Higher Order Velocity Moments Research Articles

High-order moments of velocity fluctuations around a cylinder in a dredged channel

The effect of a channel pit on the turbulence structure around an embedded cylinder was explored based on the behaviour of high-order moments of streamwise velocity fluctuations. Instantaneous velocities across the flow depth were recorded upstream and downstream of a circular cylinder in a sand bed flume with and without channel dredging. The variance of streamwise velocity fluctuations and higher-order velocity moments around the cylinder were studied for both cases. Logarithmic scaling of was observed in the down-flow upstream of the cylinder and in the wake zone downstream of the cylinder. Higher-order velocity moments up to 2p = 4 and 2p = 6 were also evaluated to validate the logarithmic scaling. The mean flow structure developed due to the fluid–solid interactions around the cylinder was found to govern the scaling characteristics of velocity fluctuations. The experimental data showed that channel dredging increased the near-bed values of at the cylinder front and also increased the peak of turbulence production downstream of the cylinder. These alterations may be linked to excess scour and undermining of bridges due to channel dredging.

Higher-Order Velocity Moments, Turbulence Scales and Energy Dissipation Rate around a Boulder in a Rock-Ramp Fish Passage

This experimental study investigated the higher-order velocity moments, turbulence time and length scales, and energy dissipation rates around an intermediately submerged boulder within a wake-interference flow regime in a rock-ramp fish passage. The results show a noticeable variation in the studied parameters in the wake of the boulder, as well as near the bed and boulder crest. The higher-order velocity moments show the presence of infrequent strong ejections downstream of the boulder, which may lead to higher sediment deposition and vertical mixing. The eddy length scales and the volumetric energy dissipation in this experimental model were discussed in relation to fish behavior for both the experimental model and a prototype. Relationships were proposed to roughly estimate integral length scales and energy dissipation rates around the boulder over the flow depth. The findings of this study may improve the design of rock-ramp fish passages considering the effects of turbulence on fish swimming performance and sediment transport.

Macroscopic and parametric study of a kinetic plasma expansion in a paraxial magnetic nozzle

A kinetic paraxial model of a collisionless plasma stationary expansion in a convergent-divergent magnetic nozzle (MN) is analyzed. Monoenergetic and Maxwellian velocity distribution functions of upstream ions are compared, leading to differences in the expansion only on second and higher-order velocity moments. Individual and collective magnetic mirror effects are analyzed. Collective ones are small on the electron population since only a weak temperature anisotropy develops, but they are significant on the ions all over the nozzle. Momentum and energy equations for ions and electrons are assessed based on the kinetic solution. The ion response is different in the hot and cold limits, with the anisotropic pressure tensor being relevant in the first case. Heat fluxes of parallel and perpendicular energies have a dominant role in the electron energy equations. They do not fulfill a Fourier-type law; they are large even when electrons are near isothermal. A crude electron fluid closure based on a constant diffusion-to-convective thermal energy ratio is shown equivalent to the much invoked polytropic law. Analytical dimensionless parameter laws are derived for the nozzle total electric potential fall and the downstream residual electron temperature. Electron confinement and related current control by a thin Debye sheath and a semi-infinite divergent MN are compared.

Deciphering Morphological Changes in a Sinuous River System by Higher-Order Velocity Moments

Bank erosion in a sinuous alluvial channel is a continuous phenomenon resulting in bank instability and migration of sediment. In this study, flume experiments were conducted in a sinuous channel to investigate its morphological changes and hydrodynamics. High-order velocity fluctuation moments are analyzed at outer and inner banks to explain the morphological variation in a sinuous river channel. The variance of streamwise velocity fluctuations on both banks of the sinuous channel follows a logarithmic law from a particular depth. In the outer bend region, the magnitude of velocity fluctuation moment is significant, indicating erosion. The trend of velocity fluctuation at higher even-order moments is similar to the variance of streamwise velocity fluctuations where the outer bend magnitude is greater than the inner bend. The premultiplied probability density functions (PDFs) and the flatness factor show greater magnitude in the outer bend of the channel as compared to the inner bend.

Stellar and dynamical masses of brightest cluster galaxies

AbstractWe investigate the stellar and dynamical mass profiles of 32 brightest cluster galaxies (BCGs, MK = −25.7 to −27.8 mag) in massive clusters (0.05 < z < 0.30), and in particular the rising velocity dispersion profiles of 23 of these BCGs found in Loubser et al. (2018). We make comprehensive measurements of the Gauss-Hermite higher order velocity moments h3 and h4, and find positive central values for h4 for all the BCGs. We model the stellar and dynamical mass profiles of 25 of the BCGs using the Multi-Gaussian Expansion (MGE) and Jeans Anisotropic Method (JAM) for an axisymmetric case, deriving the stellar mass-to-light ratio (ϒ*DYN), and anisotropy (βz). We further explicitly add a dark matter halo mass component (MDM within r200) which we constrain from weak lensing results. In this proceedings, we summarise the study and show an example of the results.

Modified κ-distribution of Solar Wind Electrons and Steady-state Langmuir Turbulence

Abstract Solar wind electrons are observed to be distributed in velocity space such that they can be empirically fitted with the κ-distribution. Among physical processes that are responsible for the generation of the observed electron distribution is the asymptotically steady-state Langmuir turbulence and the suprathermal electron distribution function associated with such a state. However, the Langmuir spectrum in such a model diverges for infinite wavelength, which is a feature that is intimately linked to the problem of diverging higher-order velocity moments in the standard κ-distribution function. The recent model of a modified κ-distribution with an exponential cutoff resolves the diverging velocity moment problem. In the present paper, it is shown that the model by Scherer et al., which the authors termed the “regularized” κ-distribution, or a variation thereof, also resolves the divergence problem associated with the steady-state Langmuir turbulence. Implications of the present findings in the context of solar wind are also discussed.

Exact collisional moments for plasma fluid theories

The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.

Turbulent jet characteristics for axisymmetric and serrated nozzles

Turbulent jet large eddy simulations (LES) are performed at Mach 0.9 and Reynolds number around 106. Implicit large-eddy simulation (ILES) is employed, namely omitting explicit subgrid scale models. The Reynolds-averaged Navier–Stokes (RANS) solution is blended into the near wall region. This makes an overall hybrid LES-RANS approach. A Hamilton–Jacobi equation is applied to remove the disparate turbulence length scales implied by hybridization. Computations are contrasted for a baseline axisymmetric (round) nozzle and a serrated (or chevron) nozzle with high bending and penetration. Jet characteristics for both nozzles are studied in detail with well documented experimental data compared. The chevron effects are demonstrated by comparing both solutions using the same mesh resolution and flow conditions. Higher order velocity moments with potential for aeroacoustic modeling and noise prediction, such as the two-point velocity spatial correlations, are also explored. Numerical simulations presented in this study utilize an in-house flow solver with improved parallel scalability and efficiency by means of data packeting and a scheduling algorithm similar to the Round Robin scheduling.

Turbulence characteristics in an open channel flow over transitionally rough bed

The results of the turbulent flow measurements in an open channel flow over transitionally rough beds using an ADV are presented in this paper. The turbulence characteristics across the flow depth were quantified by measuring the time averaged velocity components, turbulent intensity components and turbulent stresses. The characterization of higher-order velocity moments and the coherent structures of the flow are also presented. The obtained results are compared with the values for smooth and rough beds reported in literature.

Direct numerical simulation of inertial particle entrainment in a shearless mixing layer

AbstractWe present the first computational study of the dynamics of inertial particles in a shearless turbulence mixing layer. We parametrize our direct numerical simulations to isolate the effects of turbulence, Reynolds number, particle inertia, and gravity on the entrainment process. By analysing particle concentrations, particle and fluid velocities, particle size distributions, and higher-order velocity moments, we explore the impact of particle inertia and gravity on the mechanism of turbulent mixing. We neglect thermodynamic processes, including phase changes between the drops and surrounding air, which is equivalent to assuming the air is saturated (i.e. 100 % humidity). Entrainment is found to be governed by the large scales of the flow and is relatively insensitive to the Reynolds number over the range considered. Our results show that both fluid and particle velocities exhibit intermittency and that gravity and turbulent diffusion interact in unexpected ways to dictate particle dynamics. An analysis of the temporal evolution of fluid and particle statistics suggests that particle concentration profiles and velocities are self-similar under certain circumstances. We also observe large fluctuations in particle concentrations resulting from entrainment and introduce a model to estimate the impact these fluctuations have on the radial distribution function, a statistic that is often used to quantify inertial particle clustering. Our study is both a computational counterpart to and an extension of the wind tunnel experiments by Gerashchenko, Good & Warhaft (J. Fluid Mech., vol. 668, 2011, pp. 293–303) and Good, Gerashchenko, & Warhaft (J. Fluid Mech., vol. 694, 2012, pp. 371–398). We find good agreement between these experimental studies and our computational results. We anticipate that a better understanding of the role of gravity and turbulence in inertial particle entrainment will lead to improved cloud evolution predictions.

Recovery of the internal orbital structure of galaxies

We construct axisymmetric and triaxial galaxy models with a phase-space distribution function that depends on linear combinations of the three exact integrals of motion for a separable potential. These Abel models, first introduced by Dejonghe & Laurent and subsequently extended by Mathieu & Dejonghe, are the axisymmetric and triaxial generalizations of the well-known spherical Osipkov–Merritt models. We show that the density and higher order velocity moments, as well as the line-of-sight velocity distribution of these models can be calculated efficiently and that they capture much of the rich internal dynamics of early-type galaxies. We build a triaxial and oblate axisymmetric galaxy model with projected kinematics that mimic the two-dimensional kinematic observations that are obtained with integral-field spectrographs such as SAURON. We fit the simulated observations with axisymmetric and triaxial dynamical models constructed with our numerical implementation of Schwarzschild orbit-superposition method. We find that Schwarzschild method is able to recover the internal dynamics and three-integral distribution function of realistic models of early-type galaxies.

Higher-Order Moments of Velocity Fluctuations in an Open-Channel Flow with Large Bottom Roughness

The present study was undertaken to examine the effect of surface roughness on the higher-order velocity moments in a turbulent open-channel flow. The wall roughness is large and the ratio of the roughness size to the depth of flow ranges from 0.1 to 0.15. Flow over two types of roughness conditions (ribs and dunes) are examined and compared with that over a smooth open channel. In the case of the rib roughness, three different spacings are used: p∕k=4.5, 9, and 18; here, p=distance between the leading edges of two consecutive ribs and k=height of a rib with square cross section. The shape of the smooth wall dunes was geometrically similar to that commonly used in previous studies. In an effort to understand the influence of local wall roughness, rough-wall dunes are also used in the present study. The variables of interest include higher-order moments, conditional statistics based on a quadrant analysis, relationship of higher-order moments to the Reynolds stress and energy production. Although there are some similarities between open-channel flows and turbulent boundary layers, there are important differences as indicated by the third-order moments. The triple products and the second quadrant events are sensitive to the wall condition. Ejection events are found to be prevalent throughout the depth. It is also clear from the study that one needs to explicitly account for the surface condition in any model development to be able to predict transport characteristics.

The electromagnetic Darwin model for intense charged particle beams

The theoretical and numerical properties of the electromagnetic Darwin model for intense charged particle beams are investigated. The model neglects the transverse displacement current in Ampere's law and results in the elimination of high-frequency transverse electromagnetic waves and the associated retardation effects in the Vlasov–Maxwell equations. In this paper, two numerical schemes are presented for the purpose of circumventing the numerical instabilities associated with the presence of E T [ ≡ - ( 1 / c ) ∂ A / ∂ t ] in the equations of motion for particle codes, where A is the vector potential. The first relies on higher-order velocity moments for closure, and the other replaces the mechanical momentum, p = γ m v , by the canonical momentum, P = p + ( q / c ) A , as the phase-space variable. The properties of these simulations schemes in the laboratory frame as well as in the beam frame are also discussed. These new numerical methods are most suitable for studying Weibel and two-stream instabilities in heavy ion fusion research.

Scale resolved intermittency in turbulence

The deviations δζm (‘‘intermittency corrections’’) from classical (‘‘K41’’) scaling ζm=m/3 of the mth moments 〈‖u(p)‖m〉 in high Reynolds number turbulence are calculated, extending a method to approximately solve the Navier–Stokes equation described earlier. It is suggested to introduce the notion of scale resolved intermittency corrections δζm(p), because these δζm(p) are found to be large in the viscous subrange, moderate in the nonuniversal stirring subrange but, surprisingly, extremely small if not zero in the inertial subrange. If ISR intermittency corrections persisted in experiment up to the large Reynolds number limit, it would show by calculation that this could be due to the opening of phase space for larger wave vectors. In the higher order velocity moments 〈‖u(p)‖m〉 the crossover between inertial and viscous subrange is (10ηm/2)−1, thus the inertial subrange is smaller for higher order moments.