Dynamics of heavy particles in a Burgers vortex

Marcu, Bogdan; Meiburg, Eckart; Newton, Paul K.

doi:10.1063/1.868778

Cited by 56 publications

(44 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Very small particles may not have steady-state orbits, instead they reach the tube center because of the efficient radial drag. The steady-state radius, which we will refer to as the equilibrium radius, can be estimated from the equation u 2 θ /r = Ar/τ p (Marcu et al 1995). Using u θ as a function of r in Equation (A1), we see that larger friction timescales give larger equilibrium radii.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

Pan

Padoan

Scalo

et al. 2011

ApJ

121

109

View full text Add to dashboard Cite

We study the clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, St, defined as the ratio of the particle friction timescale, τ p , to the Kolmogorov timescale in the flow. In agreement with previous studies, we find that, in the dissipation range, the clustering intensity strongly peaks at St 1, and the RDF for St ∼ 1 shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these large scales, the strongest clustering is from particles with τ p in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is ∼τ p . We find that particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in two recent models for planetesimal formation. We argue that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.

show abstract

Section: Discussionmentioning

confidence: 99%

“…As it moves closer to the center, the particle rotates faster. When the centrifugal force from the rotation balances the radial drag, the particle ends up in a steadystate orbit (Marcu et al 1995). Very small particles may not have steady-state orbits, instead they reach the tube center because of the efficient radial drag.…”

Section: Discussionmentioning

confidence: 99%

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

Pan

Padoan

Scalo

et al. 2011

ApJ

121

109

View full text Add to dashboard Cite

show abstract

“…The result is a modified velocity field, whose fixed points represent equilibrium points for the particles. 20 In the absence of gravity, the streamlines of this modified velocity field are identical to the streamlines of the fluid velocity field, shown in Fig. 1͑b͒ for kϭ0.9 and ϭ4.…”

Section: A Gravity Perpendicular To the Mixing Layermentioning

confidence: 66%

“…1, so that they are unstable for particle accumulation. 20 In the following, we analyze the linear stability at the center of the vortex located at zϭ0. 25, yϭ0.…”

Section: Equilibrium Points and Their Stability In The Absence Omentioning

confidence: 99%

See 1 more Smart Citation

The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. I. Equilibrium points and their stability

Marcu

Meiburg

1996

Physics of Fluids

Self Cite

View full text Add to dashboard Cite

The dynamics of small, heavy, spherical particles are investigated in an analytical model of the stretched counterrotating streamwise braid vortices commonly found in three-dimensionally evolving mixing layers. The flow field consists of two superimposed rows of Stuart vortices of opposite sign, with an additional two-dimensional strain field. The particle dynamics are determined by a balance of inertial, gravitational, and viscous drag forces, i.e., the dimensionless Stokes and Froude numbers, St and Fr, as well as by the dimensionless strain rate, and the Stuart vortex family parameter. Equilibrium points for the particles, as well as their stability criteria, are determined analytically, both in the absence and in the presence of gravity, and for different orientations of the gravity vector. In the absence of gravity, accumulation of low St particles can occur at the center of the braid vortices. An analytical expression for the critical particle diameter, below which accumulation is possible, is derived. The presence of gravity can lead to the emergence of multiple equilibrium points, whose stability properties depend on their locations. For a horizontal mixing layer flow and strong gravity effects, unconditional accumulation can occur midway between the streamwise braid vortices in the upwelling regions. Conditionally stable accumulation regions exist a short horizontal distance away from the centers of the braid vortices. If the gravity vector lies within the plane of the mixing layer, accumulation points exist only for moderate strengths of gravity. Under these circumstances, conditional accumulation is possible near the streamwise vortex centers.

show abstract

Accumulation of Heavy Particles in Bounded Vortex Flow

IJzermans

Hagmeijer

Fluid Mechanics and Its Applications

View full text Add to dashboard Cite

Much research has been done on the motion of heavy particles in simple vortex flows. In most of this work, particle motion is investigated under the influence of fixed vortices. In the context of astrophysics, the motion of heavy particles in rotating two-dimensional flows has been investigated; the rotation follows from the laws of Kepler. In the present paper, the motion of heavy particles in potential vortex flow in a circular domain is investigated. The vortex describes a circular trajectory due to the presence of the boundary, so that a steadily rotating flow is obtained. In order to isolate the effect of particle inertia, only Stokes drag is taken into account in the equation of motion. The numerical simulations are based on a oneway coupling. They show that small heavy particles accumulate in an ellitpic region of the flow, counterrotating with respect to the vortex. When the particle Stokes number exceeds a threshold, depending on the vortex configuration, particles are expelled from the circular domain. A stability criterion for this particle accumulation is derived analytically. These results are qualitatively comparable to those obtained by others in astrophysics. 75

show abstract

Dynamics of heavy particles in a Burgers vortex

Cited by 56 publications

References 25 publications

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

The effect of streamwise braid vortices on the particle dispersion in a plane mixing layer. I. Equilibrium points and their stability

Accumulation of Heavy Particles in Bounded Vortex Flow

Contact Info

Product

Resources

About