Lagrangian and Eulerian descriptions of inertial particles in random flows

Derevyanko, Stanislav A.; Falkovich, Gregory; Turitsyn, Konstantin; Turitsyn, Sergei K.

doi:10.1080/14685240701332475

Cited by 33 publications

(39 citation statements)

References 28 publications

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“…A number of analytical results were derived for onedimensional flows [29,30,31]. Although such flows are always compressible, their study helps improving the intuition for the dynamics of inertial particles in higherdimensional random flows.…”

Section: Exact Results In One Dimensionmentioning

confidence: 99%

Stochastic suspensions of heavy particles

Bec

Cencini

Hillerbrand

et al. 2008

Physica D: Nonlinear Phenomena

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Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical and statistical properties. Substantial progress followed from the study of suspensions in model flows which, although much simpler, reproduce most of the important mechanisms observed in real turbulence. This paper presents recent developments made on the relative motion of a pair of particles suspended in time-uncorrelated and spatially self-similar Gaussian flows. This review is complemented by new results. By introducing a time-dependent Stokes number, it is demonstrated that inertial particle relative dispersion recovers asymptotically Richardson's diffusion associated to simple tracers. A perturbative (homogeneization) technique is used in the small-Stokes-number asymptotics and leads to interpreting first-order corrections to tracer dynamics in terms of an effective drift. This expansion implies that the correlation dimension deficit behaves linearly as a function of the Stokes number. The validity and the accuracy of this prediction is confirmed by numerical simulations.

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Section: Exact Results In One Dimensionmentioning

confidence: 99%

Stochastic suspensions of heavy particles

Bec

Cencini

Hillerbrand

et al. 2008

Physica D: Nonlinear Phenomena

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“…Still it is possible that in the small Stokes number regime, the statistical weight of eventual shocks is weak enough to allow to neglect them [22].…”

Section: -P4mentioning

confidence: 99%

The Eulerian description of dilute collisionless suspension

Boffetta¹,

Celani²,

Lillo³

et al. 2007

Europhys. Lett.

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We analyze the statistical properties of a Eulerian fluid model describing the evolution of a suspension of inertial particles in an incompressible flow. Regularity and compressibility of the velocity field for the inertial phase are investigated in the limit of heavy particles by means of numerical simulations in two-and three-dimensional flows. We show that in the small Stokes number regime the Eulerian fluid model is able to capture fine details of the clustering dynamics, and exhibits good agreement with fully Lagrangian simulations of inertial particle trajectories. The fluid description breaks down due to collisions at Stokes numbers 0.1, the actual value depending on the carrier flow characteristics.

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“…The role of noise is to introduce a random force working against the linear positive drift |E|z to bring the particle to the collector z − . Note that the stochastic Riccati dynamics of the type above is not uncommon in many other physical applications most notably caustic formation in turbulent particle flows [11,12]. Up until this point we have not prescribed particular statistics of the stochastic process U (x) [i.e., the considerations above are applicable to any model of the field U (x)].…”

Section: Therefore One Only Needs To Consider the Upper Trajectory mentioning

confidence: 99%

Appearance of bound states in random potentials with applications to soliton theory

Derevyanko

2011

Phys. Rev. E

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We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg-de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.

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Lagrangian and Eulerian descriptions of inertial particles in random flows

Cited by 33 publications

References 28 publications

Stochastic suspensions of heavy particles

Stochastic suspensions of heavy particles

The Eulerian description of dilute collisionless suspension

Appearance of bound states in random potentials with applications to soliton theory

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