Velocity Turbulence Statistics Research Articles

A multiscale and multicriteria generative adversarial network to synthesize 1-dimensional turbulent fields

This article introduces a new neural network stochastic model to generate a 1-dimensional stochastic field with turbulent velocity statistics. Both the model architecture and training procedure ground on the Kolmogorov and Obukhov statistical theories of fully developed turbulence, so guaranteeing descriptions of (1) energy distribution, (2) energy cascade and (3) intermittency across scales in agreement with experimental observations. The model is a generative adversarial network (GAN) with multiple multiscale optimization criteria. First, we use three physics-based criteria: the variance, skewness and flatness of the increments of the generated field, that retrieve respectively the turbulent energy distribution, energy cascade and intermittency across scales. Second, the GAN criterion, based on reproducing statistical distributions, is used on segments of different length of the generated field. Furthermore, to mimic multiscale decompositions frequently used in turbulence’s studies, the model architecture is fully convolutional with kernel sizes varying along the multiple layers of the model. To train our model, we use turbulent velocity signals from grid turbulence at Modane wind tunnel.

Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics

We define and study a fully-convolutional neural network stochastic model, NN-Turb, which generates a 1-dimensional field with some turbulent velocity statistics. In particular, the generated process satisfies the Kolmogorov 2/3 law for the second order structure function. It also presents negative skewness across scales (i.e. Kolmogorov 4/5 law) and exhibits intermittency as characterized by skewness and flatness. Furthermore, our model is never in contact with turbulent data and only needs the desired statistical behavior of the structure functions across scales for training.

The Turbulent Lagrangian Dissipative Particle Velocity Statistics

A statistical description of turbulence comprising a probability distribution for stationary flows is the basis for determining the nature of turbulent velocity fluctuations. Away from the Eulerian spatial increments of the velocity field, the Lagrangian notion of temporal velocity increments along particle trajectories appears to be the hob of turbulent velocity statistics, ostensibly in the presence of inherent intermittencies observable in particle tracking. Such intermittencies were analyzed by using the well-known velocity structure functions, which defer to the Kolmogorov similarity theory (KST). Since particle trajectories, under normal circumstances, submit to Gaussian statistics, the deviations from Kolmogorov similarity theory are considered a culprit in the event of intermittency.

Damköhler number scaling of active cascade effects in turbulent premixed combustion

Effects of combustion heat release on turbulent velocity and scalar statistics are investigated as a function of the Damköhler number using three direct numerical simulation databases of spatially developing turbulent premixed jet flames. At low Karlovitz numbers, where heat-release effects dominate turbulent kinetic energy budgets, their relative significance scales with the integral Damköhler number in a priori Reynolds-Averaged Navier–Stokes (RANS) statistics and the filter Damköhler number in Large Eddy Simulation (LES). The Damköhler-number scaling of counter-gradient transport in this regime follows theoretical arguments underpinning linear-algebraic turbulence models, which explains their efficacy at low Karlovitz numbers. Conversely, at moderate Karlovitz numbers, LES subfilter turbulence is more strongly influenced by heat-release effects than the analogous large-scale RANS turbulence. This is consistent with the notion of an “active cascade,” which postulates that heat-release-induced volumetric expansion competes on intermediate scales with classical forward-cascade energy transfer. LES exposes these dynamics as dominant subfilter-scale physics, unlike in RANS, where they are secondary to the effects of mean-shear production at the large scales. The significance of subfilter-scale interactions is promoted by the LES filter itself, which modifies the RANS spectral basis by incorporating local flame-normal averaging. This is highlighted by comparing LES fields obtained using a 3D filter to those using a modified 2D filter, excluding the flame-normal direction, which significantly reduces the apparent influence of heat-release effects but is not representative of LES in practice. The subfilter modeling challenges posed by these distinctions at moderate Karlovitz numbers and order-unity Damköhler numbers remain to be understood.

Vertically distributed wall sources of buoyancy. Part 1. Unconfined

Abstract

Large Eddy Simulation of Turbulent Channel Flows over Rough Walls with Stochastic Roughness Height Distributions

This paper studies the 3-D turbulent channel flows over rough walls with stochastic roughness height distributions by using the large eddy simulation and the immersed boundary method. The obtained mean and fluctuating velocity profiles for the smooth and rough channel flows agree well with the available numerical and experimental results. The stochastic surface roughness is found to have a more significant influence than the uniform surface roughness on the turbulent velocity statistics and the coherent structures, with the same average roughness height. With a greater variation in the roughness height, the mean velocity and the streamwise fluctuating velocity is decreased and the spanwise velocity and the wall-normal fluctuating velocity are increased. In addition, one observes larger and more profuse quasi-streamwise vortices, hairpin vortices and elongated structures above the crest plane of the roughness array in cases of highly stochastic rough walls. However, the low-speed streaky structures are broken up locally and the ejection and sweep events are depressed by the stochastic roughness below the average roughness height. The results of this study support Townsend’s wall-similarity hypothesis for both stochastic and uniform rough wall turbulences, demonstrating that in both cases the effects of the surface roughness on the turbulent flow are limited to the rough sub-layer.

Identifying the dominant physical processes for mixing in full-scale raceway tanks

Abstract Open racetrack flumes represent the most common reactor for algae cultivation in the biodiesel industry, however, despite numerous experimental and numerical studies into reactor modifications, conditions remain suboptimal for algal growth. In response, a full-scale racetrack flume was constructed at the Ecohydraulics and Ecomorphodynamics Laboratory at the University of Illinois. Experiments on the racetrack flume were conducted for various depth and velocity conditions, using acoustic doppler velocimetry and surface particle velocimetry to characterize mean and turbulent velocity statistics, and dissolved oxygen measurements to investigate the effect of turbulent structures on gas transfer at the water-air interface. Longitudinal bed modifications were introduced to induce secondary flows in the straight portions of the flume. Semicircular and triangular bars of two different sizes were tested in an effort to increase the transfer velocity at the free surface. A range of flow structures were observed including secondary currents of Prandtl's first and second kinds, vortex shedding off of bend vanes, and periodic oscillations in surface lateral currents. Findings indicate that bend dynamics introduce the strongest and most resilient flow structures, and any attempt to induce vertical mixing or accelerate transfer velocities at the free surface will need to utilize or overwhelm these existing structures.

Equivalence of turbulence statistics between monodisperse and polydisperse turbidity currents

Turbidity currents are buoyancy driven submarine flows where the source of buoyancy is typically a polydisperse sediment suspension. Sustained propagation of such flows depend on the ability of turbulence in the flow to keep the settling sediments in suspension. Recent studies by Cantero et al. (2012b) and Shringarpure et al. (2012) have investigated the interaction of monodisperse sediment suspension and turbulence in turbidity currents on smooth sloping beds. These studies showed that stable stratification of sediment suspension damps turbulence and in some cases can be fully suppress turbulence. Furthermore, it was shown that the turbulence damping effect of a monodisperse sediment suspension can be quantified by the product of shear Richardson number and the sediment settling velocity. In this study we generalize this result for a polydisperse sediment suspension. We compare the turbulence statistics of turbidity currents driven by different polydisperse suspensions and show that as long as the total amount of sediment and the product of shear Richardson number and effective settling velocity (a value representing the polydisperse suspension) are the same, the turbulent velocity statistics of the different polydisperse suspensions nearly collapse. Furthermore, if the effective settling velocity is chosen to be depth-dependent (a function of height from the bed) then the turbulence statistics involving sediment concentration also collapses between different polydisperse suspensions. These results suggest the possibility of modeling polydisperse currents with an equivalent monodisperse suspension whose total sediment load and depth-dependent settling velocity match those of the polydisperse suspension.

A laboratory study on sediment resuspension within arrays of rigid cylinders

We present results from laboratory experiments on flow through submerged arrays of rigid cylinders embedded in a sandy bed. Using rigid, cylindrical elements to mimic vegetation and benthos, we account for only the physical effects resulting from their presence, eliminating biological factors, such as biofilms and root systems. In line with previous findings, rigid arrays modify the flow mean and turbulent velocity statistics. However, even if the flow speed is significantly damped within dense arrays, the amount of sediment that gets lifted into suspension increases as the density of the array increases due to array– and cylinder-scale turbulence. We present a first attempt to provide predictive relationships of suspended sediment concentration using an alternative approach for the Shields parameter with an empirical coefficient to account for turbulence generated by submerged arrays of rigid cylinders. A similar analysis, using a ratio of populated to non-populated Shields parameter, is conducted to predict resuspension as a function of array density.

Streamwise Evolution of Statistical Events in a Model Wind-Turbine Array

Hot-wire anemometry data, obtained from a wind-tunnel experiment containing a $$3 \times 3$$ model wind-turbine array, are used to conditionally average the Reynolds stresses. Nine profiles at the centreline behind the array are analyzed to characterize the turbulent velocity statistics of the wake flow. Quadrant analysis yields statistical events occurring in the wake of the wind farm where quadrants 2 and 4 produce ejections and sweeps, respectively. The scaled difference between these two events is expressed via the $$\Delta R_{0}$$ parameter and is based on the $$\Delta S_{0}$$ quantity as introduced by M. R. Raupach (J Fluid Mech 108:363–382, 1981). $$\Delta R_{0}$$ attains a maximum value at hub height and changes sign near the top of the rotor. The ratio of quadrant events of upward momentum flux to those of the downward flux, known as the exuberance, is examined and reveals the effect of root vortices persisting to eight rotor diameters downstream. These events are then associated with the triple correlation term present in the turbulent kinetic energy equation of the fluctuations where it is found that ejections play the dual role of entraining mean kinetic energy while convecting turbulent kinetic energy out of the turbine canopy. The development of these various quantities possesses significance in closure models, and is assessed in light of wake remediation, energy transport and power fluctuations, where it is found that the maximum fluctuation is about $$30\%$$ of the mean power produced.

An examination of the high-order statistics of developing jets, lazy and forced plumes at various axial distances from their source

In this study, direct numerical simulations of a turbulent free jet (Re = 2000), a lazy plume (), and a forced plume (Re = 1684, Ri = 0.025) are compared. The evolution of the various fluxes and the so-called source parameter, Γ, are examined as a function of distance from the source. The first-, second-, and third-order statistics of the flows are calculated and discussed. The radial profiles of such statistics, as well as that of the turbulent kinetic energy balance and other second-order transport equations are examined at two axial distances, one axial distance before the flows have adjusted to their similarity solution, and the other beyond the similarity adjustment length scale. Vortical structures are visualised and discussed along with entrainment. The source term Γ was not found to monotonically decrease with axial distance from the source as predicted by past researchers. While the mean flow and turbulent velocity statistics of the simulated lazy and forced plumes took on similar behaviour far from the sources turbulent statistics which involve buoyancy did not.

On measuring the joint probability density function of three-dimensional velocity components in turbulent flows

This paper presents the underlying theory to directly measure the joint probability density function (JPDF) of turbulent velocity fields. The raw data for these measurements can come from either reconstructed tomographic particle image velocimetry (PIV) volumes or holographic PIV volumes in 3D or from planar PIV images in 2D suitably pre-processed to satisfy the conditions required as per the analysis presented here. The underlying theory has been applied to 2D and 3D Gaussian turbulence velocity fields to illustrate its ability in determining mean velocities, standard deviations of the turbulent velocity fluctuations and correlation coefficients between the turbulent velocity fluctuation components. These examples have demonstrated that the mean velocity can be estimated to very high accuracy, i.e. to better than 1% even when estimating the 2D and 3D JPDF with the simplified equation that does not account for particle size. The turbulence velocity fluctuations through their standard deviations can be measured with a typical error of 1.5% and the correlation coefficients with a typical error of 2.5% when estimating the JPDF with the result that accounts for the particle size. This is the first technique that allows the estimation of 3C-3D turbulent velocity statistics via the direct measurement of the JPDF without any detrimental effects due to the high values of velocity gradients that are typically encountered in turbulent shear flows because it is not restricted by the requirement of uniform velocity within the measurement volume.

Inertial particle relative velocity statistics in homogeneous isotropic turbulence

AbstractIn the present study, we investigate the scaling of relative velocity structure functions, of order two and higher, for inertial particles, both in the dissipation range and the inertial subrange using direct numerical simulations (DNS). Within the inertial subrange our findings show that contrary to the well-known attenuation in the tails of the one-point acceleration probability density function (p.d.f.) with increasing inertia (Bec et al., J. Fluid Mech., vol. 550, 2006, pp. 349–358), the opposite occurs with the velocity structure function at sufficiently large Stokes numbers. We observe reduced scaling exponents for the structure function when compared to those of the fluid, and correspondingly broader p.d.f.s, similar to what occurs with a passive scalar. DNS allows us to isolate the two effects of inertia, namely biased sampling of the velocity field, a result of preferential concentration, and filtering, i.e. the tendency for the inertial particle velocity to attenuate the velocity fluctuations in the fluid. By isolating these effects, we show that sampling is playing the dominant role for low-order moments of the structure function, whereas filtering accounts for most of the scaling behaviour observed with the higher-order structure functions in the inertial subrange. In the dissipation range, we see evidence of so-called ‘crossing trajectories’, the ‘sling effect’ or ‘caustics’, and find good agreement with the theory put forth by Wilkinson et al. (Phys. Rev. Lett., vol. 97, 2006, 048501) and Falkovich & Pumir (J. Atmos. Sci., vol. 64, 2007, 4497) for Stokes numbers greater than 0.5. We also look at the scaling exponents within the context of the model proposed by Bec et al. (J. Fluid Mech., vol. 646, 2010, pp. 527–536). Another interesting finding is that inertial particles at low Stokes numbers sample regions of higher kinetic energy than the fluid particle field, the converse occurring at high Stokes numbers. The trend at low Stokes numbers is predicted by the theory of Chun et al. (J. Fluid Mech., vol. 536, 2005, 219–251). This work is relevant to modelling the particle collision rate (Sundaram & Collins, J. Fluid Mech., vol. 335, 1997, pp. 75–109), and highlights the interesting array of phenomena induced by inertia.

Quantum turbulent velocity statistics and quasiclassical limit

Two research groups have measured turbulent velocity statistics in superfluid helium using different techniques. The results were in conflict: one experiment revealed Gaussian distributions (as observed in ordinary turbulence), the other experiment determined power laws. To solve the apparent puzzle, we numerically model quantum turbulence as a tangle of vortex filaments, and conclude that there is no contradiction between the two experiments. The transition from Gaussian to power law arises from the different length scales which are probed using the two techniques. We find that the average distance between the quantum vortices marks the separation between quantum and quasiclassical length scales.

Numerical study of velocity statistics in steady counterflow quantum turbulence

We investigate the velocity statistics by calculating the Biot-Savart velocity induced by vortex filaments in steady counterflow turbulence investigated in a previous study [H. Adachi, S. Fujiyama, and M. Tsubota, Phys. Rev. B 81, 104511 (2010).]. The probability density function (PDF) obeys a Gaussian distribution in the low-velocity region and a power-law distribution ${v}^{\ensuremath{-}3}$ in the high-velocity region. This transition between the two distributions occur at the velocity characterized by the mean intervortex distance. Counterflow turbulence causes anisotropy of the vortex tangle, which leads to a difference in the PDF for the velocities perpendicular to and parallel to the counterflow.

Nonclassical Velocity Statistics in a Turbulent Atomic Bose-Einstein Condensate

In a recent experiment Paoletti [Phys. Rev. Lett. 101, 154501 (2008)]10.1103/PhysRevLett.101.154501 monitored the motion of tracer particles in turbulent superfluid helium and inferred that the velocity components do not obey the Gaussian statistics observed in ordinary turbulence. Motivated by their experiment, we create a small 3D turbulent state in an atomic Bose-Einstein condensate, compute directly the velocity field, and find similar nonclassical power-law tails. We obtain similar results in 2D trapped and 3D homogeneous condensates, and in classical 2D vortex points systems. This suggests that non-Gaussian turbulent velocity statistics describe a fundamental property of quantum turbulence. We also track the decay of the vortex tangle in the presence of the thermal cloud.

Measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging

We present the first measurements of relative velocity statistics of inertial particles in a homogeneous isotropic turbulent flow with three-dimensional holographic particle image velocimetry (holographic PIV). From the measurements we are able to obtain the radial relative velocity probability density function (PDF) conditioned on the interparticle separation distance, for distances on the order of the Kolmogorov length scale. Together with measurements of the three-dimensional radial distribution function (RDF) in our turbulence chamber, these statistics, in principle, can be used to determine interparticle collision rates via the formula derived by Sundaram and Collins (1997). In addition, we show temporal development of the RDF, which reveals the existence of an extended quasi-steady-state regime in our facility. Over this regime the measured two-particle statistics are compared to direct numerical simulations (DNS) with encouraging qualitative agreement. Statistics at the same Reynolds number but different Stokes numbers demonstrate the ability of the experiment to correctly capture the trends associated with particles of different inertia. Our results further indicate that even at moderate Stokes numbers turbulence may enhance collision rates significantly. Such experimental investigations may prove valuable in validating, guiding and refining numerical models of particle dynamics in turbulent flows.

Large-Eddy Simulation of Turbulence-Radiation Interactions in a Turbulent Planar Channel Flow

Large-eddy simulation (LES) has been performed for planar turbulent channel flow between two infinite, parallel, stationary plates. The capabilities and limitations of the LES code in predicting correct turbulent velocity and passive temperature field statistics have been established through comparison to direct numerical simulation data from the literature for nonreacting cases. Mixing and chemical reaction (infinitely fast) between a fuel stream and an oxidizer stream have been simulated to generate large composition and temperature fluctuations in the flow; here the composition and temperature do not affect the hydrodynamics (one-way coupling). The radiative transfer equation is solved using a spherical harmonics (P1) method, and radiation properties correspond to a fictitious gray gas with a composition- and temperature-dependent Planck-mean absorption coefficient that mimics that of typical hydrocarbon-air combustion products. Simulations have been performed for different optical thicknesses. In the absence of chemical reactions, radiation significantly modifies the mean temperature profiles, but temperature fluctuations and turbulence-radiation interactions (TRI) are small, consistent with earlier findings. Chemical reaction enhances the composition and temperature fluctuations and, hence, the importance of TRI. Contributions to emission and absorption TRI have been isolated and quantified as a function of optical thickness.

Reconnection dynamics for quantized vortices

By analyzing trajectories of solid hydrogen tracers in superfluid 4He, we identify tens of thousands of individual reconnection events between quantized vortices. We characterize the dynamics by the minimum separation distance δ ( t ) between the two reconnecting vortices both before and after the events. Applying dimensional arguments, this separation has been predicted to behave asymptotically as δ ( t ) ≈ A ( κ | t − t 0 | ) 1 / 2 , where κ = h / m is the quantum of circulation. The major finding of the experiments and their analysis is strong support for this asymptotic form with κ as the dominant controlling feature, although there are significant event to event fluctuations. At the three-parameter level the dynamics may be about equally well-fit by two modified expressions: (a) an arbitrary power-law expression of the form δ ( t ) = B | t − t 0 | α and (b) a correction-factor expression δ ( t ) = A ( κ | t − t 0 | ) 1 / 2 ( 1 + c | t − t 0 | ) . The measured frequency distribution of α is peaked at the predicted value α = 0.5 , although the half-height values are α = 0.35 and 0.80 and there is marked variation in all fitted quantities. Accepting (b) the amplitude A has mean values of 1.24 ± 0.01 and half height values of 0.8 and 1.6 while the c distribution is peaked close to c = 0 with a half-height range of −0.9 s −1 to 1.5 s −1. In light of possible physical interpretations we regard the correction-factor expression (b), which attributes the observed deviations from the predicted asymptotic form to fluctuations in the local environment and in boundary conditions, as best describing our experimental data. The observed dynamics appear statistically time-reversible, which suggests that an effective equilibrium has been established in quantum turbulence on the time scales (≤0.25 s) investigated. We discuss the impact of reconnection on velocity statistics in quantum turbulence and, as regards classical turbulence, we argue that forms analogous to (b) could well provide an alternative interpretation of the observed deviations from Kolmogorov scaling exponents of the longitudinal structure functions.

Universal Intermittent Properties of Particle Trajectories in Highly Turbulent Flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.