Total Turbulent Kinetic Energy Research Articles

A Cloud-Resolving Model with an Adaptive Vertical Grid for Boundary Layer Clouds

Abstract Accurate cloud-resolving model simulations of cloud cover and cloud water content for boundary layer clouds are difficult to achieve without vertical grid spacing well below 100 m, especially for inversion-topped stratocumulus. The need for fine vertical grid spacing presents a significant impediment to global or large regional simulations using cloud-resolving models, including the Multiscale Modeling Framework (MMF), in which a two-dimensional or small three-dimensional cloud-resolving model is embedded into each grid cell of a global climate model in place of more traditional cloud parameterizations. One potential solution to this problem is to use a model with an adaptive vertical grid (i.e., a model that is able to add vertical layers where and when needed) rather than trying to use a fixed grid with fine vertical spacing throughout the boundary layer. This article examines simulations with an adaptive vertical grid for three well-studied stratocumulus cases based on observations from the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) experiment, the Atlantic Stratocumulus Transition Experiment (ASTEX), and the Atlantic Trade Cumulus Experiment (ATEX). For each case, three criteria are examined for determining where to add or remove vertical layers. One criterion is based on the domain-averaged potential temperature profile; the other two are based on the ratio of the estimated subgrid-scale to total water flux and turbulent kinetic energy. The results of the adaptive vertical grid simulations are encouraging in that these simulations are able to produce results similar to simulations using fine vertical grid spacing throughout the boundary layer, while using many fewer vertical layers.

Coherent Turbulent Structures Across a Vegetation Discontinuity

The study of turbulent flow across a vegetation discontinuity is of significant interest as such landscape features are common, and as there is no available theory to describe this regime adequately. We have simulated the three-dimensional dynamics of the airflow across a discontinuity between a forest (with a leaf area index of 4) and a clearing surface using large-eddy simulation. The properties of the bulk flow, as well as the large-scale coherent turbulent structures across the forest-to-clearing transition and the clearing-to-forest transition, are systematically explored. The vertical transport of the bulk flow upstream of the leading edge gives rise to the enhanced gust zone around the canopy top, while the transport downstream of the trailing edge leads to the formation of a recirculation zone above the clearing surface. The large-scale coherent structures across the two transitions exhibit both similarities with and differences from those upstream of the corresponding transition. For example, the ejection motion is dominant over the sweep motion in most of the region 1 < z/h < 2 (h is the canopy height) immediately downstream of the trailing edge, much as in the forested area upstream. Also, the streamwise vortex pair, which has previously been observed within the canopy sublayer and the atmospheric boundary layer, is consistently found across both transitions. However, the inflection observed both in the mean streamwise velocity, as well as in the vertical profiles of the coherent structures in the forested area, disappears gradually across the forest-to-clearing transition. The coherence of the turbulence, quantified by the percentage of the total turbulence kinetic energy that the coherent structures capture from the flow, decreases sharply immediately downstream of the trailing edge of the forest and increases downstream of the leading edge of the forest. The effects of the ratio of the forest/clearing lengths under a given streamwise periodicity on flow statistics and coherent turbulent structures are presented as well.

DNS study of decaying homogeneous isotropic turbulence with polymer additives

In order to investigate the turbulent drag reduction phenomenon and understand its mechanism, direct numerical simulation (DNS) was carried out on decaying homogeneous isotropic turbulence (DHIT) with and without polymer additives. We explored the polymer effect on DHIT from the energetic viewpoint, i.e. the decay of the total turbulent kinetic energy and energy distribution at each scale in Fourier space and from the phenomenological viewpoint, i.e. the alterations of vortex structures, the enstrophy and the strain. It was obtained that in DHIT with polymer additives the decay of the turbulent kinetic energy is faster than that in the Newtonian fluid case and a modification of the turbulent kinetic energy transfer process for the Newtonian fluid flow is observed due to the release of the polymer elastic energy into flow structures at certain small scales. Besides, we deduced the transport equations of the enstrophy and the strain, respectively, for DHIT with polymer additives. Based on the analyses of these transport equations, it was found that polymer additives depress both the enstrophy and the strain in DHIT as compared to the Newtonian fluid case, indicating the inhibition effect on small-scale vortex structures and turbulence intensity by polymers.

Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data

Data from a 1152×760×1280 direct numerical simulation (DNS) [N. J. Mueschke and O. Schilling, “Investigation of Rayleigh–Taylor turbulence and mixing using direct numerical simulation with experimentally measured initial conditions. I. Comparison to experimental data,” Phys. Fluids 21, 014106 (2009)] of a transitional Rayleigh–Taylor mixing layer modeled after a small Atwood number water channel experiment is used to comprehensively investigate the structure of mean and turbulent transport and mixing. The simulation had physical parameters and initial conditions approximating those in the experiment. The budgets of the mean vertical momentum, heavy-fluid mass fraction, turbulent kinetic energy, turbulent kinetic energy dissipation rate, heavy-fluid mass fraction variance, and heavy-fluid mass fraction variance dissipation rate equations are constructed using Reynolds averaging applied to the DNS data. The relative importance of mean and turbulent production, turbulent dissipation and destruction, and turbulent transport are investigated as a function of Reynolds number and across the mixing layer to provide insight into the flow dynamics not presently available from experiments. The analysis of the budgets supports the assumption for small Atwood number, Rayleigh–Taylor driven flows that the principal transport mechanisms are buoyancy production, turbulent production, turbulent dissipation, and turbulent diffusion (shear and mean field production are negligible). As the Reynolds number increases, the turbulent production in the turbulent kinetic energy dissipation rate equation becomes the dominant production term, while the buoyancy production plateaus. Distinctions between momentum and scalar transport are also noted, where the turbulent kinetic energy and its dissipation rate both grow in time and are peaked near the center plane of the mixing layer, while the heavy-fluid mass fraction variance and its dissipation rate initially grow and then begin to decrease as mixing progresses and reduces density fluctuations. All terms in the transport equations generally grow or decay, with no qualitative change in their profile, except for the pressure flux contribution to the total turbulent kinetic energy flux, which changes sign early in time (a countergradient effect). The production-to-dissipation ratios corresponding to the turbulent kinetic energy and heavy-fluid mass fraction variance are large and vary strongly at small evolution times, decrease with time, and nearly asymptote as the flow enters a self-similar regime. The late-time turbulent kinetic energy production-to-dissipation ratio is larger than observed in shear-driven turbulent flows. The order of magnitude estimates of the terms in the transport equations are shown to be consistent with the DNS at late-time, and also confirms both the dominant terms and their evolutionary behavior. These results are useful for identifying the dynamically important terms requiring closure, and assessing the accuracy of the predictions of Reynolds-averaged Navier–Stokes and large-eddy simulation models of turbulent transport and mixing in transitional Rayleigh–Taylor instability-generated flow.

The Effects of Vegetation Density on Coherent Turbulent Structures within the Canopy Sublayer: A Large-Eddy Simulation Study

Terrestrial ecosystems are characterized by a wide range of canopy vegetation density, which is known to affect turbulent transport processes across the canopy–atmosphere interface. In the presence of a dense and horizontally homogeneous canopy, the canopy sublayer has been described as resembling a plane mixing layer. At the other extreme, where the canopy is essentially absent, the canopy sublayer is typically assumed to be similar to a turbulent boundary layer over a rough surface. However, it remains unclear how the canopy turbulence changes from boundary-layer-like to mixing-layer-like as the vegetation density increases. We use large-eddy simulation to study five different vegetation densities varying from an extremely sparse canopy to an extremely dense canopy. This investigation draws on the study of flow statistics as well as large-scale coherent turbulent structures within the canopy sublayer. The coherent structures are identified through the use of proper orthogonal decomposition. The results of skewness of velocity components and characteristic length scales suggest that, as the vegetation density increases, the canopy turbulence gradually undergoes a transition from resembling a rough-wall boundary layer to being similar to a mixing layer. As demonstrated by others, we found that the coherent structures within the canopy sublayer consist of a strong sweep/ejection motion framed by a counter-rotating vortex pair with elliptical cross-sections. As the canopy becomes denser, these important structures are shown here to be more elevated. Vegetation density does not appear to have a significant effect on the percentage of the total turbulent kinetic energy that is represented by the coherent structures.

Assessment Measures for Engineering LES Applications

Abstract Anticipating that large eddy simulations will increasingly become the future engineering tool for research, development, and design, it is deemed necessary to formulate some quality assessment measures that can be used to judge the resolution of turbulent scales and the accuracy of predictions. In this context some new and refined measures are proposed and compared with those already published by the authors in the common literature. These measures involve (a) fraction of the total turbulent kinetic energy, (b) relative grid size with respect to Kolmogorov or Taylor scales, and (c) relative effective subgrid/numerical viscosity with respect to molecular viscosity. In addition, an attempt is made to segregate the contributions from numerical and modeling errors. Proposed measures are applied to various test cases and validated against fully resolved large eddy simulation and/or direct numerical simulation whenever possible.

Effect of axisymmetric forcing on the structure of a swirling turbulent jet

With the aid of the Stereo PIV technique, the local structure of swirling free turbulent jets is investigated under the following flow conditions: the Reynolds number was equal to 8900, and the swirl number varied from 0 to 1.0. The effect on the jet flow structure of external periodical forcing, applied with an axisymmetric mode to the inlet velocity, was studied. Also investigated were the flow response to the forcing at two Strouhal numbers, St = 0.52 and 1.2, and with various forcing amplitudes. Additional measurements with application of the conditional sampling approach were performed in order to analyze spatio-temporal dynamics of the large-scale ring-like vortices, generated in the forced jet at a low swirl rate. The greatest effect of the forcing on the swirling jet structure was observed in the case of the high swirl rate ( S = 1.0), which was previously considered to be largely insensitive to external forcing. The forcing at St = 1.2 with relatively high amplitude resulted in an abrupt change in the turbulent structure of the flow: an increase of total turbulent kinetic energy and strong anisotropy of its components took place.

Laboratory and modeling studies of cloud–clear air interfacial mixing: anisotropy of small-scale turbulence due to evaporative cooling

Small-scale mixing between cloudy air and unsaturated clear air is investigated in numerical simulations and in a laboratory cloud chamber. Despite substantial differences in physical conditions and some differences in resolved scales of motion, results of both studies indicate that small-scale turbulence generated through cloud–clear air interfacial mixing is highly anisotropic. For velocity fluctuations, numerical simulations and cloud chamber observations demonstrate that the vertical velocity variance is up to a factor of two larger than the horizontal velocity variance. The Taylor microscales calculated separately for the horizontal and vertical directions also indicate anisotropy of turbulent eddies. This anisotropy is attributed to production of turbulent kinetic energy (TKE) by buoyancy forces due to evaporative cooling of cloud droplets at the cloud–clear air interface. Numerical simulations quantify the effects of buoyancy oscillations relative to the values expected from adiabatic and isobaric mixing, standardly assumed in cloud physics. The buoyancy oscillations result from microscale transport of liquid water due to the gravitational sedimentation of cloud droplets. In the particular modeling setup considered here, these oscillations contribute to about a fifth of the total TKE production.

Large scale rotating motions in a multiple jets combustor

The flow dynamics of a multiple jet combustor is investigated using large eddy simulation. This particular combustor geometry is designed to mix hot combustion products from a central recirculation zone into the surrounding fuel/air jets. Using proper orthogonal decomposition, a large scale rotation of the central recirculation zone around the combustor axis was identified, though the averaged flow field does not exhibit any azimuthal motion. The rotating mode was found to have a relatively low frequency and to contain about 10% of the total turbulent kinetic energy. The occurrence of this mode was explained using the nonlinear delay saturation model.

Consequences of Urban Stability Conditions for Computational Fluid Dynamics Simulations of Urban Dispersion

Abstract The validity of omitting stability considerations when simulating transport and dispersion in the urban environment is explored using observations from the Joint Urban 2003 field experiment and computational fluid dynamics simulations of that experiment. Four releases of sulfur hexafluoride, during two daytime and two nighttime intensive observing periods (IOPs), are simulated using the building-resolving computational fluid dynamics model called the Finite Element Model in 3-Dimensions and Massively Parallelized (FEM3MP) to solve the Reynolds-averaged Navier–Stokes equations with two options of turbulence parameterizations. One option omits stability effects but has a superior turbulence parameterization using a nonlinear eddy viscosity (NEV) approach, and the other considers buoyancy effects with a simple linear eddy viscosity approach for turbulence parameterization. Model performance metrics are calculated by comparison with observed winds and tracer data in the downtown area and with observed winds and turbulence kinetic energy (TKE) profiles at a location immediately downwind of the central business district in the area labeled as the urban shadow. Model predictions of winds, concentrations, profiles of wind speed, wind direction, and friction velocity are generally consistent with and compare reasonably well to the field observations. Simulations using the NEV turbulence parameterization generally exhibit better agreement with observations. To explore further the assumption of a neutrally stable atmosphere within the urban area, TKE budget profiles slightly downwind of the urban wake region in the urban shadow are examined. Dissipation and shear production are the largest terms that may be calculated directly. The advection of TKE is calculated as a residual; as would be expected downwind of an urban area, the advection of TKE produced within the urban area is a very large term. Buoyancy effects may be neglected in favor of advection, shear production, and dissipation. For three of the IOPs, buoyancy production may be neglected entirely; for one IOP, buoyancy production contributes approximately 25% of the total TKE at this location. For both nighttime releases, the contribution of buoyancy to the total TKE budget is always negligible though positive. Results from the simulations provide estimates of the average TKE values in the upwind, downtown, downtown shadow, and urban wake zones of the computational domain. These values suggest that building-induced turbulence can cause the average turbulence intensity in the urban area to increase by as much as 7 times average upwind values, explaining the minimal role of buoyant forcing in the downtown region. The downtown shadow exhibits an exponential decay in average TKE, whereas the distant downwind wake region approaches the average upwind values. For long-duration releases in downtown and downtown shadow areas, the assumption of neutral stability is valid because building-induced turbulence dominates the budget. However, farther downwind in the urban wake region, which is found to be approximately 1500 m beyond the perimeter of downtown Oklahoma City, Oklahoma, the levels of building-induced turbulence greatly subside, and therefore the assumption of neutral stability is less valid.

Large-eddy simulation of the flow in a lid-driven cubical cavity

Large-eddy simulations of the turbulent flow in a lid-driven cubical cavity have been carried out at a Reynolds number of 12000 using spectral element methods. Two distinct subgrid-scales models, namely a dynamic Smagorinsky model and a dynamic mixed model, have been both implemented and used to perform long-lasting simulations required by the relevant time scales of the flow. All filtering levels make use of explicit filters applied in the physical space (on an element-by-element approach) and spectral (modal) spaces. The two subgrid-scales models are validated and compared to available experimental and numerical reference results, showing very good agreement. Specific features of lid-driven cavity flow in the turbulent regime, such as inhomogeneity of turbulence, turbulence production near the downstream corner eddy, small-scales localization and helical properties are investigated and discussed in the large-eddy simulation framework. Time histories of quantities such as the total energy, total turbulent kinetic energy or helicity exhibit different evolutions but only after a relatively long transient period. However, the average values remain extremely close.

On the parameterization of turbulent fluxes over the tropical Eastern Pacific

Abstract. We present estimates of turbulent fluxes of heat and momentum derived from low level (~30 m) aircraft measurements over the tropical Eastern Pacific and provide empirical relationships that are valid under high wind speed conditions (up to 25 ms−1). The estimates of total momentum flux and turbulent kinetic energy can be represented very accurately (r2=0.99, when data are binned every 1 ms−1) by empirical fits with a linear and a cubic terms of the average horizontal wind speed. The latent heat flux shows a strong quadratic dependence on the horizontal wind speed and a linear relationship with the difference between the air specific humidity and the saturated specific humidity at the sea surface, explaining 96% of the variance. The estimated values were used to evaluate the performance of three currently used parameterizations of turbulence fluxes, varying in complexity and computational requirements. The comparisons with the two more complex parameterizations show good agreement between the observed and parameterized latent heat fluxes, with less agreement in the sensible heat fluxes, and one of them largely overestimating the momentum fluxes. A third, very simple parameterization shows a surprisingly good agreement of the sensible heat flux, while momentum fluxes are again overestimated and a poor agreement was observed for the latent heat flux (r2=0.62). The performance of all three parameterizations deteriorates significantly in the high wind speed regime (above 10–15 ms−1). The dataset obtained over the tropical Eastern Pacific allows us to derive empirical functions for the turbulent fluxes that are applicable from 1 to 25 ms−1, which can be introduced in meteorological models under high wind conditions.

The effect of standing biomass on flow velocity and turbulence in Spartina alterniflora canopies

Plant-flow interactions on the surface of tidal wetlands result in flow characteristics that are profoundly different from non-vegetated flows. Reductions in mean flow velocity and turbulence, especially the vertical components, limit vertical mixing and may impact a wide range of processes including geochemical exchanges at the sediment water interface, larval recruitment and dispersion, and sediment deposition and retention. The goal of this paper is to quantify horizontal and vertical components of velocity, turbulence intensity and total turbulent kinetic energy in Spartina alterniflora canopies in southeastern North Carolina and to relate flow characteristics to particulate transport on the marsh surface. Another aim of this paper is to assess the extent to which the distribution of standing biomass affects mean flow and turbulence by comparing S. alterniflora data to other canopy types and through a series of canopy manipulations which altered canopy height and stem densities. The results of this study indicate that flow velocity, turbulence intensity, and total turbulent kinetic energy (TKE) are significantly reduced within the vegetated canopy and that this reduction is inversely related to the amount of biomass present in the water column. Within the canopy, approximately 50% of the initial mean velocity and TKE is reduced within 5 m of the canopy edge. Within the canopy, mean velocity and TKE horiz usually exceeded vertical velocity or TKE vert and the vertical components of flow were attenuated more strongly than the horizontal. These results suggest that within the vegetation, turbulence contributes more to lateral advection than to vertical mixing. As a result, total suspended solid concentrations were shown to decrease logarithmically with distance from the canopy edge and to decrease at a faster rate in more densely vegetated regions of the canopy (i.e. lower TKE vert) as compared to areas of sparser vegetation (i.e. higher TKE vert).

3D Unsteady RANS Modeling of Complex Hydraulic Engineering Flows. II: Model Validation and Flow Physics

A chimera overset grid flow solver is developed for solving the unsteady Reynolds-averaged Navier-Stokes (RANS) equations in arbitrarily complex, multiconnected domains. The details of the numerical method were presented in Part I of this paper. In this work, the method is validated and applied to investigate the physics of flow past a real-life bridge foundation mounted on a fixed flat bed. It is shown that the numerical model can reproduce large-scale unsteady vortices that contain a significant portion of the total turbulence kinetic energy. These coherent motions cannot be captured in previous steady three-dimensional (3D) models. To validate the importance of the unsteady motions, experiments are conducted in the Georgia Institute of Technology scour flume facility. The measured mean velocity and turbulence kinetic energy profiles are compared with the numerical simulation results and are shown to be in good agreement with the numerical simulations. A series of numerical tests is carried out to examine the sensitivity of the solutions to grid refinement and investigate the effect of inflow and far-field boundary conditions. As further validation of the numerical results, the sensitivity of the turbulence kinetic energy profiles on either side of the complex pier bent to a slight asymmetry of the approach flow observed in the experiments is reproduced by the numerical model. In addition, the computed flat-bed flow characteristics are analyzed in comparison with the scour patterns observed in the laboratory to identify key flow features responsible for the initiation of scour. Regions of maximum shear velocity are shown to correspond to maximum scour depths in the shear zone to either side of the upstream pier, but numerical values of vertical velocity are found to be very important in explaining scour and deposition patterns immediately upstream and downstream of the pier bent.

The Influence of Idealized Heterogeneity on Wet and Dry Planetary Boundary Layers Coupled to the Land Surface

AbstractThis manuscript describes numerical experiments investigating the influence of 2–30-km striplike heterogeneity on wet and dry convective boundary layers coupled to the land surface. The striplike heterogeneity is shown to dramatically alter the structure of the convective boundary layer by inducing significant organized circulations that modify turbulent statistics. The impact, strength, and extent of the organized motions depend critically on the scale of the heterogeneity λ relative to the boundary layer height zi. The coupling with the land surface modifies the surface fluxes and hence the circulations resulting in some differences compared to previous studies using fixed surface forcing. Because of the coupling, surface fluxes in the middle of the patches are small compared to the patch edges. At large heterogeneity scales (λ/zi ∼18) horizontal surface-flux gradients within each patch are strong enough to counter the surface-flux gradients between wet and dry patches allowing the formation of small cells within the patch coexisting with the large-scale patch-induced circulations. The strongest patch-induced motions occur in cases with 4 &amp;lt; λ/zi &amp;lt; 9 because of strong horizontal pressure gradients across the wet and dry patches. Total boundary layer turbulence kinetic energy increases significantly for surface heterogeneity at scales between λ/zi = 4 and 9; however, entrainment rates for all cases are largely unaffected by the striplike heterogeneity.Velocity and scalar fields respond differently to variations of heterogeneity scale. The patch-induced motions have little influence on total vertical scalar flux, but the relative contribution to the flux from organized motions compared to background turbulence varies with heterogeneity scale. Patch-induced motions are shown to dramatically impact point measurements in a free-convective boundary layer. The magnitude and sign of this impact depends on the location of the measurement within the region of heterogeneity.

The Use of Large-Eddy Simulations in Lagrangian Particle Dispersion Models

AbstractA Lagrangian dispersion model driven by velocity fields from large-eddy simulations (LESs) is presented for passive particle dispersion in the planetary boundary layer (PBL). In this combined LES–Lagrangian stochastic model (LSM), the total velocity is divided into resolved or filtered and unresolved or subfilter-scale (SFS) velocities. The random SFS velocity is modeled using an adaptation of Thomson's LSM in which the ensemble-mean velocity and velocity variances are replaced by the resolved velocity and SFS variances, respectively. The random SFS velocity forcing has an amplitude determined by the SFS fraction of the total turbulent kinetic energy (TKE); the fraction is about 0.15 in the bulk of the simulated convective boundary layer (CBL) used here and reaches values as large as 0.31 and 0.37 in the surface layer and entrainment layer, respectively.For the proposed LES–LSM, the modeled crosswind-integrated concentration (CWIC) fields are in good agreement with the 1) surface-layer similarity (SLS) theory for a surface source in the CBL and 2) convection tank measurements of the CWIC for an elevated release in the CBL surface layer. The second comparison includes the modeled evolution of the vertical profile shape with downstream distance, which shows the attainment of an elevated CWIC maximum and a vertically well-mixed CWIC far downstream, in agreement with the tank data. For the proposed model, the agreement with the tank data and SLS theory is better than that obtained with an earlier model in which the SFS fraction of the TKE is assumed to be 1, and significantly better than a model that neglects the SFS velocities altogether.

A simple turbulent energy-based model of fine suspended sediments in the Irish Sea

Energy is required to maintain a particle heavier than water in suspension in the sea. In equilibrium, energy must be supplied at a rate equal to the product of the weight of the particle and its sinking velocity. If the energy supply rate is known, it becomes possible to predict the total weight, and hence the concentration of suspended particles in the sea. This principle has been applied to a model of fine suspended sediments in the Irish Sea. The model is used to test the hypothesis that the supply of turbulent kinetic energy (TKE) alone controls both the spatial pattern and seasonal changes in concentration. TKE is supplied by the tide and wind, and a fixed fraction of this energy is used to keep sediment in suspension. There is assumed to be a readily available supply of fine sediments at the sea bed, which rises into suspension as soon as TKE becomes available, and sinks down again when it is not. The model incorporates 2-layer thermal stratification and vertical mixing between layers but there is no horizontal advection or diffusion. The model is driven by smoothly varying wind speeds and heating over the year and spatially varying tidal stirring. The particles have a constant settling velocity of 10 m day −1, and a density twice that of water. A fraction 0.00006 of the total (tide+wind) TKE energy input is used to stir the sediment. The results of the model are in agreement with both the observed spatial pattern and the seasonal variation of fine suspended sediments in the surface waters of the Irish Sea to within the limits of measurement accuracy and natural variability. This energy model performs at least as well as conventional stress-driven models in this regard. We therefore conclude that the general behaviour of fine suspended sediments in the Irish Sea can be explained by TKE supply alone. Other factors, such as changes in particle size and density over the year, can be used for fine tuning but are not necessary to give a broadly correct picture. The result is that we have a simple, physically coherent, method of predicting the turbidity (and hence the light regime) of a shelf sea from physical inputs alone.

Interfacial mixing in a highly stratified estuary 2. A “method of constrained differences” approach for the determination of the momentum and mass balances and the energy of mixing

This article is part 2 of a set of papers addressing mixing in a highly stratified estuary. In Part 2, turbulence and mean flow measurements are together used to understand the role of mixing in the overall dynamics of the system. Estimates of the partition of energy dissipation between bed‐generated and internal mixing suggest that internal mixing accounts for about two thirds of the total turbulent kinetic energy (TKE) produced in the salt‐wedge reach of the Columbia River estuary during the neap‐tide, moderate river‐flow observation period. This suggests that internal mixing plays a larger role in the energetics of such systems than has previously been recognized. The lack of near‐bed mixing on the neap is also likely a major factor in the accumulation of sediment in the estuary on neap tides. Profiles of estimated turbulent kinetic energy (TKE) dissipation were obtained using a new approach, which we call the “method of constrained differences,” that allows the calculation of all major terms in the momentum and density balances during ebb mixing events from data obtained by a single vessel. The method of constrained differences uses a local equilibrium turbulence closure and measured velocity and density profiles to determine the density flux divergence necessary for internal consistency in the momentum and mass equations. The calculated mixing rates from the iterative procedure compare favorably with measured dissipation rates, tending to validate both the measurements and the procedure. Although this method involves a constraint of the form of a known or inferred stress at some point in the water column, it has the potential for wide application, especially if point measurements of TKE dissipation rates are available.

Subgrid-scale modeling for large-eddy simulations of compressible turbulence

We present two phenomenological subgrid-scale (SGS) models for large-eddy simulations (LES) of compressible turbulent flows. A nonlinear model and a stretched-vortex model are tested in LES of compressible decaying isotropic turbulence. Results of LES at 323, 483, and 643 resolution are compared to corresponding 2563 direct numerical simulations (DNS) at a turbulent Mach number, Mt∼0.4. We use numerical schemes based on compact finite differences and study the effects of their order of accuracy on LES results. Both models give satisfactory agreement with DNS for the decay of the total turbulent kinetic energy. The probability densities (pdf) of energy transfer to subgrid scales obtained from filtered DNS and the SGS models are compared. Both models produce a narrower distribution of energy transfer than corresponding filtered DNS data, with less backscatter. The pdf of the alignment of components of the subgrid stress tensor and the eigenvectors of the rate-of-strain tensor obtained from the models reproduces some features of the DNS results. The pdfs of both energy transfer and relative eigenvector alignment are obtained from DNS and LES after about one large-eddy turnover time from the same initial condition. All tests of the present LES models are therefore a posteriori and none is a priori.

Large-scale modes of turbulent channel flow: transport and structure

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.