Effects Of Turbulent Mixing Research Articles

Characterizing turbulent overturns in CTD-data

We are concerned with the shape of overturns due to irreversible effects of turbulent mixing through internal wave breaking in the ocean. Vertical (z) overturn displacements (d) are computed from ship-borne SeaBird-911 CTD-data using the well-established method of reordering unstable portions in vertical density profiles. When displayed as a function of z, the displacements d(z) reveal a characteristic zigzag shape. Here, we primarily investigate the particular slope (z/d) of this zigzag signature after assigning the displacements to the end-point depths. Using model-overturns we show that this slope equals ½ for a solid-body-rotation, while a more sophisticated Rankine-vortex overturn-model, here employed in the vertical, has slopes slightly >½ in the interior and >1 along the sides. In the case of a near-homogeneous layer, displacement-points fill a parallelogram with side-edges having a slope of 1. The models are used to interpret overturn shapes in NE-Atlantic-Ocean-data from moderately deep, turbulent waters above Rockall Bank (off Ireland) and from deep, weakly stratified waters above Mount Josephine (off Portugal). These are compared with salinity-compensated intrusion data in Mediterranean-outflow-waters in the Canary Basin. Dynamically, most overturns are found to resemble the half-turn Rankine-vortex model and very few a, small-only, solid-body-rotation. Additionally, the usefulness and uselessness of upcast-CTD-data are discussed for overturn characterization.

Formation, growth, and transport of soot in a three-dimensional turbulent non-premixed jet flame

The formation, growth, and transport of soot is investigated via large scale numerical simulation in a three-dimensional turbulent non-premixed n-heptane/air jet flame at a jet Reynolds number of 15,000. For the first time, a detailed chemical mechanism, which includes the soot precursor naphthalene and a high-order method of moments are employed in a three-dimensional simulation of a turbulent sooting flame. The results are used to discuss the interaction of turbulence, chemistry, and the formation of soot. Compared to temperature and other species controlled by oxidation chemistry, naphthalene is found to be affected more significantly by the scalar dissipation rate. While the mixture fraction and temperature fields show fairly smooth spatial and temporal variations, the sensitivity of naphthalene to turbulent mixing causes large inhomogeneities in the precursor fields, which in turn generate even stronger intermittency in the soot fields. A strong correlation is apparent between soot number density and the concentration of naphthalene. On the contrary, while soot mass fraction is usually large where naphthalene is present, pockets of fluid with large soot mass are also frequent in regions with very low naphthalene mass fraction values. From the analysis of Lagrangian statistics, it is shown that soot nucleates and grows mainly in a layer close to the flame and spreads on the rich side of the flame due to the fluctuating mixing field, resulting in more than half of the total soot mass being located at mixture fractions larger than 0.6. Only a small fraction of soot is transported towards the flame and is completely oxidized in the vicinity of the stoichiometric surface. These results show the leading order effects of turbulent mixing in controlling the dynamics of soot in turbulent flames. Finally, given the difficulties in obtaining quantitative data in experiments of turbulent sooting flames, this simulation provides valuable data to guide the development of models for Large Eddy Simulation and Reynolds Average Navier Stokes approaches.

Gas transfer velocities of methane and carbon dioxide in a subtropical shallow pond

Two diel field campaigns under different weather patterns were carried out in the summer and autumn of 2013 to measure CO2 and CH4 fluxes and to probe the rates of gas exchange across the air–water interface in a subtropical eutrophic pond in China. Bubble emissions of CH4 accounted for 99.7 and 91.67% of the total CH4 emission measured at two sites in the summer; however, no bubble was observed in the autumn. The pond was supersaturated with CO2 and CH4 during the monitoring period, and the saturation ratios (i.e. observed concentration/equilibrium concentration) of CH4 were much higher than that of CO2. Although the concentration of dissolved CO2 in the surface water collected in the autumn was 1.24 times of that in the summer, the mean diffusive CO2 flux across the water–air interface measured in the summer is almost twice compared with that in the autumn. The mean concentration of dissolved CH4 in the surface water in the autumn was around half of that in the summer, but the mean diffusive CH4 flux in the summer is 4–5 times of that in the autumn. Our data showed that the variation in gas exchange rate was dominated by differences in weather patterns and primary production. Averaged k600-CO2 and k600-CH4 (the gas transfer velocity normalised to a Schmidt number of 600) were 0.65 and 0.55 cm/h in the autumn, and 2.83 and 1.64 cm/h in the summer, respectively. No statistically significant correlation was found between k600 and U10 (wind speed at 10 m height) in the summer at low wind speeds in clear weather. Diffusive gas fluxes increased during the nights, which resulted from the nighttime cooling effect of water surface and stronger turbulent mixing in the water column. The chemical enhancements for CO2 were estimated up to 1.94-fold in the hot and clear summer with low wind speeds, which might have been resulted from the increasing hydration reactions in water due to the high water temperature and active metabolism in planktonic algae. However, both the air and surface water temperatures decreased continually, and relatively lower temperature and overcast weather with occasionally light rain dominated the second campaign in the autumn. The concentration of dissolved oxygen in the surface water and U10 controlled gas transfer velocities of CO2 and CH4, respectively, in the cool autumn. When the surface water temperature was higher than the air temperature, higher CO2 flux was observed because the water body was unstable and overturned quickly, inducing quick CO2 emitted from plankton algae in surface water to the atmosphere.

Large-scale dynamical influence of a gravity wave generated over the Antarctic Peninsula – regional modelling and budget analysis

ABSTRACTThe case study of a mountain wave triggered by the Antarctic Peninsula on 6 October 2005, which has already been documented in the literature, is chosen here to quantify the associated gravity wave forcing on the large-scale flow, with a budget analysis of the horizontal wind components and horizontal kinetic energy. In particular, a numerical simulation using the Weather Research and Forecasting (WRF) model is compared to a control simulation with flat orography to separate the contribution of the mountain wave from that of other synoptic processes of non-orographic origin. The so-called differential budgets of horizontal wind components and horizontal kinetic energy (after subtracting the results from the simulation without orography) are then averaged horizontally and vertically in the inner domain of the simulation to quantify the mountain wave dynamical influence at this scale. This allows for a quantitative analysis of the simulated mountain wave's dynamical influence, including the orographically induced pressure drag, the counterbalancing wave-induced vertical transport of momentum from the flow aloft, the momentum and energy exchanges with the outer flow at the lateral and upper boundaries, the effect of turbulent mixing, the dynamics associated with geostrophic re-adjustment of the inner flow, the deceleration of the inner flow, the secondary generation of an inertia–gravity wave and the so-called baroclinic conversion of energy between potential energy and kinetic energy.

Numerical simulation of tropospheric ozone depletion in the polar spring

This study addresses the modeling of the tropospheric ozone depletion event in polar spring where the aim is an improved understanding of the underlying physical and chemical processes. For this purpose, a model is developed and implemented into the open source software Open source Field Operations And Manipulations (OpenFOAM). A detailed chemical reaction mechanism is analyzed with the software package KInetic aNALysis of reaction mechanics (KINAL), and a skeletal mechanism is derived for use in the three-dimensional simulations. The 3D compressible Navier–Stokes equations are solved to predict the effect of turbulent mixing, advection of the fluid, and chemical reactions. Large eddy simulation accounts for the turbulence, and the Smagorinsky model is employed as sub-grid model. The temporal and spatial distributions of the chemical species are captured. The mixing ratio of ozone in the troposphere drops to a value near zero within several days including an “induction stage” and a “depletion stage,” which confirms previous findings. Moreover, the vertical turbulent mixing of air parcels occurs below the height of the polar boundary layer, leading to a nonuniform vertical distribution of the chemical species concentrations. Both the wind speed and the boundary layer stability may affect the boundary layer height, thus influencing the ozone depletion rate.

Influence of hydraulics on the uptake of ammonium by two freshwater plants

Summary Macrophytes are important in the biogeochemistry of flowing rivers, although most information so far has relied on measurements of nutrients in plant tissues. This yields only indirect information on the nutrient uptake fluxes by roots and shoots and about nutrient translocation between roots and shoots. Here, we studied nitrogen uptake through experiments with enriched 15N stable isotopes. Two macrophytes (Potamogeton natans and Ranunculus fluitans) were grown in a closed race track‐shaped flume, allowing us to control the hydraulic conditions in and around the plants. Overall ammonium uptake rates (μmol g−1 dry mass h−1) were higher for R. fluitans than P. natans. In addition to differences between the species, the spatial position of individuals within the plant patch and water flow were also important in explaining ammonium uptake. Thus, ammonium uptake was high at the leading edge of the patch and increased with velocity. Plant characteristic, such as the angle at which the plants bent in the flow, was also correlated with ammonium uptake. Differences in nutrient uptake associated with hydrodynamic parameters raised the question of how the two are related. For both species, uptake was not correlated with Reynolds stress, indicating the poor effect of turbulent mixing in determining ammonium uptake.

Various air distribution modes on commercial airplanes—Part 2: Computational fluid dynamics modeling and validation

Both experimental test and numerical modeling can be used to investigate air distribution on commercial airplanes. Numerical modeling by computational fluid dynamics has gained popularity; however, current computational fluid dynamics modeling efforts are concentrated primarily on the mixing-air distribution mode. To fully evaluate computational fluid dynamics modeling for different air distribution modes, the flow, heat transfer, and pollutant species transport in a twin-aisle aircraft cabin mockup is modeled. Three air distribution modes, namely the mixing, under-aisle displacement, and personal air distribution modes, are studied. The steady renormalization group k-ϵ model together with the standard wall function has been employed for turbulence modeling and the near-wall treatment. The experimental data in terms of the velocity field, temperature, and CO2 concentration profiles are applied to validate the numerical models. This study finds that the renormalization group k-ϵ model is able to solve major air distribution parameters in reasonable agreement with the measured values. When carrying out the steady computational modeling by resolving the Reynolds-averaged Navier-Stokes equations, it should be noted that the models may underestimate the turbulent mixing effect.

Mixing of an interflow into the ambient water of Lake Iseo

River water flowing as an interflow was investigated using field data, collected in Lake Iseo (Italy), and theory. A theory for the lateral falling mechanism of plunging was developed for inflows when the initial densimetric Froude number (Fr0) is slightly larger than unity. The ratio of the river width to the offshore extent of the plunge region was equal to Fr0. The mixing ratio in the plunge region was 0.06. Theoretical results were quantitatively consistent with the length scale and mixing ratio of the observed plunge region. The progression of the inflow was interpreted as: initially a laterally falling plunge region with little mixing; followed by a steep underflow region with substantial mixing; and finally an intrusion. The intrusion was at first controlled dynamically by an inertia‐buoyancy force balance. Further from the liftoff point, turbulent mixing effects dominated over those due to inertia. Ultimately, the intrusion diffused into the adjacent layers in such a way that the interflow fluid was effectively indistinguishable from the lake water.

ASSESSMENT OF THERMAL FATIGUE IN MIXING TEE BY FSI ANALYSIS

Thermal fatigue is a significant long-term degradation mechanism in nuclear power plants. In particular, as operating plants become older and life time extension activities are initiated, operators and regulators need screening criteria to exclude risks of thermal fatigue and methods to determine significant fatigue relevance. In general, the common thermal fatigue issues are well understood and controlled by plant instrumentation at fatigue susceptible locations. However, incidents indicate that certain piping system Tee connections are susceptible to turbulent temperature mixing effects that cannot be adequately monitored by common thermocouple instrumentations. Therefore, in this study thermal fatigue evaluation of piping system Tee-connections is performed using the fluid-structure interaction (FSI) analysis. From the thermal hydraulic analysis, the temperature distributions are determined and their results are applied to the structural model of the piping system to determine the thermal stress. Using the rain-flow method the fatigue analysis is performed to generate fatigue usage factors. The procedure for improved load thermal fatigue assessment using FSI analysis shown in this study will supply valuable information for establishing a methodology on thermal fatigue.

A New Soot Emission Model for Diesel Methanol Dual Fuel Engine

The modified Hiroyasu soot model is widely used to describe the soot emission from diesel engine, but diesel methanol dual fuel engine is different from diesel one. In order to obtain quantitative comparisons with experiments, a new soot emission model was presented, which was formulated to incorporate the effects of both chemical kinetics and turbulent mixing. The model was applied to simulate soot emission from diesel methanol dual fuel engine. The calculating results indicate that the predicted soot emission from the new model agrees well with the measured data.

Boussinesq modelling of a rip current at Haeundae Beach in South Korea

Bae, J.S., Yoon, S.B., Choi, J., 2013. Boussinesq Modelling of a Rip Current at Haeundae Beach.The rip current occurring at Haeundae beach in Busan, South Korea was numerically investigated under directional random wave environment. The numerical simulations were performed using a fully nonlinear Boussinesq equation model, FUNWAVE which is capable of resolving phase interaction and simulating nearshore circulation since it includes the effect of wave-induced momentum flux and horizontal turbulent mixing. To examine the modelling, the rip current occurred on the 12th of June, 2011 at Haeundae beach was simulated by using observations. The results of numerical simulation showed the time-dependent evolution of the wave-induced nearshore circulation that was caused by transformation of random waves due to the unique topography of Haeundae beach. And, it was found that the rip current was well generated and developed through the region where relatively lower wave heights were caused by refraction and diffraction of waves due to the topographical characteristics (i.e., submerged shoal). In addition, we found that a narrow-banded spectral wave (i.e., a swell spectrum) close to a regular wave generates stronger rip current than a broad-banded spectral wave under an equivalent wave height and period condition.

Nutrients and phytoplankton biomass distribution and activity at the Barents Sea Polar Front during summer near Hopen and Storbanken

In this paper we present data on hydrography, nutrients, phytoplankton biomass distribution and photosynthetic activity from a cruise in early August 2007, covering the waters between the island of Hopen on Spitsbergenbanken and of Storbanken in the Barents Sea. The Polar Front, which separates Atlantic and Arctic waters, was observed along the eastern slope of Spitsbergenbanken at 29.5°E and the western slope of Storbanken around 33°. A surface layer front associated with the meltwater appeared near 26.7°E on Spitsbergenbanken, with strong horizontal temperature and salinity gradients, but relatively weak horizontal density gradients. Phytoplankton biomass was generally low with chlorophyll a (Chl a) concentrations lower than 2mgm−3. No stimulatory front effect was found in this context. The highest concentrations were found as subsurface maximum over Spitsbergenbanken. Nutrients were also low, probably limiting phytoplankton growth. However, enhanced photosynthetic activity was seen near the pycnocline on Storbanken and Spitsbergenbanken, probably an effect of turbulent mixing caused by strong tidal currents, bringing phytoplankton cells in contact with more nutrient rich water, originating from below the pycnocline. Low-light acclimated phytoplankton cells were found at depth in stratified Atlantic Water. About 60% of the nitrate winter reservoir for the upper 100m of the water column had been consumed during the growth season prior to the cruise. This corresponds to a new primary production of 48gCm−2. At the time of the cruise, however, primary production was probably based on regenerated nutrients, conditions that seemed to favour dominance of the coccolithophore Emiliania huxleyi and ultraplankton (<5μm) flagellates.

Stereoscopic-PIV measurement of turbulent jets issuing from a sharp-edged circular nozzle with multiple triangular tabs

Three-dimensional (3D) flow structures of a turbulent jet issuing from a sharp-edged circular nozzle having multiple triangular tabs are experimentally studied by employing a stereoscopic-PIV (SPIV) system. Two different sharp-edged jet nozzles having 4 and 8 tabs are investigated at a jet Reynolds number of Re = 10,000. The SPIV measurements are carried out at 5 different cross-sectional planes along the jet direction. Spatial distributions of turbulent statistics including mean velocity, mean vorticity, and turbulent kinetic energy are obtained at each cross-sectional plane. The jet entrainment rate showing the mixing of the jet and ambient fluids is also estimated using the measured 3D velocity field information. As a result, the jet issuing from the nozzle with 4 tabs shows better turbulent mixing effect at further downstream position than the 8 tabs case because of the reduced reciprocal interactions of the streamwise vortices that promote the turbulent dissipation.

Turbulent mixing and wave radiation in non-Boussinesq internal bores

Bores, or hydraulic jumps, appear in many natural settings and are useful in many industrial applications. If the densities of the two fluids between which a bore propagates are very different (i.e., water and air), the less dense fluid can be neglected when modeling a bore analytically—a single-layer hydraulic model will accurately predict a bore's speed of propagation. A two-layer model is required, however, if the densities are more similar. Mass is conserved separately in each layer and momentum is conserved globally, but the model requires for closure an assumption about the loss of energy across a bore. In the Boussinesq limit, it is known that there is a decrease of the total energy flux across a bore, but in the expanding layer, turbulent mixing at the interface entrains high speed fluid from the contracting layer, resulting in an increase in the flux of kinetic energy across the expanding layer of a bore. But it is unclear if this finding will extend to non-Boussinesq bores. We directly examine the flux of energy within non-Boussinesq bores using two-dimensional direct numerical simulations and find that a gain of energy across the expanding layer only occurs for bores where the density ratio, defined as the ratio of the density of the lighter fluid to the heavier fluid, is greater than approximately one half. For smaller density ratios, undular waves generated at the bore's front dominate over the effects of turbulent mixing, and the expanding layer loses energy across the bore. Based on our results, we show that if one can predict the amount of energy radiated by bores through undular waves, it is possible to derive an accurate model for the propagation of non-Boussinesq bores.

Water in Protoplanetary Disks

AbstractInfrared water line emission from protoplanetary disks, recently observed by the Spitzer and Herschel space telescopes, is thought to trace the surface layer of the inner to outer regions of the disks. We have modelled the water abundance profile and line emission, especially focusing on the effects of dust size growth and turbulent mixing. Comparison between model calculations and observations suggests a small grain model with turbulent mixing is preferred.

Effects of 3-D channel blockage and turbulent wake mixing on the limit of power extraction by tidal turbines

Three-dimensional incompressible Reynolds-averaged Navier–Stokes (RANS) computations are performed for water flow past an actuator disk model (representing a tidal turbine) placed in a rectangular channel of various blockages and aspect ratios. The study focuses on the effects of turbulent mixing behind the disk, as well as on the effects of channel blockage and aspect ratio on the prediction of the hydrodynamic limit of power extraction. To qualitatively account for the effect of turbulence generated by the turbine (rather than by the shear flow behind the turbine), we propose a new approach, called a blade-induced turbulence model, which does not use any additional model coefficients other than those used in the original RANS turbulence model. Results demonstrate that the power removed from the mean flow by the disk increases as the strength of turbulent mixing behind the disk increases, being consistent with the turbulent shear stress on the interface between the bypass and core flow passages acting in such a way as to decelerate the bypass flow and accelerate the core flow. The channel aspect ratio also affects the flow downstream of the disk but has less influence upstream of the disk; hence its effect on the limit of power extraction is relatively minor compared to that of the channel blockage, which is shown to be significant but satisfactorily estimated using one-dimensional inviscid theory previously reported in the literature.

Cloud microphysical effects of turbulent mixing and entrainment

Turbulent mixing and entrainment at the boundary of a cloud is studied by means of direct numerical simulations that couple the Eulerian description of the turbulent velocity and water vapor fields with a Lagrangian ensemble of cloud water droplets that can grow and shrink by condensation and evaporation, respectively. The focus is on detailed analysis of the relaxation process of the droplet ensemble during the entrainment of subsaturated air, in particular the dependence on turbulence timescales, droplet number density, initial droplet radius and particle inertia. We find that the droplet evolution during the entrainment process is captured best by a phase relaxation time that is based on the droplet number density with respect to the entire simulation domain and the initial droplet radius. Even under conditions favoring homogeneous mixing, the probability density function of supersaturation at droplet locations exhibits initially strong negative skewness, consistent with droplets near the cloud boundary being suddenly mixed into clear air, but rapidly approaches a narrower, symmetric shape. The droplet size distribution, which is initialized as perfectly monodisperse, broadens and also becomes somewhat negatively skewed. Particle inertia and gravitational settling lead to a more rapid initial evaporation, but ultimately only to slight depletion of both tails of the droplet size distribution. The Reynolds number dependence of the mixing process remained weak over the parameter range studied, most probably due to the fact that the inhomogeneous mixing regime could not be fully accessed when phase relaxation times based on global number density are considered.

Effects of turbulent mixing on critical behaviour: renormalization-group analysis of the Potts model

The critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field-theoretic renormalization group. Specifically, the relaxational stochastic dynamics of a non-conserved multicomponent order parameter of the Ashkin–Teller–Potts model, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken to be Gaussian, white in time, with a correlation function of the form ∝δ(t − t′)/|k⊥|d − 1 + ξ, where k⊥ is the component of the wave vector, perpendicular to the distinguished direction (‘direction of the flow’)—the d-dimensional generalization of the ensemble was introduced by Avellaneda and Majda (1990 Commun. Math. Phys. 131 381) within the context of passive scalar advection. This model can describe a rich class of physical situations. It is shown that, depending on the values of the parameters that define the self-interaction of the order parameter and the relation between the exponent ξ and the space dimension d, the system exhibits various types of large-scale scaling behaviour, associated with different infrared attractive fixed points of the renormalization-group equations. In addition to known asymptotic regimes (critical dynamics of the Potts model and passively advected field without self-interaction), the existence of a new, non-equilibrium and strongly anisotropic, type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the leading order of the double expansion in ξ and ε = 6 − d (one-loop approximation). The scaling appears to be strongly anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different.

A Lagrangian model of air-mass photochemistry and mixing using a trajectory ensemble: the Cambridge Tropospheric Trajectory model of Chemistry And Transport (CiTTyCAT) version 4.2

Abstract. A Lagrangian model of photochemistry and mixing is described (CiTTyCAT, stemming from the Cambridge Tropospheric Trajectory model of Chemistry And Transport), which is suitable for transport and chemistry studies throughout the troposphere. Over the last five years, the model has been developed in parallel at several different institutions and here those developments have been incorporated into one "community" model and documented for the first time. The key photochemical developments include a new scheme for biogenic volatile organic compounds and updated emissions schemes. The key physical development is to evolve composition following an ensemble of trajectories within neighbouring air-masses, including a simple scheme for mixing between them via an evolving "background profile", both within the boundary layer and free troposphere. The model runs along trajectories pre-calculated using winds and temperature from meteorological analyses. In addition, boundary layer height and precipitation rates, output from the analysis model, are interpolated to trajectory points and used as inputs to the mixing and wet deposition schemes. The model is most suitable in regimes when the effects of small-scale turbulent mixing are slow relative to advection by the resolved winds so that coherent air-masses form with distinct composition and strong gradients between them. Such air-masses can persist for many days while stretching, folding and thinning. Lagrangian models offer a useful framework for picking apart the processes of air-mass evolution over inter-continental distances, without being hindered by the numerical diffusion inherent to global Eulerian models. The model, including different box and trajectory modes, is described and some output for each of the modes is presented for evaluation. The model is available for download from a Subversion-controlled repository by contacting the corresponding authors.

Comment on “Particle dispersal due to interplay of motions in the surface layer of a small reservoir” (by P. Okely, J. Imberger, and K. Shimizu) and “Processes affecting horizontal mixing and dispersion in Winam Gulf, Lake Victoria” (by P. Okely, J. Imberger, and J. P. Antenucci)

Okely et al. (2010a,b) are concerned with horizontal dispersion and mixing in lakes and employ numerical modeling to estimate horizontal dispersion coefficients. In both papers, the dispersal of four numerical Lagrangian particles is employed to estimate dispersion coefficients, and the authors explicitly claim that ‘‘...this method measures horizontal dispersion due to large-scale horizontal shear only, and the influence of other processes, such as turbulent diffusion, is not accounted for’’ (Okely et al. 2010b, p. 591). However, we demonstrate here that without a diffusive process, e.g., molecular or turbulent diffusion, the dispersal rate estimated from Lagrangian particles as in Okely et al. (2010a,b) should be zero in principal for largescale nondivergent horizontal flow fields, independent of the horizontal shear. The particle dispersal presented by Okely et al. (2010a,b) is not a measure of horizontal dispersion due to horizontal shear but depends on the initial position of the particles and the divergence of the simulated mean flow field and may be affected by undersampling of the flow field, since only four particles were considered. Whereas the study of Okely et al. (2010b) was entirely based on this Lagrangian particle technique, Okely et al. (2010a) compared horizontal dispersion coefficients estimated from this technique with coefficients determined from the spread of numerically simulated tracer distributions. According to Okely et al. (2010a), their horizontal dispersion coefficients agree reasonably well with an estimate based on the assumption that the effects of vertical shear and vertical turbulent mixing (Kz) determine horizontal dispersion (see Table 1 and Eq. 11 in Okely et al. 2010a). Okely et al. (2010a, p. 1875) state that ‘‘The vertical shear dispersion scaling was a good approximation for the magnitude and spatial variation of the average horizontal dispersion rates.’’ However, the horizontal dispersion coefficients obtained from Eq. 11 using the observed vertical diffusivities are an order of magnitude smaller than the values presented in Table 1 of Okely et al. (2010a) and thus are substantially smaller than the horizontal dispersion coefficients obtained from the tracer simulations. Hence, the combined effect of vertical shear and vertical diffusion cannot explain the large horizontal dispersion in the simulation of Okely et al. (2010a). Finally, the Lagrangian particle technique and also the dispersion of the simulated tracer clouds appear to depend mainly on the horizontal divergence of the simulated flow field. Comparison of simulated and observed particle tracks and horizontal currents at a single location indicates that the quality of the simulated flow field is not sufficient to provide the divergence of the true flow field in the lakes studied. Hence, Okely et al. (2010a,b) may provide estimates of the spread of particles and tracers in their simulated flow field but cannot contribute information on horizontal particle dispersal or horizontal dispersion and mixing under field conditions in lakes.