Real Turbulence Research Articles

A priori and a posteriori tests of inflow conditions for large-eddy simulation

Comparisons of inflow conditions for large-eddy simulations of turbulent, wall-bounded flows are carried out. Consistent with previous investigations, it is found that the spectral content of the inflow velocity is important. Inflow conditions based on random-noise, or small-scale eddies only, dissipate quickly. Temporal and spatial filtering of a time series obtained from a separate calculation indicates that it is important to capture eddies of dimensions equal to or larger than the integral length scale of the flow. Three methods for generating inflow velocity fields are tested in a simulation of spatially developing turbulent channel flow. Synthetic turbulence generation methods that introduce realistic length scales are more suitable than uncorrelated random noise, but still require fairly long development lengths before realistic turbulence is established. A recycling method based on the use of turbulent data obtained from a separate calculation, in different flow conditions, was found to result in more rapid transition. A forcing method that includes a control loop also appears to be effective by generating turbulence with the correct Reynolds stresses and correlations within less than ten channel half heights.

Theory and simulation of real and ideal magnetohydrodynamic turbulence

Incompressible, homogeneous magnetohydrodynamic (MHD) turbulence consists of fluctuating vorticity and magnetic fi elds, which are represented in terms of their Fourier coefficients. Here, a set of fi ve Fourier spectral transform method numerical simulations of two-dimensional (2-D) MHD turbulence on a $512^2$ grid is described. Each simulation is a numerically realized dynamical system consisting of Fourier modes associated with wave vectors $\mathbf{k}$, with integer components, such that $k = |\mathbf{k}| \le k_{max}$. The simulation set consists of one ideal (non-dissipative) case and four real (dissipative) cases. All fi ve runs had equivalent initial conditions. The dimensions of the dynamical systems associated with these cases are the numbers of independent real and imaginary parts of the Fourier modes. The ideal simulation has a dimension of $366104$, while each real simulation has a dimension of $411712$. The real runs vary in magnetic Prandtl number $P_M$, with $P_M \in {0.1, 0.25, 1, 4}$. In the results presented here, all runs have been taken to a simulation time of $t = 25$. Although ideal and real Fourier spectra are quite di fferent at high $k$, they are similar at low values of $k$. Their low $k$ behavior indicates the existence of broken symmetry and coherent structure in real MHD turbulence, similar to what exists in ideal MHD turbulence. The value of $P_M$ strongly affects the ratio of kinetic to magnetic energy and energy dissipation (which is mostly ohmic). The relevance of these results to 3-D Navier-Stokes and MHD turbulence is discussed.

Effects of Noise on Thorpe Scales and Run Lengths

Abstract Estimating the diapycnal mixing rate from standard CTD data by identifying overturning regions in the water column (the Thorpe-scale approach) provides good spatial and temporal coverage but is sometimes limited by instrument noise. This noise leads to spurious density inversions that are difficult to distinguish from real turbulent overturns. Previous efforts to eliminate noise may have overcorrected and hence underestimated the level of mixing. Here idealized density profiles are used to identify the magnitude and characteristics of overturning regions arising entirely from instrument noise, in order to establish a standard against which CTD data can be compared. The key nondimensional parameters are 1) the amplitude of the noise scaled by the density change over the section of profile considered, and 2) the number of data points in the section of profile. In some cases the product of these, which is equal to the amplitude of the noise scaled by the average density difference between consecutive measurements, is more useful than the second parameter. The probability distribution of “run length,” a useful diagnostic, varies significantly across this parameter space. Reasons for this are discussed, and it is shown that CTD data very rarely lie in a region of parameter space where comparison with the probability density function (PDF) of run lengths for a random uncorrelated series, or its rms value 6, is appropriate. The distribution of Thorpe displacements arising entirely from instrument noise, as well as the Thorpe scale and the statistics of density inversions, is also discussed. Analysis of CTD data from the interfaces of the thermohaline staircase in the deep Canada Basin illustrates how the results can be applied in practice to help to distinguish between signal and noise in marginal regimes. Density inversions seen in these data are shown to be no different from those that would result from instrument noise.

Cosmic‐Ray Scattering and Streaming in Compressible Magnetohydrodynamic Turbulence

Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for revisions in the picture of cosmic ray transport. In this paper we use recently obtained scaling laws for MHD modes to obtain the scattering frequency for cosmic rays. Using quasilinear theory we calculate gyroresonance with MHD modes (Alfv\'{e}nic, slow and fast) and transit-time damping (TTD) by fast modes. We provide calculations of cosmic ray scattering for various phases of interstellar medium with realistic interstellar turbulence driving that is consistent with the velocity dispersions observed in diffuse gas. We account for the turbulence cutoff arising from both collisional and collisionless damping. We obtain analytical expressions for diffusion coefficients that enter Fokker-Planck equation describing cosmic ray evolution. We obtain the scattering rate and show that fast modes provide the dominant contribution to cosmic ray scattering for the typical interstellar conditions in spite of the fact that fast modes are subjected to damping. We determine how the efficiency of the scattering depends on the characteristics of ionized media, e.g. plasma $\beta$. We calculate the range of energies for which the streaming instability is suppressed by the ambient MHD turbulence.

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

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

Large-Eddy Simulation of Coherent Turbulence Structures Associated with Scalar Ramps Over Plant Canopies

Large-eddy simulations were performed of a neutrally-stratified turbulent flow within and above an ideal, horizontally- and vertically-homogeneous plant canopy. Three simulations were performed for shear-driven flows in small and large computational domains, and a pressure-driven flow in a small domain, to enable the nature of canopy turbulence unaffected by external conditions to be captured. The simulations reproduced quite realistic canopy turbulence characteristics, including typical ramp structures appearing in time traces of the scalar concentration near the canopy top. Then, the spatial structure of the organised turbulence that caused the scalar ramps was examined using conditional sampling of three-dimensional instantaneous fields, triggered by the occurrence of ramp structures. A wavelet transform was used for the detection of ramp structures in the time traces. The ensemble-averaged results illustrate that the scalar ramps are associated with the microfrontal structure in the scalar, the ejection-sweep structure in the streamwise and vertical velocities, a laterally divergent flow just around the ramp-detection point, and a positive, vertically-coherent pressure perturbation. These vertical structures were consistent with previous measurements made in fields or wind tunnels. However, the most striking feature is that the horizontal slice of the same structure revealed a streamwise-elongated region of high-speed streamwise velocity impacting on another elongated region of low-speed velocity. These elongated structures resemble the so-called streak structures that are commonly observed in near-wall shear layers. Since elongated structures of essentially similar spatial scales were observed in all of the runs, these streak structures appear to be inherent in near-canopy turbulence. Presumably, strong wind shear formed just above the canopy is involved in their formation. By synthesis of the ensemble-averaged and instantaneous results, the following processes were inferred for the development of scalar microfronts and their associated flow structures: (1) a distinct scalar microfront develops where a coherent downdraft associated with a high-speed streak penetrates into the region of a low-speed streak; (2) a stagnation in flow between two streaks of different velocities builds up a vertically-coherent high-pressure region there; (3) the pressure gradients around the high-pressure region work to reduce the longitudinal variations in streamwise velocity and to enhance the laterally-divergent flow and lifted updrafts downstream of the microfront; (4) as the coherent mother downdraft impinges on the canopy, canopy-scale eddies are formed near the canopy top in a similar manner as observed in conventional mixing-layer turbulence.

Turbulent diffusion of momentum and suspended particles: A finite-mixing-length theory

A finite-mixing-length theory is presented for turbulent mixing. This theory contains Fickian diffusion as the limiting case for lm/L→0, where lm is the mixing length and L is the scale of the distribution under consideration. The new model is of similar generality to that of Taylor (1921), “Diffusion by continuous movements.” However, while Taylor’s model, being strictly Lagrangian, is difficult to apply to inhomogeneous scenarios, the new model is Eulerian and easily applicable to bottom boundary layers and other inhomogeneous flows. When applied to steady suspended sediment concentrations c(z), the theory predicts the observed trend of apparent Fickian diffusivities εFick=−wsc/(dc/dz) being larger for particles with larger settling velocity ws, in a given flow. The corresponding nature of the ratios between apparent Fickian sediment diffusivities and eddy viscosities, β=εFick/vt, for different particles in the same flow, is also revealed. That is, β is an increasing function of the particle settling velocity and may be greater or smaller than unity depending on the relative magnitude of the vertical scales for concentrations Lc and for horizontal velocity Lu. Applied to the case of wave motion over ripples, even the observed trend of fine sand indicating decreasing εFick(z) while coarse sand shows increasing εFick(z) can be modelled with realistic turbulence parameters. Different Fickian diffusivities displayed by different species like density, heat, and salinity in a given turbulent flow may also be qualitatively explainable in terms of finite-mixing-length effects.

The effect of resuspension on the fate of total mercury and methyl mercury in a shallow estuarine ecosystem: a mesocosm study

Sediments are the major repository of mercury in estuaries and could be a significant source of Hg to the overlying water column via release from the solid phase during resuspension. There is, however, little information on the effect of resuspension on Hg partitioning and release to the water column. The objective of this study was to determine the effect of resuspension on the cycling of THg and MeHg between the water column and the sediment. Tidal resuspension was simulated using the MEERC STORM facility. The facility can mimic both realistic bottom shear stress and water column turbulence simultaneously. There were three replicates of each resuspension (R) and no resuspension (NR) mesocosms. Two 4-week experiments were conducted in July and October of 2001: experiment 1 without clams and experiment 2 with clams. Both experiments showed that resuspension of muddy sediment introduced significantly higher particulate THg to the water column as TSS increased. The results suggest that THg was mostly bound to sediment particles with very little release during the resuspension events. In contrast, particulate MeHg was significantly lower in the R tanks where sediment particles with poor MeHg were dominant in the water column during the resuspension events. Dissolved THg and MeHg did not change in concert with changes in particulate load, suggesting that the dynamics between dissolved and particulate phases for both THg and MeHg cannot be explained by an equilibrium partitioning.

Refined Structure of Energy Spectrum and Energy Cascade in Atmospheric Turbulence

AbstractUsing wavelet and Fourier transform we make an analysis of velocity fluctuation data of atmospheric turbulence on the near surface layer. We find that there are some abrupt points in the well‐known energy spectrum of “–5/3” scaling law in the wave‐number domain. If the timescale of wavelet transform varies as 2j, j = 1, 2, …, j0, the eddy of high‐frequency components will cascade in a manner of 2(j−2) − 1, (j > 1), which is in accordance with the physical picture of synchro‐cascade pattern. There are no characteristic spectrum components, because the effects of the high frequency components on the properties of spectrum are the same in the region in which the scaling law is held. We get the same result using different basic functions to data of atmosphere turbulence at different heights. The comparison experiments are also made between a number of random series about the fractal Brownian motion with Husrt exponent H=1/3.The results show that the deviation of real full developed atmopheric turbulence from Guassian distibution is very small, and the difference only occurs in the case of the high order scaling law.

Combined water-column mixing and benthic boundary-layer flow in mesocosms: key for realistic benthic-pelagic coupling studies

We developed 2 scaled linked mesocosms that realistically mimicked both water-col- umn mixing and benthic boundary-layer flow, enabling more realistic benthic-pelagic coupling experiments. The first was a 'large' 1000 l system linking a mesocosm with an annular flume; the sec- ond a 'small' 100 l system linking a mesocosm with a Gust microcosm. We compared bottom shear velocity, flow speeds, and internal mixing energies between linked and isolated mesocosms that were the same in volume and shape, and compared them to nature. In addition, we performed scaled 4 wk long comparative ecosystem experiments with oysters in the large and small mesocosms to determine if a realistically mimicked benthic boundary-layer flow and system shape could signifi- cantly affect ecosystem processes. We scaled all 4 systems to have the same realistic water-column turbulence levels and increased bottom shear velocity to moderate levels in the linked mesocosms. Bottom shear remained unrealistically low compared to nature in the isolated tanks. In addition, the water column and the sediment-water interface were more realistically connected in the linked than in the isolated mesocosms. The linked mesocosms had a similar scaling relationship of turbulence intensity and bottom shear velocity of 1.6, as found in nature. System shape and bottom shear signif- icantly affected ecosystem properties through changes in light, microphytobenthos biomass growth and erosion, sediment inorganic nutrient fluxes, oyster growth, and water column nutrient dynamics. In this study we show that a commonly used system shape in ecosystem studies and unrealistically low bottom shear in mesocosms both produce significant artifacts in benthic-pelagic coupling stud- ies. We also demonstrate improved systems without these artifacts. System shape, bottom shear, water-column turbulence levels, and their ratios should all be considered in designing mesocosms to mimic natural processes.

Confining turbulence in plasmas

The transport properties of electrostatic turbulence in plasmas are investigated by using test-particle simulations. In particular, the possibility of control of the transport in a given synthetic turbulent field, which evolves both in space and time, is explored. The fluctuations are built up taking into account observations of real turbulence in laboratory plasmas, that is, by allowing the field to contain structures lying on all dynamically interesting scales. It is shown that, inside a given region of space, the transport can be reduced when phases of the field are randomized, that is, when correlations of the field, which are responsible for the generation of structures, are annihilated. This means that a barrier for the transport can be achieved in a plasma even without actually suppressing turbulence. When the barrier is active, a flux of particles toward the center of the simulation box is present inside the region where the barrier has been located.

On the application of congruent upwind discretizations for large eddy simulations

Upwind schemes were judged inappropriate for performing accurate large eddy simulations of turbulent flow owing to the artificial dissipation that is present at high wavenumbers of the energy content. Such a conclusion has been drawn also from some results obtained by adopting Finite Difference schemes. The present paper illustrates the performances of some new Finite Volume upwind discretization of the convective terms in the case of the 1-D Burgers model equation while studying the effects of numerical discretization on several Sub-Grid Scales turbulence models, starting from the classical static and dynamic eddy viscosity models through the recent deconvolution-based ones. Basing on previously published papers, large eddy simulations along with a deconvolution-based procedure for de-filtering the evolving variable, have been originally developed and applied. It will be shown how the coherent application of the procedure allows us to develop high-order accurate Finite Volume upwind schemes, which maintain a good spectral resolution in the entire range of resolved scale. Such schemes can be candidate for performing accurate simulations of real turbulence.

VARIABLE-COEFFICIENT FORCED BURGERS SYSTEM IN NONLINEAR FLUID MECHANICS AND ITS POSSIBLY OBSERVABLE EFFECTS

The forced Burgers equation works as a testing ground for a real turbulence, and as the qualitative model for a wide variety of problems including charge density waves, vortex lines in superconductors, disordered solids and epitaxial growth, etc. Its variable-coefficient generalizations call for better modeling of the physical situations. In this paper, we investigate a variable-coefficient generalization of the forced Burgers equation, and obtain several sets of exact soliton-like and other exact analytic solutions, via the extension of a generalized hyperbolic-function method with computerized symbolic computation. We also discuss the Wu method. We find some possibly observable effects, which might be discovered with the relevant experiments.

Turbulence with pressure: anomalous scaling of a passive vector field.

The field theoretic renormalization group (RG) and the operator-product expansion are applied to the model of a transverse (divergence-free) vector quantity, passively advected by the "synthetic" turbulent flow with a finite (and not small) correlation time. The vector field is described by the stochastic advection-diffusion equation with the most general form of the inertial nonlinearity; it contains as special cases the kinematic dynamo model, linearized Navier-Stokes (NS) equation, the special model without the stretching term that possesses additional symmetries and has a close formal resemblance with the stochastic NS equation. The statistics of the advecting velocity field is Gaussian, with the energy spectrum E(k) proportional to k(1-epsilon) and the dispersion law omega proportional to k(-2+eta), k being the momentum (wave number). The inertial-range behavior of the model is described by seven regimes (or universality classes) that correspond to nontrivial fixed points of the RG equations and exhibit anomalous scaling. The corresponding anomalous exponents are associated with the critical dimensions of tensor composite operators built solely of the passive vector field, which allows one to construct a regular perturbation expansion in epsilon and eta; the actual calculation is performed to the first order (one-loop approximation), including the anisotropic sectors. Universality of the exponents, their (in)dependence on the forcing, effects of the large-scale anisotropy, compressibility, and pressure are discussed. In particular, for all the scaling regimes the exponents obey a hierarchy related to the degree of anisotropy: the more anisotropic is the contribution of a composite operator to a correlation function, the faster it decays in the inertial range. The relevance of these results for the real developed turbulence described by the stochastic NS equation is discussed.

Influence of low-frequency wind speed fluctuations on the aeroelastic stability of suspension bridges

Starting from the standard multimode approach to the aeroelastic instability of a long span suspension bridge, that gives the critical flutter speed in the ideal case of a wind constant both in time and in space (turbulence neglected), this paper describes a procedure to evaluate in a closed form the worst effects that can ever be expected as a consequence of a turbulence with a given spectrum. To this respect, only low-frequency wind speed fluctuations strongly correlated along the span are taken into account, neglecting the beneficial effects due to a loss of coherence or to higher frequency components. This allows to obtain a flutter speed certainly safe in comparison with any realistic turbulence field. The proposed formulation is then applied to the current design of the bridge on the Messina Strait (Italy).

Analytic calculation of the parallel mean free path of heliospheric cosmic rays

The parallel mean free path of cosmic ray particles in partially turbulent electromagnetic fields is calculated for two particular turbulence models: slab-like dynamical and random sweeping turbulence. Using the general results for the pitch-angle Fokker-Planck coefficient from Teufel & Schlickeiser (2002) the rigidity dependence and the absolute value of the mean free path for these specific turbulence models are calculated for a turbulence power spectrum with finite wave amplitude at very small wavenumbers. We demonstrate that this modification affects especially the mean free path at very large rigidities. We also derive approximations for the mean free path for realistic Kolmogorov-type turbulence power spectra which include the steepening at high wavenumbers due to turbulence dispersion and/or dissipation.

Some dynamical properties of a differential model for the bursting cycle in the near-wall turbulence

In the last years several investigations have been devoted to model the bursting cycle in the near-wall turbulence by means of low-dimensional systems, with the aim of having simple mathematical models for the dynamics of coherent structures. The present paper deals with a low-dimension differential model, recently proposed by the authors. It is directly deduced from the velocity time series measured in a turbulent flow and well mimics the velocity oscillations typical of the bursting events. After studying the linear stability of the model, its behavior when an external forcing is added, both deterministic and stochastic, is analyzed. It is found that the essential characteristic of the dynamics described by the model is a Hopf bifurcation that, when excited by a stochastic forcing, produces time series with fluctuations that have similarities with the real turbulence signals.

From Differential Image Motion to Seeing

ABSTRACTThe theory of the differential image motion monitor (DIMM), a standard and widely spread method of measuring astronomical seeing, is reviewed and extended. More accurate coefficients for computing the Fried parameter from the measured variance of image motion are given. They are tested by numerical simulations that show that any DIMM measures Zernike tilts, not image centroids as generally assumed. The contribution of CCD readout noise to image motion variance is modeled. It can substantially bias DIMM results if left unsubtracted. The second most important DIMM bias comes from the used exposure time, which is typically not short enough to freeze image motion completely. This effect is studied quantitatively for real turbulence and wind profiles, and its correction by interlaced short and long exposures is validated. Finally, the influence of turbulence outer scale reduces image size in large telescopes by 10% or more compared to the standard theory; new formulae to compute FWHM and half‐energy diameter of the atmospheric point‐spread function that take into account outer scale are provided.

Analytic calculation of the parallel mean free path of heliospheric cosmic rays

The parallel mean free path of cosmic ray particles in partially turbulent electromagnetic fields is a key input param- eter for cosmic ray transport. Here the parallel mean free paths of cosmic ray protons, electrons and positrons are calculated for two particular turbulence models: slab-like dynamical and random sweeping turbulence. After outlining the general quasilinear formalism for deriving the pitch-angle Fokker-Planck coecient in weak turbulence from the particle's equation of motion, the rigidity dependence and the absolute value of the mean free path for these specific turbulence models are calculated. Approximations for the mean free path for realistic Kolmogorov-type turbulence power spectra which include the steepening at high wavenumbers due to turbulence dispersion and/or dissipation are given.

Acoustic Waves in the Turbulent Atmosphere: A Review

Abstract The subject of atmospheric acoustics and its role in atmospheric research and in development of modern methods of ground-based remote sensing of the atmosphere are outlined. A historical overview of investigations of the effect of atmospheric turbulence on sound propagation is presented, with an emphasis on the research carried out in Russia simultaneously with the creation of the Kolmogorov–Obukhov theory of locally homogenous and locally isotropic turbulence. The main theoretical and experimental results on acoustic wave fluctuations and scattering, which were obtained on the basis of the classic Kolmogorov–Obukhov theory, are summarized. Departures of the real atmospheric turbulence from the classic model and present-day conceptions of turbulence are discussed briefly. Some results of the current experimental study of sonic and infrasonic wave propagation in the atmospheric boundary layer and in the middle atmosphere are presented. It is shown that the peculiarities of the real atmospheric tur...