ozonesonde data. The third method is preferred a priori as it represents the tightest coupling option studied in this work for turbulent mixing processes between the meteorological and air quality models. It was found to accurately reproduce the upper bounds of turbulent mixing and provide the best agreement between predicted h and ozonesonde observed relative humidity profile inferred h for sites investigated in this study. However, this did not translate into the best agreement in surface O₃ concentrations. Overall verification results during the test period of two weeks in August 2006, did not show superiority of this method over the other 2 methods in all regions of the continental U.S. Further efforts in model improvement for the parameterizations of turbulent mixing and other surface O₃ forecast related processes are warranted.     

Large-Eddy Simulations of the Atmospheric Boundary Layer Using a New Subgrid-Scale Model – II. Weakly and moderately stable cases

A series of simulations under weakly to moderately stable boundary layers (SBLs) have been performed using the proposed subgrid-scale (SGS) model implemented into the Terminal Area Simulation System (TASS). The proposed SGS model incorporates some aspects of the two-part eddy viscosity SGS model of Sullivan et al. (1994) and further refinements which include the dependence of SGS mixing length on stratification, two-part separation of the SGS eddy diffusivity of heat, and more realistic empirical forms of Monin–Obukhov similarity functions. The potential temperature profiles from simulations clearly show a three-layer structure: a stable surface layer of strong gradients, a middle layer of small gradients, and an inversion layer on the top. The wind speed profiles show the formation of low level jet (LLJ). However, the sub-layer structures under moderately SBLs differ from those under weakly SBLs. Both the momentum and heat fluxes decrease almost linearly in the lower part of the SBL. The near surface values of the normalized turbulent kinetic energy (TKE/u _* ²) in all simulations are about 4 which is much less than the typical value of 5.5 under the neutral condition. The decay of turbulence first occurs in the area with large values of Richardson number (R _i<0.2). Generally, instantaneous values of the TKE and R _i at the various grid points are negatively correlated, but there is not a unique relationship between the two parameters.     

A new model for the CBL growth based on the turbulent kinetic energy equation

Starting from the evolution equation for the turbulent energy density spectrum (EDS), we develop a new model for the growth of the Convective boundary layer (CBL). We apply dimensional analysis to parameterize the unknown inertial transport and convective source term in the dynamic equation for the three-dimensional (3-D) spectrum and solve the 3-D EDS equation. The one-dimensional vertical spectrum is derived from the 3-D spectrum, employing a weight function. This allows us to select the magnitude of the vertical spectral component for the construction of the growing 3-D EDS. Furthermore, we employ the vertical component of the energy spectrum to calculate the eddy diffusivity (required in dispersion models). Currently there are no available experimental data to directly verify our EDS model.     

Beyond eddy diffusivity: an alternative model for turbulent dispersion

Turbulent dispersion proceeds not only much faster but also in a qualitatively different manner than molecular diffusion. Yet, the majority of hydraulic, oceanic and atmospheric models rely on the concept of an eddy diffusivity. It is shown here that an alternative model can be developed to exhibit observed behavior. The new term in the diffusion equation, which is non-local, may be interpreted in terms of the probability density function (pdf) of the turbulent velocity. Different assumptions about this distribution lead to a family of models, one of which is the model proposed here and another, the classical Fickian model of diffusion. A connection is also made with models using fractional calculus.     

A new view of dispersion in well-mixed estuaries

A two-dimensional simulation of Delaware estuary hydrodynamics has been constructed. This simulation has been achieved through a rational estimate of the character of natural turbulence. Non-homogeneous velocities, on the cross-section, are employed in two-dimensional, laterally homogeneous species mass balances. In turn, concentration profiles are interpreted in the form of classical, one-dimensional dispersion coefficients. Variation of dispersion as a function of both freshwater inflow and longitudinal distance was generated. Variation of dispersion in time within a tidal cycle was found to be insignificant while no significant variation from one tidal cycle to the next has been detected.The modeling process involves the solution of tractable equations by implicit numerical methods and is capable of being excited by a wide range of input conditions.A study of the sensitivity of dispersion due to vertical mass diffusion revealed that longitudinal mixing characteristics are inversely proportional to vertical eddy diffusivity and analysis of the numerical results showed the dispersion coefficient is essentially insensitive to variation of longitudinal mass diffusivity. This leads to the conclusion that turbulent diffusivity of mass in the longitudinal direction may be taken as constant for most purposes in the study of a two-dimensional species mass balance model.A field program was carried out near the Delaware Memorial Bridge to collect velocity profiles. Substantial portions of the scheme have been verified (i.e. one- and two-dimensional tidal dynamic models) through the use of these data.     

Turbulent kinetic energy budgets in a model canopy: comparisons between LES and wind-tunnel experiments

A comparative study of turbulence in a wind-tunnel model canopy is performed, using Large eddy simulation (LES) and experimental data from PIV and hot-wire anemometry measurements. The model canopy is composed of thin cylindrical stalks. In the LES, these are represented using a plant-scale approach, while the scale-dependent Lagrangian dynamic model is used as subgrid-scale model. LES predictions of turbulence statistics and energy spectra are found to be in good agreement with the experimental data. Turbulent kinetic energy (TKE) budgets from the LES simulation are analyzed to provide more information absent in the measurements. Results confirm that sloshing motions at the low levels of the canopy are mainly driven by pressure fluctuations. A difference between the energy flux obtained from the energy spectrum and the SGS dissipation rate is observed, consistent with a spectral bypass mechanism in which the real spectral flux due to cascade is smaller than that implied by the energy-spectrum level, due to direct drain by the canopy.     

On the behaviour of the residence time at the bottom of the mixed layer

To understand why the findings of Deleersnijder et al. [(2006), Environ Fluid Mech 6: 25–42]—the residence time in the mixed layer in not necessarily zero at the pycnocline—are consistent with those of Delhez and Deleersnijder [(2006), Ocean Dyn 56:139–150]—the residence time in a control domain vanishes at the open boundaries of this control domain—, it is necessary to consider a control domain that includes part of the pycnocline, in which the eddy diffusivity is assumed to be zero. Then, depending on the behaviour of the eddy diffusivity near the bottom of the mixed layer, the residence time may be seen to exhibit a discontinuity at the interface between the mixed layer and the pycnocline. If such a discontinuity exists, the residence time is non-zero in the former and zero in the latter. This is illustrated by analytical solutions obtained under the assumption that the eddy diffusivity is constant in the mixed layer.     

多极涡流管式混合器的设计与混合效能

本文主要论述了依据絮凝动力学中涡旋理论设计的多极涡流管式混合器及其絮凝试验的研究结果，同时讨论了影响多极涡流管式混合器混合效能的管径及流量等因素，结果证实，该混合器适合于无机高分子絮凝剂的絮凝动力学反应特点，具有较高的工程推广和应用价值。     

Eddy diffusivity: a single dispersion analysis of high resolution drifters in a tidal shallow estuary

In an estuary, mixing and dispersion resulting from turbulence and small scale fluctuation has strong spatio-temporal variability which cannot be resolved in conventional hydrodynamic models while some models employs parameterizations large water bodies. This paper presents small scale diffusivity estimates from high resolution drifters sampled at 10 Hz for periods of about 4 h to resolve turbulence and shear diffusivity within a tidal shallow estuary (depth <3 m). Taylor’s diffusion theorem forms the basis of a first order estimate for the diffusivity scale. Diffusivity varied between 0.001 and 0.02 m²/s during the flood tide experiment. The diffusivity showed strong dependence (R² > 0.9) on the horizontal mean velocity within the channel. Enhanced diffusivity caused by shear dispersion resulting from the interaction of large scale flow with the boundary geometries was observed. Turbulence within the shallow channel showed some similarities with the boundary layer flow which include consistency with slope of 5/3 predicted by Kolmogorov’s similarity hypothesis within the inertial subrange. The diffusivities scale locally by 4/3 power law following Okubo’s scaling and the length scale scales as 3/2 power law of the time scale. The diffusivity scaling herein suggests that the modelling of small scale mixing within tidal shallow estuaries can be approached from classical turbulence scaling upon identifying pertinent parameters.     

Scale-invariant movements of fishermen: the same foraging strategy as natural predators.

We analyzed the movement of fishing vessels during fishing trips in order to understand how fishermen behave in space while searching for fish. For that purpose we used hourly geo-referenced positions of vessels, provided by a satellite vessel monitoring system, for the entire industrial fleet (809 vessels) of the world's largest single species fishery (Peruvian anchovy, Engraulis ringens) from December 1999 to March 2003. Observed trajectories of fishing vessels are well modeled by Lévy random walks, suggesting that fishermen use a stochastic search strategy which conforms to the same search statistics as non-human predators. We show that human skills (technology, communication, or others) do not result in the fishermen's spatial behavior being fundamentally different from that of animal predators. With respect to probability of prey encounter, our results suggest that fishermen, on average, evolved an optimal movement pattern (mu = 2.00) among the family of Lévy random walks. This Lagrangian approach opens several perspectives in terms of operational management of the pelagic fish stock.     

Influence of the secondary motions on pollutant mixing in a meandering open channel flow

This paper presents large eddy simulation of turbulent flow in a meandering open channel with smooth wall and rectangular cross-section. The Reynolds number based on the channel height is 40,000 and the aspect ratio of the cross-section is 4.48. The depth-averaged mean stream-wise velocity agree well to experimental measurements. In this specific case, two interacting cells are formed that swap from one bend to the other. Transport and mixing of a pollutant is analysed using three different positions of release, e.g. on the inner bank, on the outer bank and on the centre of the cross section. The obtained depth-average mean concentration profiles are reasonably consistent with available experimental data. The role of the secondary motions in the mixing processes is the main focus of the discussion. It is found that the mixing when the scalar is released on the centre of the cross-section is stronger and faster than the mixing of the scalar released on the sides. When the position of release is close to a bank side, the mixing is weaker and a clear concentration of scalar close to the corresponding side-wall can be observed in both cases.     

A methodological framework for integrating computational fluid dynamics and ecological models applied to juvenile freshwater mussel dispersal in the Upper Mississippi River

Interdisciplinary research in hydraulics and ecology for river management and restoration must integrate processes that occur over a wide range of spatial and temporal scales, which presents a challenge to ecohydraulics modelers. Computational fluid dynamics (CFD) models are being more widely used to determine flow fields for ecohydraulics applications. In the Upper Mississippi River (UMR), the mussel dynamics model was developed as a tool for management and conservation of freshwater mussels (Unionidae), which are benthic organisms, imperiled in North America, that are inextricably linked with the hydraulics of river flow. We updated the juvenile dispersal component of the mussel dynamics model by using stochastic Lagrangian particle tracking in a three dimensional flow field output from CFD models of reaches in the UMR. We developed a methodological framework to integrate hydrodynamic data with the mussel dynamics model, and we demonstrate the use of the juvenile dispersal model employed within the methodological framework in two reaches of the UMR. The method was used to test the hypothesis that impoundment affects the relationship of some hydraulic parameters with juvenile settling distribution. Simulation results were consistent with this hypothesis, and the relationships of bed shear stress and Froude number with juvenile settling were altered by impoundment most likely through effects on local hydraulics. The methodological framework is robust, integrates Eulerian and Lagrangian reference frameworks, and incorporates processes over a wide range of temporal and spatial scales, from watershed scale hydrologic processes (decades), to reach scale (km) processes that occur over hours or days, and turbulent processes on spatial scales of meter to millimeter and times scales of seconds. The methods are presently being used to assess the impacts of pre- and early post-settlement processes on mussel distributions, including the effects of bed shear stress, and the sensitivity of the location of the host fish when juveniles excyst, on juvenile settling distribution.     

Wave mixing rise inferred from Lyapunov exponents

We study the horizontal surface mixing and the transport induced by waves in a coastal environment. A comparative study is addressed by computing the Lagrangian coherent structures, via Finite Size Lyapunov Exponents, that arise in two different numerical settings: with and without wave coupled to currents. In general, we observe that mixing is increased in the area due to waves. Besides, the methodology presented here is tested by deploying a set of eight Lagrangian drifters at different locations. This dynamical approach is shown as a valuable tool to extract information about transport, mixing and residence embedded in the Eulerian time dependent velocity fields obtained from numerical models.