Velocity Statistics Research Articles

Caustic spin wave beams in soft thin films: Properties and classification

In the context of wave propagation, caustics are usually defined as the envelope of a finite-extent wavefront; folds and cusps in a caustic result in enhanced wave amplitudes. Here, we tackle a related phenomenon, namely, the existence of well-defined beams originating solely from the geometric properties of the corresponding dispersion relation. This directional emission, termed caustic beam, is enabled by a stationary group velocity direction, and has been observed first in the case of phonons. We propose an overview of this ``focusing'' effect in the context of spin waves excited in soft, thin ferromagnetic films. Based on an analytical dispersion relation, we provide tools for a systematic survey of caustic spin wave beams. Our theoretical approach is validated by time-resolved microscopy experiments using the magneto-optical Kerr effect. Then, we identify two cases of particular interest both from fundamental and applicative perspectives. Indeed, both of them enable broadband excitations (in terms of wave vectors) to result in narrow-band beams of low divergence.

Direct numerical simulation of flow and heat transport in a closely-spaced bare rod bundle

Direct Numerical Simulation (DNS) of fully-developed flow and heat transfer is performed for a bare rod bundle with a low pitch-to-diameter ratio using the highly-scalabale spectral element code Nek5000. The simulation is performed at a Reynolds number, Reh, based on the bulk velocity and hydraulic diameter, of 9800, with iso-temperature and iso-flux thermal boundary conditions and Prandtl numbers 0.025, 1.0 and 2.0. The mean velocity and temperature statistics are first validated against the experimental measurements of Hooper et al. (1983) and complementary DNS results of Lai et al. (2019) which are reported in the literature at a higher Reh of 22,600. The mean flow and temperature are demonstrated a similar behaviour at the present low Renolds number and the higher Reynolds number of Lai et al. (2019), indicating the Reynolds number scaling of the mean flow. The anisotropy of the flow is illustrated using distribution of normal and Reynolds stresses, and the Lumley invariant map. It is shown that the turbulence in the subchannel region is characteristic of wall-bounded turbulent flows such as channel flows. In the narrow gap, however, turbulence is suppressed, only enhanced in the streamwise direction due to flow pulsations. Further, temperature statistics with both thermal boundary conditions are presented, demonstrating the effect of the Prandtl number on the mean and fluctuating quantities. The temperature statistics with iso-temperature wall boundary conditions, not reported in literature before, are shown to behave differently in the interstitial subchannel region and the narrow gap between two rods. The distribution of turbulent heat flux is also presented. The streamwise component of turbulent heat flux is again shown to be enhanced, in comparison to the same in the subchannel. The pulsating motion of flow across the narrow gap is discussed further. A frequency analysis of the velocity in the narrow gap elucidates the frequency of flow pulsations. Unlike mean flow statistics, the flow pulsations are shown to exhibit a low Reynolds number effect. The reference DNS data presented in the present work, complementary to that of Lai et al. (2019), serves as a benchmark against which lower order turbulence models may be further developed or improved. In particular, the newly presented anisotropy data and the turbulence heat flux data are essential for further development, improvement and validation of turbulent heat transfer models at different Prandtl numbers.

Galaxy clustering from the bottom up: a streaming model emulator I

ABSTRACT In this series of papers, we present a simulation-based model for the non-linear clustering of galaxies based on separate modelling of clustering in real space and velocity statistics. In the first paper, we present an emulator for the real-space correlation function of galaxies, whereas the emulator of the real-to-redshift space mapping based on velocity statistics is presented in the second paper. Here, we show that a neural network emulator for real-space galaxy clustering trained on data extracted from the dark quest suite of N-body simulations achieves sub-per cent accuracies on scales 1 < r < 30 $h^{-1} \, \mathrm{Mpc}$, and better than 3 per cent on scales r < 1 $h^{-1}\, \mathrm{Mpc}$ in predicting the clustering of dark-matter haloes with number density 10−3.5$(h^{-1}\, \mathrm{Mpc})^{-3}$, close to that of SDSS LOWZ-like galaxies. The halo emulator can be combined with a galaxy–halo connection model to predict the galaxy correlation function through the halo model. We demonstrate that we accurately recover the cosmological and galaxy–halo connection parameters when galaxy clustering depends only on the mass of the galaxies’ host halos. Furthermore, the constraining power in σ8 increases by about a factor of 2 when including scales smaller than 5 $h^{-1} \, \mathrm{Mpc}$. However, when mass is not the only property responsible for galaxy clustering, as observed in hydrodynamical or semi-analytic models of galaxy formation, our emulator gives biased constraints on σ8. This bias disappears when small scales (r < 10 $h^{-1}\, \mathrm{Mpc}$) are excluded from the analysis. This shows that a vanilla halo model could introduce biases into the analysis of future data sets.

Ultraviolet digital holographic microscopy (DHM) of micron-scale particles from shocked Sn ejecta.

A cloud of very fast, O(km/s), and very fine, O(µm), particles may be ejected when a strong shock impacts and possibly melts the free surface of a solid metal. To quantify these dynamics, this work develops an ultraviolet, long-working distance, two-pulse Digital Holographic Microscopy (DHM) configuration and is the first to replace film recording with digital sensors for this challenging application. A proposed multi-iteration DHM processing algorithm is demonstrated for automated measures of the sizes, velocities, and three-dimensional positions of non-spherical particles. Ejecta as small as 2 µm diameter are successfully tracked, while uncertainty simulations indicate that particle size distributions are accurately quantified for diameters ≥4 µm. These techniques are demonstrated on three explosively driven experiments. Measured ejecta size and velocity statistics are shown to be consistent with prior film-based recording, while also revealing spatial variations in velocities and 3D positions that have yet to be widely investigated. Having eliminated time-consuming analog film processing, the methodologies proposed here are expected to significantly accelerate future experimental investigation of ejecta physics.

Performance of the porous disk wind turbine model at a high Reynolds number: Solidity distribution and length scales effects

A new design methodology for porous disk wind turbine modeling is proposed, where a disk is matched to a horizontal axis wind turbine (HAWT) on (i) thrust coefficient, (ii) radial solidity distribution, and (iii) length scale criteria. Three disk designs are tested, allowing for isolation of the effects of each criterion, with performance evaluated through experimental wake comparisons with a model HAWT at a diameter-based Reynolds number of 4 × 106 and free-stream turbulence intensity of 1.2%. Wake velocity measurements reveal excellent agreement on mean profiles in the near wake (as early as 112 diameters downstream) when the rotor’s radial solidity distribution is incorporated into the disk design. Higher order velocity statistics can also be matched farther downstream (312 diameters). To match the higher order moments, the disk must generate near wake turbulence of similar characteristics to the rotor, since this turbulence dominates the development of the wake in a high Reynolds number, low free-stream turbulence environment. This is achieved by the third design criterion, where physical features that match the rotor length scales are incorporated. Thus, including all three criteria in a single porous disk yields a model that performs well at field-relevant Reynolds numbers, is not performance dependent on the free-stream turbulence intensity, and does not require iterative tuning.

On the effect of adverse pressure gradients on wall-pressure statistics in a controlled-diffusion aerofoil turbulent boundary layer

Wall-pressure and velocity statistics in the turbulent boundary layer (TBL) on a cambered controlled-diffusion aerofoil at $8^{\circ }$ incidence, a Mach number of 0.25 and a chord-based Reynolds number ${Re}_c=1.5\times 10^{5}$ are analysed at four locations on the suction side with zero and adverse pressure gradients (ZPG and APG), characterised by increasing Reynolds numbers based on momentum thickness, ${Re}_{\theta }=319$ , 390, 877 and $1036$ . The strong APG yields a highly non-equilibrium TBL at the trailing edge that significantly affects the turbulent flow statistics. Different normalisations of the full wall-pressure statistics involved in trailing-edge noise are analysed for the first time in such strong APG with convex curvature, and compared with available experimental and numerical data. Good overall agreement is found in the ZPG region, and most results obtained in previous APG TBL can be extended to the present highly non-equilibrium case. The presence of strong APG augments the intensity of wall-pressure fluctuations noticeably at low frequencies, shortens the streamwise and broadens the spanwise coherence of wall-pressure fluctuations in both time and space, and significantly reduces the convection velocity. The wall-pressure power spectral density are found to scale with the displacement thickness, the Zaragola–Smits velocity and the root-mean-squared pressure, the latter possibly being replaced by the local maximum Reynolds shear stress. The other two key parameters to trailing-edge noise modelling, the spanwise coherence length and the convection velocity, rather scale with displacement thickness and friction velocity, respectively.

Material surfaces in stochastic flows: Integrals of motion and intermittency.

We consider the line, surface, and volume elements of fluid in stationary isotropic incompressible stochastic flow in d-dimensional space and investigate the long-time evolution of their statistic properties. We report the discovery of a family of d!-1 stochastical integrals of motion that are universal in the sense that their explicit form does not depend on the statistics of velocity. Only one of them has been discussed previously.

Passive scalar transport in a turbulent spot within a poiseuille flow

A pair of counter-rotating vortices are introduced in a Poiseuille flow to trigger the by-pass transition. The accent is put on the passive scalar transport within the resulting transitional spot. The latter is identified and tracked in time and space using the fluctuating vorticity and temperature fields it induces. The velocity and temperature statistics are determined strictly within the spot. They are scaled by the inner variables, related to the shear velocity and the wall temperature flux induced by the spot. The statistics are compared with those of the corresponding fully developed turbulent channel flow, in order to determine the degree of similarity between the internal structure of the spot and the fully developed wall turbulence. The analysis includes the fine structure of the fluctuating temperature field, its transport equations and the effect of the coherent structures within the spot. It is found that the turbulent part of the spot is closely similar to the turbulent wall flow, both for the fluctuating flow, and the passive scalar fields. The root-mean-square of the temperature fluctuations determined in the entire spot is nearly twice larger than that in the fully developed wall turbulence in the outer part of the flow. The transport is enhanced and the turbulent fluxes increase compared to the fully developed turbulent channel flow. This is due to the wave area of the spot that contains, in their great majority, the structures coming from the breakdown process of waves. The latter is responsible for the increase of the small-scale mixing and of the large peripheral temperature fluctuations, which is rather good news from an application point of view.

Particle transport in a turbulent pipe flow: direct numerical simulations, phenomenological modelling and physical mechanisms

In particle-laden turbulent wall flows, transport of particles towards solid walls is phenomenologically thought to be governed by the wall-normal turbulence intensity supporting the underlying particle–eddy interactions that are usually modelled by a combination of turbophoresis and turbulent diffusion. We estimate the turbophoretic and turbulent diffusive coefficients as a function of wall-normal coordinate directly from a generated direct numerical simulation (DNS) database of low volume fraction point particles in a turbulent pipe flow. These coefficients are then used in an advection–diffusion equation to estimate the particle concentration as a function of wall-normal distance and time, with favourable comparison against DNS for smaller Stokes number ( $St^+$ ) particles suggesting a limitation of the common gradient diffusion hypothesis for larger $St^+$ particles. Using DNS we explore the non-trivial effects of $St^+$ , pipe wall condition (particle absorbing or elastic) as well as the influence of drag and lift force on the velocity and particle statistics giving rise to different particle concentrations. We then appraise various Eulerian-based models of turbophoretic and turbulent diffusive coefficients and, finally, use physical insights from Lagrangian correlation times, conditional quadrant analysis and flow topology to shed further light on the particle transport as a function of various parameters and the limits of gradient diffusion hypothesis.

Level dynamics and avoided level crossings in driven disordered quantum dots

The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the first model the external drivings are realized by a continuous variation of the on-site energies, in the second one it is generated by deformations of a parabolic potential. We concentrate on the effects of the potential on the localization properties and investigate the statistics of the energy level velocities and curvatures regarding their typical magnitudes and domain of agreement with the predictions of Random Matrix Theory (RMT) for the Gaussian Orthogonal, Unitary and Symplectic ensembles. Moreover, the statistical properties of the avoided level crossings are investigated in terms of the corresponding Landau-Zener parameters. We find that the strength of the Landau-Zener transitions exhibits universal behavior which also implies universal single-particle dynamics for slow perturbations independent of the disorder and potential strength, the system size and the symmetry class. These results can be verified experimentally by measurements of single-particle energy spectra in quantum dots.

Turbulent Taylor-Couette flow of dilute polymeric solutions: a10-year retrospective.

This retrospective aims to present a coherent history of important findings in direct numerical simulations and experiments in turbulent Taylor-Couette (TC) flow of dilute polymeric solutions in the last decade. Specifically, the sequence of flow transitions due to a continuous increase of fluid elasticity from classical Newtonian, to inertially and in turn to elastically dominated, and finally to the inertialess purely elastic turbulence, is presented. In each elastically modified flow state, the drag modification, coherent flow structures, velocity and elastic stress statistics, mechanism of turbulent kinetic energy production, spectral features as well as the self-sustaining cycles of turbulence, are discussed. Finally, to provide a broader perspective, an overview of important similarities and differences between elastically induced turbulence in prototypical curvilinear and rectilinear shear flows including the curvature-free limit of TC flow, namely, the spanwise-rotating plane Couette flow, is presented. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Using of large eddy simulation model for a spatially developing turbulent natural convection boundary layer in water along a side-heated vertical wall with high Rayleigh number ([formula omitted

To further understand the turbulent natural convection in the residual heat removal process of a nuclear reactor in accidental condition, a spatially developing natural convection boundary layer along a side-heated vertical plane in water is simulated with Large Eddy Simulation (LES) strategy. The maximum modified Rayleigh number (Ra*=Ra×Nu) reaches 8×1014 with the uniform heat flux input (≈10000W/m2). In particular, the buoyancy driven flow is simulated by an incompressible flow solver with Boussinesq approximation. The Wall Adaptive Local Eddy (WALE) model is selected as the sub-grid scale model for the LES simulation. After comparing with available measurements, it is found that reasonable agreement has been achieved in wall temperature distribution along the heated wall, heat transfer rate as well as mean temperature, mean velocity and turbulent statistics in the boundary layer. The detailed vortex structure and velocity spectra in the boundary layer corresponding to different regime are clearly demonstrated. It is shown that the transition process in the boundary layer can be accurately presented with the refined mesh (x+≈0.1) in the near wall region. To be more specific, the appeared ordered vortex street in the transition stage and the estimated critical Rayleigh number for turbulence inception correspond well to previous experimental observations. The significant effect of early transformation of two-dimensional (2D) linear Tollmien–Schlichting waves on the heat transfer is also proved. It is expected that current study can enhance the understanding of turbulent boundary layer at high heat flux and high Rayleigh number.

Stationary states of activity-driven harmonic chains.

We study the stationary state of a chain of harmonic oscillators driven by two active reservoirs at the two ends. These reservoirs exert correlated stochastic forces on the boundary oscillators which eventually leads to a nonequilibrium stationary state of the system. We consider three most well-known dynamics for the active force, namely, the active Ornstein-Uhlenbeck process, run-and-tumble process, and active Brownian process, all of which have exponentially decaying two-point temporal correlations but very different higher-order fluctuations. We show that, irrespective of the specific dynamics of the drive, the stationary velocity fluctuations are Gaussian in nature with a kinetic temperature which remains uniform in the bulk. Moreover, we find the emergence of an "equipartition of energy" in the bulk of the system-the bulk kinetic temperature equals the bulk potential temperature in the thermodynamic limit. We also calculate the stationary distribution of the instantaneous energy current in the bulk which always shows a logarithmic divergence near the origin and asymmetric exponential tails. The signatures of specific active driving become visible in the behavior of the oscillators near the boundary. This is most prominent for the RTP- and ABP-driven chains where the boundary velocity distributions become non-Gaussian and the current distribution has a finite cutoff.

Diffusion Properties of a Brownian Ratchet with Coulomb Friction

The motion of a Brownian particle in the presence of Coulomb friction and an asymmetric spatial potential was evaluated in this study. The system exhibits a ratchet effect, i.e., an average directed motion even in the absence of an external force, induced by the coupling of non-equilibrium conditions with the spatial asymmetry. Both the average motion and the fluctuations of the Brownian particle were analysed. The stationary velocity shows a non-monotonic behaviour as a function of both the temperature and the viscosity of the bath. The diffusion properties of the particle, which show several time regimes, were also investigated. To highlight the role of non-linear friction in the dynamics, a comparison is presented with a linear model of a Brownian particle driven by a constant external force, which allows for analytical treatment. In particular, the study unveils that the passage times between different temporal regimes are strongly affected by the presence of Coulomb friction.

Влияние концентрации поверхностно-активного вещества на динамику всплытия кластера пузырьков

The results of an experimental study of the stationary velocity of ascent of a spherical cluster of monodispersed air bubbles in glycerin at various concentrations of a surfactant in the range of Reynolds numbers Re<0.1 are presented. New method for obtaining the cluster of monodispersed bubbles to study the process of ascent of a consolidated system of bubbles is proposed.

Lagrangian and Eulerian time and length scales of mesoscale ocean chlorophyll from Bio-Argo floats and satellites

Abstract. Phytoplankton form the base of marine food webs and play an important role in carbon cycling, making it important to quantify rates of biomass accumulation and loss. As phytoplankton drift with ocean currents, rates should be evaluated in a Lagrangian as opposed to an Eulerian framework. In this study, we quantify the Lagrangian (from Bio-Argo floats and surface drifters with satellite ocean colour) and Eulerian (from satellite ocean colour and altimetry) statistics of mesoscale chlorophyll and velocity by computing decorrelation time and length scales and relate the frames by scaling the material derivative of chlorophyll. Because floats profile vertically and are not perfect Lagrangian observers, we quantify the mean distance between float and surface geostrophic trajectories over the time spanned by three consecutive profiles (quasi-planktonic index, QPI) to assess how their sampling is a function of their deviations from surface motion. Lagrangian and Eulerian statistics of chlorophyll are sensitive to the filtering used to compute anomalies. Chlorophyll anomalies about a 31 d time filter reveal an approximate equivalence of Lagrangian and Eulerian tendencies, suggesting they are driven by ocean colour pixel-scale processes and sources or sinks. On the other hand, chlorophyll anomalies about a seasonal cycle have Eulerian scales similar to those of velocity, suggesting mesoscale stirring helps set distributions of biological properties, and ratios of Lagrangian to Eulerian timescales depend on the magnitude of velocity fluctuations relative to an evolution speed of the chlorophyll fields in a manner similar to earlier theoretical results for velocity scales. The results suggest that stirring by eddies largely sets Lagrangian time and length scales of chlorophyll anomalies at the mesoscale.

Local Scour Patterns around a Bridge Pier with Cable-Wrapping

The performance of cable flow-altering bed scour countermeasures was experimentally evaluated based on the scour reduction, bed morphology, and the effects on the flow field. An unprotected 40 mm diameter pier was compared to piers protected with spiral cables (2, 4, 6, 8 and 10 mm diameters) wrapped at a 15-degree angle for two-bed sediment sizes with median grain sizes of 0.86 and 1.83 mm, for a cylinder Reynolds number of 7120. The scour depth was reduced by the cables by up to 52 percent compared to the unprotected pier case, a reduction that increased with increasing cable diameter for both sediment beds. Scour depth and sediment deposition varied by sediment size, where the scour hole was up to 45 percent deeper for the finer sediment bed than that of the coarser bed. Velocity and turbulence statistics showed that cables attenuated the flow within the scour hole by diminishing the downflow and horseshoe vortex, whereas in the case of finer sediment, spatially averaged turbulent kinetic energy and Reynolds shear stresses were respectively up to 1.4 and 1.8 times higher for the unprotected pier than the protected pier, resulting in scour depth reduction. The presence of the cable also reduced the vortex shedding frequency in the pier wake as indicated by a Strouhal number of around 0.175. The results demonstrate the potential of cable threading as a flow-altering scour countermeasure to reduce bridge pier scour.

Velocity Prediction Program for a Hydrofoiling Lake Racer

The aim of this paper is to develop an accurate and robust six degrees of freedom stationary velocity prediction program (VPP) applied to a high-performance sailing yacht. The model is set up to assist NC Raceboats with the VPP based hydrofoil design, considering the sailing performance in three modes: displacement, transition and hydrofoil. The yacht is a lightweight monohull designed for light wind conditions with up to five crew members. The design includes a self-stabilizing hydrofoil configuration and an elevator rudder. The software tool, which is used for the velocity prediction program, is FS-Equilibrium, developed by DNV. The software offers a modular workbench in which each force can be modelled with semi-empirical force modules, which are based on validated methods and theories. The performance prediction is interpreted and discussed: as foreseen, the performance of the high-performance lake racer in hydrofoiling condition is significantly improved compared to its assessment in displacement sailing mode. In medium breeze conditions, the yacht is able to lift up on its hydrofoils and attain flight mode. The minimum hydrofoiling speed investigation demonstrates that the VPP is able to consistently iterate Through the transition mode. This paper shows that it is possible to develop a VPP model for a hydrofoiling sailing yacht on the basis of relatively simple assumptions and theories.

A local measurement of the growth rate from peculiar velocities and galaxy clustering correlations in the 6dF Galaxy Survey

ABSTRACT Galaxy peculiar velocities provide an integral source of cosmological information that can be harnessed to measure the growth rate of large-scale structure and constrain possible extensions to General Relativity. In this work, we present a method for extracting the information contained within galaxy peculiar velocities through an ensemble of direct peculiar velocity and galaxy clustering correlation statistics, including the effects of redshift space distortions, using data from the 6-degree Field Galaxy Survey. Our method compares the auto- and cross-correlation function multipoles of these observables, with respect to the local line of sight, with the predictions of cosmological models. We find that the uncertainty in our measurement is improved when combining these two sources of information in comparison to fitting to either peculiar velocity or clustering information separately. When combining velocity and density statistics in the range $27 \lt s \lt 123 \, h^{-1}$ Mpc we obtain a value for the local growth rate of fσ8 = 0.358 ± 0.075 and for the linear redshift distortion parameter β = 0.298 ± 0.065, recovering both with 20.9 per cent and 21.8 per cent accuracy, respectively. We conclude this work by comparing our measurement with other recent local measurements of the growth rate, spanning different data sets and methodologies. We find that our results are in broad agreement with those in the literature and are fully consistent with ΛCDM cosmology. Our methods can be readily scaled to analyse upcoming large galaxy surveys and achieve accurate tests of the cosmological model.

Kinematic simulations as a subgrid-scale model for particle motion: a priori LES of homogeneous isotropic turbulence

In this work we investigated the impact of filtering and subgrid-scale modeling on particle settling velocity and collision-related statistics in a turbulent flow. To reduce the complexity of this task we first studied the motion of inertial particles in the low-pass filtered homogeneous and isotropic turbulence, which was subsequently enriched with the subgrid-scale velocity components obtained from a frozen high-pass filtered velocity field. Particular emphasis has been put on the radial distribution function and the radial relative velocity of nearly touching particles both in the presence or absence of the gravitational settling. These statistics are the key input parameters to the kinematic collision kernel which is of crucial importance in determining the collision rate of inertial particles in a turbulent flow. Furthermore, kinematic simulations were selected as a means of enhancing the fluid velocity at particle locations. We analyzed a wide range of Stokes numbers, i.e. a measure of particle inertia, and, in contrast to scientific premises found in the literature, we observed no improvement of particle statistics when the low-pass filtered fluid velocity was enriched with both a synthetic or spectrally-filtered small-scale structures. We discuss the shortages of any frozen-velocity-based subgrid-scale model in predicting both single- and two-point particle statistics. We also indicate that in some cases, particularly concerning the collision rate of particles suspended in homogeneous and isotropic turbulence, subgrid-scale contribution in the particle equation of motion can be neglected.