The Experts below are selected from a list of 300 Experts worldwide ranked by ideXlab platform
Piero Olla - One of the best experts on this subject based on the ideXlab platform.
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Preferential concentration versus clustering in inertial particle transport by Random Velocity Fields.
Physical Review E, 2010Co-Authors: Piero OllaAbstract:The concept of preferential concentration in the transport of inertial particles by Random Velocity Fields is extended to account for the possibility of zero correlation time and compressibility of the Velocity Field. It is shown that, in the case of an uncorrelated in time Random Velocity Field, preferential concentration takes the form of a condition on the Field history leading to the current particle positions. This generalized form of preferential concentration appears to be a necessary condition for clustering in the uncorrelated in time case. The standard interpretation of preferential concentration is recovered considering local time averages of the Velocity Field. In the compressible case, preferential concentration occurs in regions of negative divergence of the Field. In the incompressible case, it occurs in regions of simultaneously high strain and negative Field skewness.
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Preferential concentration vs. clustering in inertial particle transport by Random Velocity Fields
arXiv: Statistical Mechanics, 2008Co-Authors: Piero OllaAbstract:The concept of preferential concentration in the transport of inertial particles by Random Velocity Fields is extended to account for the possibility of zero correlation time and compressibility of the Velocity Field. It is shown that, in the case of an uncorrelated in time Random Velocity Field, preferential concentration takes the form of a condition on the Field history leading to the current particle positions. This generalized form of preferential concentration appears to be a necessary condition for clustering in the uncorrelated in time case. The standard interpretation of preferential concentration is recovered considering local time averages of the Velocity Field. In the compressible case, preferential concentration occurs in regions of negative divergence of the Field. In the incompressible case, it occurs in regions of simultaneously high strain and negative Field skewness.
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Perturbation theory for large Stokes number particles in Random Velocity Fields
The European Physical Journal B, 2008Co-Authors: Piero Olla, Maria Raffaella VuoloAbstract:We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated Random Velocity Field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the Velocity Field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision Velocity statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.
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Clustering and collision of inertial particles in Random Velocity Fields.
Physical review. E Statistical nonlinear and soft matter physics, 2008Co-Authors: Piero OllaAbstract:The influence of clustering on the collision rate of inertial particles in a smooth Random Velocity Field, mimicking the smaller scales of a turbulent flow, is analyzed. For small values of the ratio between the relaxation time of the particle Velocity and the characteristic time of the Field, the effect of clusters is to make more energetic collisions less likely. The result is independent of the flow dimensionality and is due only to the origin of collisions in the process of caustic formation.
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perturbation theory for large stokes number particles in Random Velocity Fields
arXiv: Statistical Mechanics, 2008Co-Authors: Piero Olla, Maria Raffaella VuoloAbstract:We derive a perturbative approach to study, in the large inertia limit, the dynamics of solid particles in a smooth, incompressible and finite-time correlated Random Velocity Field. We carry on an expansion in powers of the inverse square root of the Stokes number, defined as the ratio of the relaxation time for the particle velocities and the correlation time of the Velocity Field. We describe in this limit the residual concentration fluctuations of the particle suspension, and determine the contribution to the collision statistics produced by clustering. For both concentration fluctuations and collision velocities, we analyze the differences with the compressible one-dimensional case.
Dmitry Sokoloff - One of the best experts on this subject based on the ideXlab platform.
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Mean-Field theory for a passive scalar advected by a turbulent Velocity Field with a Random renewal time.
Physical Review E, 2001Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:Mean-Field theory for turbulent transport of a passive scalar ~e.g., particles and gases! is discussed. Equations for the mean number density of particles advected by a Random Velocity Field, with a finite correlation time, are derived. Mean-Field equations for a passive scalar comprise spatial derivatives of high orders due to the nonlocal nature of passive scalar transport in a Random Velocity Field with a finite correlation time. A turbulent Velocity Field with a Random renewal time is considered. This model is more realistic than that with a constant renewal time used by Elperin et al. @Phys. Rev. E 61, 2617 ~2000!#, and employs two characteristic times: the correlation time of a Random Velocity Fieldt c , and a mean renewal time t. It is demonstrated that the turbulent diffusion coefficient is determined by the minimum of the times t c and t. The mean-Field equation for a passive scalar was derived for different ratios of t/t c . The important role of the statistics of the Field of Lagrangian trajectories in turbulent transport of a passive scalar, in a Random Velocity Field with a finite correlation time, is demonstrated. It is shown that in the case t c!t!t N the form of the mean-Field equation for a passive scalar is independent of the statistics of the Velocity Field, where t N is the characteristic time of variations of a mean passive scalar Field.
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Mean-Field theory for a passive scalar advected by a turbulent Velocity Field with a Random renewal time.
Physical review. E Statistical nonlinear and soft matter physics, 2001Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:Mean-Field theory for turbulent transport of a passive scalar (e.g., particles and gases) is discussed. Equations for the mean number density of particles advected by a Random Velocity Field, with a finite correlation time, are derived. Mean-Field equations for a passive scalar comprise spatial derivatives of high orders due to the nonlocal nature of passive scalar transport in a Random Velocity Field with a finite correlation time. A turbulent Velocity Field with a Random renewal time is considered. This model is more realistic than that with a constant renewal time used by Elperin et al. [Phys. Rev. E 61, 2617 (2000)], and employs two characteristic times: the correlation time of a Random Velocity Field tau(c), and a mean renewal time tau. It is demonstrated that the turbulent diffusion coefficient is determined by the minimum of the times tau(c) and tau. The mean-Field equation for a passive scalar was derived for different ratios of tau/tau(c). The important role of the statistics of the Field of Lagrangian trajectories in turbulent transport of a passive scalar, in a Random Velocity Field with a finite correlation time, is demonstrated. It is shown that in the case tau(c)
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Passive scalar transport in a Random flow with a finite renewal time: Mean-Field equations
Physical Review E, 2000Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:A mean-Field equation for a passive scalar (e.g., for a mean number density of particles) in a Random Velocity Field (incompressible and compressible) with a finite constant renewal time is derived. The finite renewal time of a Random Velocity Field results in the appearance of high-order spatial derivatives in the mean-Field equation for a passive scalar. We considered three models of a Random Velocity Field: (i) a Velocity Field with a small renewal time; (ii) the Gaussian approximation for Lagrangian trajectories; and (iii) a small inhomogeneity of the Velocity and mean passive scalar Fields. For a small renewal time we recovered results obtained using the $\ensuremath{\delta}$-function-correlated in time Random Velocity Field. The finite renewal time and compressibility of the Velocity Field can cause a depletion of turbulent diffusion and a modification of an effective drift Velocity. For a compressible Velocity Field the form of the mean-Field equation for a passive scalar depends on the details of the Velocity Field, i.e., the universality is lost. For an incompressible Velocity Field the universality exists in spite of the finite renewal time. Results by Saffman [J. Fluid Mech. 8, 273 (1960)] for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of a compressible and anisotropic Random Velocity Field. The obtained results may be of relevance in some atmospheric phenomena (e.g., atmospheric aerosols and smog formation).
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Turbulent transport of atmospheric aerosols and formation of large-scale structures
Physics and Chemistry of the Earth Part A: Solid Earth and Geodesy, 2000Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:Abstract Turbulent transport of aerosols and droplets in a Random Velocity Field with a finite correlation time is studied. We derived a mean-Field equation and an equation for the second moment for a number density of aerosols. The finite correlation time of Random Velocity Field results in the appearance of the high-order spatial derivatives in these equations. The finite correlation time and compressibility of the Velocity Field can cause a depletion of turbulent diffusion and a modification of an effective mean drift Velocity. The coefficient of turbulent diffusion in the vertical direction can be depleted by 25 % due to the finite correlation time of a turbulent Velocity Field. The latter result is in compliance with the known anisotropy of the coefficient of turbulent diffusion in the atmosphere. The effective mean drift Velocity is caused by a compressibility of particles Velocity Field and results in formation of large-scale inhomogeneities in spatial distribution of aerosols in the vicinity of the atmospheric temperature inversion. Results obtained by Saffman (1960) for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of compressible and anisotropic Random Velocity Field. A mechanism of formation of small-scale inhomogeneities in particles spatial distribution is also discussed. This mechanism is associated with an excitation of a small-scale instability of the second moment of number density of particles. The obtained results are important in the analysis of various atmospheric phenomena, e.g., atmospheric aerosols, droplets and smog formation.
Valerii I. Klyatskin - One of the best experts on this subject based on the ideXlab platform.
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Simple example of the development of cluster structure of a passive tracer Field in Random flows
Physics-Uspekhi, 2000Co-Authors: Valerii I. Klyatskin, Konstantin V KoshelAbstract:As a follow-up to Ref. (1), the formation of particle clusters (Lagrangian description) and cluster structure of the Field of a passive tracer (Eulerian description) in a Random Velocity Field is analyzed for a simple problem amenable to an analytical solution.
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Statistical theory of the diffusion of a passive tracer in a Random Velocity Field
Journal of Experimental and Theoretical Physics, 1997Co-Authors: Valerii I. Klyatskin, A. I. SaichevAbstract:A passive tracer on the surface of an incompressible liquid behaves like a tracer in two-dimensional compressible flows, whose characteristic feature is the formation of cluster structures, i.e., compact regions of increased density surrounded by vast low-density regions. The cluster formation dynamics are studied, and statistical spatiotemporal characteristics of the density Fields, which faithfully reflect the properties of the cluster structures, are calculated.
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Statistical description of the diffusion of a passive tracer in a Random Velocity Field
Physics-Uspekhi, 1994Co-Authors: Valerii I. KlyatskinAbstract:A single functional approach is used to treat the problem of the diffusion of a tracer in a Random Velocity Field, posed in a general form. Approximate methods leading to various approximate solutions and the conditions of their validity are examined. Plane parallel average flow is considered in detail and some features of statistical solutions are discussed for the simplest case.
Tov Elperin - One of the best experts on this subject based on the ideXlab platform.
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Mean-Field theory for a passive scalar advected by a turbulent Velocity Field with a Random renewal time.
Physical Review E, 2001Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:Mean-Field theory for turbulent transport of a passive scalar ~e.g., particles and gases! is discussed. Equations for the mean number density of particles advected by a Random Velocity Field, with a finite correlation time, are derived. Mean-Field equations for a passive scalar comprise spatial derivatives of high orders due to the nonlocal nature of passive scalar transport in a Random Velocity Field with a finite correlation time. A turbulent Velocity Field with a Random renewal time is considered. This model is more realistic than that with a constant renewal time used by Elperin et al. @Phys. Rev. E 61, 2617 ~2000!#, and employs two characteristic times: the correlation time of a Random Velocity Fieldt c , and a mean renewal time t. It is demonstrated that the turbulent diffusion coefficient is determined by the minimum of the times t c and t. The mean-Field equation for a passive scalar was derived for different ratios of t/t c . The important role of the statistics of the Field of Lagrangian trajectories in turbulent transport of a passive scalar, in a Random Velocity Field with a finite correlation time, is demonstrated. It is shown that in the case t c!t!t N the form of the mean-Field equation for a passive scalar is independent of the statistics of the Velocity Field, where t N is the characteristic time of variations of a mean passive scalar Field.
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Mean-Field theory for a passive scalar advected by a turbulent Velocity Field with a Random renewal time.
Physical review. E Statistical nonlinear and soft matter physics, 2001Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:Mean-Field theory for turbulent transport of a passive scalar (e.g., particles and gases) is discussed. Equations for the mean number density of particles advected by a Random Velocity Field, with a finite correlation time, are derived. Mean-Field equations for a passive scalar comprise spatial derivatives of high orders due to the nonlocal nature of passive scalar transport in a Random Velocity Field with a finite correlation time. A turbulent Velocity Field with a Random renewal time is considered. This model is more realistic than that with a constant renewal time used by Elperin et al. [Phys. Rev. E 61, 2617 (2000)], and employs two characteristic times: the correlation time of a Random Velocity Field tau(c), and a mean renewal time tau. It is demonstrated that the turbulent diffusion coefficient is determined by the minimum of the times tau(c) and tau. The mean-Field equation for a passive scalar was derived for different ratios of tau/tau(c). The important role of the statistics of the Field of Lagrangian trajectories in turbulent transport of a passive scalar, in a Random Velocity Field with a finite correlation time, is demonstrated. It is shown that in the case tau(c)
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Passive scalar transport in a Random flow with a finite renewal time: Mean-Field equations
Physical Review E, 2000Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:A mean-Field equation for a passive scalar (e.g., for a mean number density of particles) in a Random Velocity Field (incompressible and compressible) with a finite constant renewal time is derived. The finite renewal time of a Random Velocity Field results in the appearance of high-order spatial derivatives in the mean-Field equation for a passive scalar. We considered three models of a Random Velocity Field: (i) a Velocity Field with a small renewal time; (ii) the Gaussian approximation for Lagrangian trajectories; and (iii) a small inhomogeneity of the Velocity and mean passive scalar Fields. For a small renewal time we recovered results obtained using the $\ensuremath{\delta}$-function-correlated in time Random Velocity Field. The finite renewal time and compressibility of the Velocity Field can cause a depletion of turbulent diffusion and a modification of an effective drift Velocity. For a compressible Velocity Field the form of the mean-Field equation for a passive scalar depends on the details of the Velocity Field, i.e., the universality is lost. For an incompressible Velocity Field the universality exists in spite of the finite renewal time. Results by Saffman [J. Fluid Mech. 8, 273 (1960)] for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of a compressible and anisotropic Random Velocity Field. The obtained results may be of relevance in some atmospheric phenomena (e.g., atmospheric aerosols and smog formation).
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Turbulent transport of atmospheric aerosols and formation of large-scale structures
Physics and Chemistry of the Earth Part A: Solid Earth and Geodesy, 2000Co-Authors: Tov Elperin, Nathan Kleeorin, Igor Rogachevskii, Dmitry SokoloffAbstract:Abstract Turbulent transport of aerosols and droplets in a Random Velocity Field with a finite correlation time is studied. We derived a mean-Field equation and an equation for the second moment for a number density of aerosols. The finite correlation time of Random Velocity Field results in the appearance of the high-order spatial derivatives in these equations. The finite correlation time and compressibility of the Velocity Field can cause a depletion of turbulent diffusion and a modification of an effective mean drift Velocity. The coefficient of turbulent diffusion in the vertical direction can be depleted by 25 % due to the finite correlation time of a turbulent Velocity Field. The latter result is in compliance with the known anisotropy of the coefficient of turbulent diffusion in the atmosphere. The effective mean drift Velocity is caused by a compressibility of particles Velocity Field and results in formation of large-scale inhomogeneities in spatial distribution of aerosols in the vicinity of the atmospheric temperature inversion. Results obtained by Saffman (1960) for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of compressible and anisotropic Random Velocity Field. A mechanism of formation of small-scale inhomogeneities in particles spatial distribution is also discussed. This mechanism is associated with an excitation of a small-scale instability of the second moment of number density of particles. The obtained results are important in the analysis of various atmospheric phenomena, e.g., atmospheric aerosols, droplets and smog formation.
Nicolae Suciu - One of the best experts on this subject based on the ideXlab platform.
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diffusion in Random Velocity Fields with applications to contaminant transport in groundwater
Advances in Water Resources, 2014Co-Authors: Nicolae SuciuAbstract:Abstract The process of diffusion in a Random Velocity Field is the mathematical object underlying currently used stochastic models of transport in groundwater. The essential difference from the normal diffusion is given by the nontrivial correlation of the increments of the process which induces transitory or persistent dependence on initial conditions. Intimately related to these memory effects is the ergodicity issue in subsurface hydrology. These two topics are discussed here from the perspectives of Ito and Fokker–Planck complementary descriptions and of recent Monte Carlo studies. The latter used a global Random walk algorithm, stable and free of numerical diffusion. Beyond Monte Carlo simulations, this algorithm and the mathematical frame of the diffusion in Random Fields allow efficient solutions to evolution equations for the probability density of the Random concentration.
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Spatially inhomogeneous transition probabilities as memory effects for diffusion in statistically homogeneous Random Velocity Fields.
Physical Review E, 2010Co-Authors: Nicolae SuciuAbstract:Whenever one uses translation invariant mean Green's functions to describe the behavior in the mean and to estimate dispersion coefficients for diffusion in Random Velocity Fields, the spatial homogeneity of the transition probability of the transport process is implicitly assumed. This property can be proved for deterministic initial conditions if, in addition to the statistical homogeneity of the space-Random Velocity Field, the existence of unique classical solutions of the transport equations is ensured. When uniqueness condition fails and translation invariance of the mean Green's function cannot be assumed, as in the case of nonsmooth samples of Random Velocity Fields with exponential correlations, asymptotic dispersion coefficients can still be estimated within an alternative approach using the Ito equation. Numerical simulations confirm the predicted asymptotic behavior of the coefficients, but they also show their dependence on initial conditions at early times, a signature of inhomogeneous transition probabilities. Such memory effects are even more relevant for Random initial conditions, which are a result of the past evolution of the process of diffusion in correlated Velocity Fields, and they persist indefinitely in case of power law correlations. It was found that the transition probabilities for successive times can be spatially homogeneous only if a long-time normal diffusion limit exits. Moreover, when transition probabilities, for either deterministic or Random initial states, are spatially homogeneous, they can be explicitly written as Gaussian distributions.
