scholarly journals Eddy diffusivities of inertial particles under gravity

2012 ◽  
Vol 694 ◽  
pp. 426-463 ◽  
Author(s):  
Marco Martins Afonso ◽  
Andrea Mazzino ◽  
Paolo Muratore-Ginanneschi
Keyword(s):  
Particle Velocity ◽  
Large Scale ◽  
Particle Concentration ◽  
Mass Density ◽  
Concentration Field ◽  
Eddy Diffusivity ◽  
Inertial Particles ◽  
Differential Problem ◽  
Carrier Flow ◽  
Eddy Diffusivities

AbstractThe large-scale/long-time transport of inertial particles of arbitrary mass density under gravity is investigated by means of a formal multiple-scale perturbative expansion in the scale-separation parameter between the carrier flow and the particle concentration field. The resulting large-scale equation for the particle concentration is determined, and is found to be diffusive with a positive definite eddy diffusivity. The calculation of the latter tensor is reduced to the resolution of an auxiliary differential problem, consisting of a coupled set of two differential equations in a $(6+ 1)$-dimensional coordinate system (three space coordinates plus three velocity coordinates plus time). Although expensive, numerical methods can be exploited to obtain the eddy diffusivity, for any desirable non-perturbative limit (e.g. arbitrary Stokes and Froude numbers). The aforementioned large-scale equation is then specialized to deal with two different relevant perturbative limits: (i) vanishing of both Stokes time and sedimenting particle velocity; (ii) vanishing Stokes time and finite sedimenting particle velocity. Both asymptotics lead to a greatly simplified auxiliary differential problem, now involving only space coordinates and thus easily tackled by standard numerical techniques. Explicit, exact expressions for the eddy diffusivities have been calculated, for both asymptotics, for the class of parallel flows, both static and time-dependent. This allows us to investigate analytically the role of gravity and inertia on the diffusion process by varying relevant features of the carrier flow, such as the form of its temporal correlation function. Our results exclude a universal role played by gravity and inertia on the diffusive behaviour: regimes of both enhanced and reduced diffusion may exist, depending on the detailed structure of the carrier flow.

Statistical properties of particle segregation in homogeneous isotropic turbulence

2011 ◽  
Vol 686 ◽  
pp. 338-351 ◽  
Author(s):  
Elena Meneguz ◽  
Michael W. Reeks
Keyword(s):  
Particle Concentration ◽  
Isotropic Turbulence ◽  
Concentration Field ◽  
Threshold Value ◽  
Stokes Number ◽  
Statistical Properties ◽  
Inertial Particles ◽  
Concentration Changes ◽  
Non Gaussian ◽  
Good Agreement

AbstractA full Lagrangian method (FLM) is used in direct numerical simulations (DNS) of incompressible homogeneous isotropic and statistically stationary turbulent flow to measure the statistical properties of the segregation of small inertial particles advected with Stokes drag by the flow. Qualitative good agreement is observed with previous kinematic simulations (KS) (IJzermans, Meneguz & Reeks, J. Fluid Mech., vol. 653, 2010, pp. 99–136): in particular, the existence of singularities in the particle concentration field and a threshold value for the particle Stokes number $\mathit{St}$ above which the net compressibility of the particle concentration changes sign (from compression to dilation). A further KS analysis is carried out by examining the distribution in time of the compression of an elemental volume of particles, which shows that it is close to Gaussian as far as the third and fourth moments but non-Gaussian (within the uncertainties of the measurements) for higher-order moments when the contribution of singularities in the tails of the distribution increasingly dominates the statistics. Measurements of the rate of occurrence of singularities show that it reaches a maximum at $\mathit{St}\ensuremath{\sim} 1$, with the distribution of times between singularities following a Poisson process. Following the approach used by Fevrier, Simonin & Squires (J. Fluid Mech., vol. 553, 2005, pp. 1–46), we also measured the random uncorrelated motion (RUM) and mesoscopic components of the compression for $\mathit{St}= 1$ and show that the non-Gaussian highly intermittent part of the distribution of the compression is associated with the RUM component and ultimately with the occurrence of singularities. This result is consistent with the formation of caustics (Wilkinson et al. Phys. Fluids, vol. 19, 2007, p. 113303), where the activation of singularities precedes the crossing of trajectories (RUM).

Explicit expressions for eddy-diffusivity fields and effective large-scale advection in turbulent transport

2016 ◽  
Vol 795 ◽  
pp. 524-548 ◽  
Author(s):  
S. Boi ◽  
A. Mazzino ◽  
G. Lacorata
Keyword(s):  
Large Scale ◽  
Spectral Gap ◽  
Environmental Flows ◽  
Turbulent Transport ◽  
Eddy Diffusivity ◽  
Small Scale ◽  
Eddy Diffusivities ◽  
Perturbative Methods ◽  
Tracer Dispersion ◽  
Explicit Expressions

Large-scale transport is investigated in terms of new explicit expressions for eddy diffusivities and effective advection obtained from asymptotic perturbative methods. The carrier flow is formed by a large-scale component plus a small-scale contribution mimicking a turbulent flow. The scalar dynamics is observed in its pre-asymptotic regimes (i.e. on scales comparable to those of the large-scale velocity). The resulting eddy diffusivity is thus a tensor field which explicitly depends on the large-scale velocity. Small-scale interactions also cause the emergence of an effective large-scale (compressible) advection field which, as a result of the present study however, turns out to be of negligible importance. Two issues are addressed by means of Lagrangian simulations: quantifying the possible deterioration of the eddy-diffusivity/effective advection description by reducing to zero the spectral gap separating the large-scale velocity component from the small-scale component; comparing the accuracy of our closure against other simple, reasonable, options. Answering these questions is important in view of possible applications of our closure to tracer dispersion in environmental flows.

scholarly journals In Search of Random Uncorrelated Particle Motion (RUM) in a Simple Random Flow Field

2006 ◽  
Author(s):  
Michael W. Reeks ◽  
Luca Fabbro ◽  
Alfredo Soldati
Keyword(s):  
Flow Field ◽  
Particle Velocity ◽  
Particle Motion ◽  
Particle Concentration ◽  
Concentration Field ◽  
Spatial Separation ◽  
Stokes Number ◽  
Velocity Correlation ◽  
Pair Separation ◽  
Random Flow

DNS studies of dispersed particle motion in isotropic homogeneous turbulence [1] have revealed the existence of a component of random uncorrelated motion (RUM) dependent on the particle inertia τp (normalised particle response time or Stoke number). This paper reports the presence of RUM in a simple linear random smoothly varying flow field of counter rotating vortices where the two-particle velocity correlation was measured as a function of spatial separation. Values of the correlation less than one for zero separation indicated the presence of RUM. In terms of Stokes number, the motion of the particles in one direction corresponds to either a heavily damped (τp < 0.25) or lightly damped (τp > 0.25) harmonic oscillator. In the lightly damped case the particles overshoot the stagnation lines of the flow and are projected from one vortex to another (the so-called sling-shot effect). It is shown that RUM occurs only when τp > 0.25, increasing monotonically with increasing Stokes number. Calculations of the particle pair separation distribution function show that equilibrium of the particle concentration field is never reached, the concentration at zero separation increasing monotonically with time. This is consistent with the calculated negative values of the average Liapounov exponent (finite compressibility) of the particle velocity field.

scholarly journals Can We Infer Diapycnal Mixing Rates from the World Ocean Temperature–Salinity Distribution?

2016 ◽  
Vol 46 (12) ◽  
pp. 3751-3775 ◽  
Author(s):  
Olivier Arzel ◽  
Alain Colin de Verdière
Keyword(s):  
General Circulation ◽  
Large Scale ◽  
Water Mass ◽  
World Ocean ◽  
Eddy Diffusivity ◽  
Regional Variability ◽  
Diapycnal Mixing ◽  
Inverse Models ◽  
The World ◽  
The Difference

AbstractThe turbulent diapycnal mixing in the ocean is currently obtained from microstructure and finestructure measurements, dye experiments, and inverse models. This study presents a new method that infers the diapycnal mixing from low-resolution numerical calculations of the World Ocean whose temperatures and salinities are restored to the climatology. At the difference of robust general circulation ocean models, diapycnal diffusion is not prescribed but inferred. At steady state the buoyancy equation shows an equilibrium between the large-scale diapycnal advection and the restoring terms that take the place of the divergence of eddy buoyancy fluxes. The geography of the diapycnal flow reveals a strong regional variability of water mass transformations. Positive values of the diapycnal flow indicate an erosion of a deep-water mass and negative values indicate a creation. When the diapycnal flow is upward, a diffusion law can be fitted in the vertical and the diapycnal eddy diffusivity is obtained throughout the water column. The basin averages of diapycnal diffusivities are small in the first 1500 m [O(10−5) m2 s−1] and increase downward with bottom values of about 2.5 × 10−4 m2 s−1 in all ocean basins, with the exception of the Southern Ocean (50°–30°S), where they reach 12 × 10−4 m2 s−1. This study confirms the small diffusivity in the thermocline and the robustness of the higher canonical Munk’s value in the abyssal ocean. It indicates that the upward dianeutral transport in the Atlantic mostly takes place in the abyss and the upper ocean, supporting the quasi-adiabatic character of the middepth overturning.

scholarly journals Properties of Steady Geostrophic Turbulence with Isopycnal Outcropping

2012 ◽  
Vol 42 (1) ◽  
pp. 18-38 ◽  
Author(s):  
G. Roullet ◽  
J. C. McWilliams ◽  
X. Capet ◽  
M. J. Molemaker
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Mechanical Energy ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Primary Source ◽  
Eddy Diffusivity ◽  
Energy Cycle ◽  
Geostrophic Turbulence ◽  
Pv Gradient

Abstract High-resolution simulations of β-channel, zonal-jet, baroclinic turbulence with a three-dimensional quasigeostrophic (QG) model including surface potential vorticity (PV) are analyzed with emphasis on the competing role of interior and surface PV (associated with isopycnal outcropping). Two distinct regimes are considered: a Phillips case, where the PV gradient changes sign twice in the interior, and a Charney case, where the PV gradient changes sign in the interior and at the surface. The Phillips case is typical of the simplified turbulence test beds that have been widely used to investigate the effect of ocean eddies on ocean tracer distribution and fluxes. The Charney case shares many similarities with recent high-resolution primitive equation simulations. The main difference between the two regimes is indeed an energization of submesoscale turbulence near the surface. The energy cycle is analyzed in the (k, z) plane, where k is the horizontal wavenumber. In the two regimes, the large-scale buoyancy forcing is the primary source of mechanical energy. It sustains an energy cycle in which baroclinic instability converts more available potential energy (APE) to kinetic energy (KE) than the APE directly injected by the forcing. This is due to a conversion of KE to APE at the scale of arrest. All the KE is dissipated at the bottom at large scales, in the limit of infinite resolution and despite the submesoscales energizing in the Charney case. The eddy PV flux is largest at the scale of arrest in both cases. The eddy diffusivity is very smooth but highly nonuniform. The eddy-induced circulation acts to flatten the mean isopycnals in both cases.

Snowflakes in the atmospheric surface layer: observation of particle–turbulence dynamics

2017 ◽  
Vol 814 ◽  
pp. 592-613 ◽  
Author(s):  
Andras Nemes ◽  
Teja Dasari ◽  
Jiarong Hong ◽  
Michele Guala ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Volume Fraction ◽  
Response Times ◽  
Field Measurements ◽  
Stokes Number ◽  
Inertial Particles ◽  
Natural Setting ◽  
Scale Particle ◽  
Particle Imaging

We report on optical field measurements of snow settling in atmospheric turbulence at $Re_{\unicode[STIX]{x1D706}}=940$. It is found that the snowflakes exhibit hallmark features of inertial particles in turbulence. The snow motion is analysed in both Eulerian and Lagrangian frameworks by large-scale particle imaging, while sonic anemometry is used to characterize the flow field. Additionally, the snowflake size and morphology are assessed by digital in-line holography. The low volume fraction and mass loading imply a one-way interaction with the turbulent air. Acceleration probability density functions show wide exponential tails consistent with laboratory and numerical studies of homogeneous isotropic turbulence. Invoking the assumption that the particle acceleration has a stronger dependence on the Stokes number than on the specific features of the turbulence (e.g. precise Reynolds number and large-scale anisotropy), we make inferences on the snowflakes’ aerodynamic response time. In particular, we observe that their acceleration distribution is consistent with that of particles of Stokes number in the range $St=0.1{-}0.4$ based on the Kolmogorov time scale. The still-air terminal velocities estimated for the resulting range of aerodynamic response times are significantly smaller than the measured snow particle fall speed. This is interpreted as a manifestation of settling enhancement by turbulence, which is observed here for the first time in a natural setting.

Particle energization inside plasmoids: numerical and analytical investigations

2021 ◽  
Author(s):  
Xiaozhou Zhao ◽  
Rony Keppens ◽  
Fabio Bacchini
Keyword(s):  
Test Particle ◽  
Large Scale ◽  
Mass Density ◽  
Magnetic Islands ◽  
Chaotic Flow ◽  
Reynolds Decomposition ◽  
Particle Simulations ◽  
Particle Energization ◽  
Periodic Setting ◽  
A Current

<div> <div> <div> <p>In an idealized system where four magnetic islands interact in a two-dimensional periodic setting, we follow the detailed evolution of current sheets forming in between the islands, as a result of an enforced large-scale merging by magnetohydrodynamic (MHD) simulation. The large-scale island merging is triggered by a perturbation to the velocity field, which drives one pair of islands move towards each other while the other pair of islands are pushed away from one another. The "X"-point located in the midst of the four islands is locally unstable to the perturbation and collapses, producing a current sheet in between with enhanced current and mass density. Using grid-adaptive resistive magnetohydrodynamic (MHD) simulations, we establish that slow near-steady Sweet-Parker reconnection transits to a chaotic, multi-plasmoid fragmented state, when the Lundquist number exceeds about 3×10<sup>4</sup>, well in the range of previous studies on plasmoid instability. The extreme resolution employed in the MHD study shows significant magnetic island substructures. Turbulent and chaotic flow patters are also observed inside the islands. We set forth to explore how charged particles can be accelerated in embedded mini-islands within larger (monster)-islands on the sheet. We study the motion of the particles in a MHD snapshot at a fixed instant of time by the Test-Particle Module incorporated in AMRVAC (). The planar MHD setting artificially causes the largest acceleration in the ignored third direction, but does allow for full analytic study of all aspects leading to the acceleration and the in-plane, projected trapping of particles within embedded mini-islands. The analytic result uses a decomposition of the test particle velocity in slow and fast changing components, akin to the Reynolds decomposition in turbulence studies. The analytic results allow a complete fit to representative proton test particle simulations, which after initial non-relativistic motion throughout the monster island, show the potential of acceleration within a mini-island beyond (√2/2)c≈0.7c, at which speed the acceleration is at its highest efficiency. Acceleration to several hundreds of GeVs can happen within several tens of seconds, for upward traveling protons in counterclockwise mini-islands of sizes smaller than the proton gyroradius.</p> </div> </div> </div><div></div><div></div>

scholarly journals On the Jump Conditions for Shock Waves in Condensed Materials

2021 ◽  
Author(s):  
R K Anand
Keyword(s):  
Stainless Steel ◽  
Mach Number ◽  
Shock Front ◽  
Particle Velocity ◽  
Mass Density ◽  
Jump Conditions ◽  
Condensed Material ◽  
Material Parameters ◽  
Stainless Steel 304 ◽  
Condensed Materials

Abstract In this article, we have proposed Rankine–Hugoniot (RH) boundary conditions at the normal shock-front which is passing through the condensed material. These RH conditions are quite general, and their convenient forms for the particle velocity, mass density, pressure and temperature have been presented in terms of the upstream Mach number, and the material parameters for the weak and the strong shocks, respectively. Finally, the effects on the mechanical quantities of the shock compressed materials e.g. titanium Ti6Al4V, stainless steel 304, aluminum 6061-T6, etc. have been discussed.

scholarly journals Anisotropic clustering of inertial particles in homogeneous shear flow

2009 ◽  
Vol 629 ◽  
pp. 25-39 ◽  
Author(s):  
P. GUALTIERI ◽  
F. PICANO ◽  
C. M. CASCIOLA
Keyword(s):  
Relaxation Time ◽  
Shear Flow ◽  
Large Scale ◽  
Inertial Particles ◽  
Spatial Homogeneity ◽  
Homogeneous Shear ◽  
Multi Scale ◽  
Angular Distribution Function ◽  
Homogeneous Shear Flow ◽  
Anisotropic Clustering

Recently, clustering of inertial particles in turbulence has been thoroughly analysed for statistically homogeneous isotropic flows. Phenomenologically, spatial homogeneity of particle configurations is broken by the advection of a range of eddies determined by the Stokes relaxation time of the particles. This in turn results in a multi-scale distribution of local particle concentration and voids. Much less is known concerning anisotropic flows. Here, by addressing direct numerical simulations (DNS) of a statistically steady particle-laden homogeneous shear flow, we provide evidence that the mean shear preferentially orients particle patterns. By imprinting anisotropy on large-scale velocity fluctuations, the shear indirectly affects the geometry of the clusters. Quantitative evaluation is provided by a purposely designed tool, the angular distribution function (ADF) of particle pairs, which allows to address the anisotropy content of particle aggregates on a scale-by-scale basis. The data provide evidence that, depending on the Stokes relaxation time of the particles, anisotropic clustering may occur even in the range of scales in which the carrier phase velocity field is already recovering isotropy. The strength of the singularity in the anisotropic component of the ADF quantifies the level of fine-scale anisotropy, which may even reach values of more than 30% direction-dependent variation in the probability to find two closeby particles at viscous-scale separation.

Efficient 3D elastic full-waveform inversion using wavefield reconstruction methods

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. R45-R55 ◽  
Author(s):  
Espen Birger Raknes ◽  
Wiktor Weibull
Keyword(s):  
Particle Velocity ◽  
Large Scale ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Reconstruction Method ◽  
Full Waveform Inversion ◽  
Reverse Time ◽  
Full Waveform ◽  
Time Migration ◽  
Reconstruction Methods

In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wavefields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The crosscorrelation condition requires both fields to be available at the same time instants. For large-scale 3D problems, it is not possible, in practice, to store snapshots of the wavefields during forward modeling due to extreme storage requirements. We have developed an approximate wavefield reconstruction method that uses particle velocity field recordings on the boundaries to reconstruct the forward wavefields during the computation of the reverse time wavefields. The method is computationally effective and requires less storage than similar methods. We have compared the reconstruction method to a boundary reconstruction method that uses particle velocity and stress fields at the boundaries and to the optimal checkpointing method. We have tested the methods on a 2D vertical transversely isotropic model and a large-scale 3D elastic FWI problem. Our results revealed that there are small differences in the results for the three methods.

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