Dynamics of heavy particles in a Burgers vortex

Marcu, Bogdan

doi:10.1016/s0301-9322(97)88508-4

Cited by 12 publications

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“…In order to investigate this point more quantitatively, we extend here the stability analysis performed in Ref. 23 for the dynamics of heavy particles advected by the velocity field of a ͑steady͒ Burgers vortex, 24 to the case of particles with a generic density ratio ␤. The axial, radial and angular components of the model fluid velocity field associate to a Burgers vortex are given ͑in nondimensional form͒ by…”

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On the measurement of vortex filament lifetime statistics in turbulence

2010

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A numerical study of turbulence seeded with light particles is presented. We analyze the statistical properties of coherent, small-scale structures by looking at the trapping events of light particles inside vortex filaments. We study the properties of particles attracting set, measuring its fractal dimension and the probability that the separation between two particles remains within the dissipative scale, even for time lapses as long as the large-scale correlation time, T L . We show how to estimate the vortex lifetime by studying the moment of inertia of bunches of particles, showing the presence of an exponential lifetime distribution, with events up to T L . © 2010 American Institute of Physics. ͓doi:10.1063/1.3431660͔ Vorticity dynamics, in general, and vortex filaments, in particular, have been the subject of many theoretical, phenomenological and experimental studies. [1][2][3][4] According to their inertia properties particles respond differently to fluctuations of the advecting-Eulerian-velocity field producing locally nonhomogeneous concentration, a phenomenon dubbed as "preferential concentration." 5,6 Thanks to their capability of strongly concentrating in high vorticity regions, very light particles ͑i.e., small bubbles in water͒ have been used to visualize small scale vortex filaments, 7,8 and to measure pressure statistics. 9 Similar phenomena, based on complex response of microscopic hydrogen particles in quantum fluids, have also been exploited recently to visualize quantized vortices. 10 In the present work, we study the statistical correlation between light-particle dynamics and the one of small scale vortex filaments. Previous numerical 11 and experimental 12 works have assessed in great detail the spatial distribution and correlation of intense vortex filaments. Here we want to focus on different properties: their temporal evolution. Thanks to the correlation with the trajectories of light particles, we measure the vortex filament lifetime distribution.Data come from a direct numerical simulation ͑DNS͒ of 3D fully periodic Navier-Stokes equations plus particles. Together with the Eulerian field, we integrated the Lagrangian evolution of particles by mean of a model of dilute, passively advected, suspensions of spherical particles 13,14In the above equations, x͑t͒ and v͑t͒ denote the particle position and velocity, respectively, p = a 2 / ͑3␤ ͒ is the particle response time, a is the particle radius, St= p / is the Stokes number of the particle, is the dissipative time, and ␤ =3 f / ͑ f +2 p ͒ is related to the contrast between the density of the particle, p , and that of the fluid, f . Let us stress that in the model particles are not defined in terms of their material physical properties ͑size and density͒ but in terms of their dynamical properties ͑response time and density contrast͒ and that the formula given for p is a physical interpretation connecting the two points of view. For instance ␤ =0 ͑limit of very heavy particles͒ with finite Stokes is then only valid assuming vanishing part...

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“…As in Ref. 23, we will limit ourselves to consider the two-dimensional dynamics in the ͑r , ͒ plane, where the velocity field reads ͑in Cartesian coordinates͒…”

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On the measurement of vortex filament lifetime statistics in turbulence

2010

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“…In the frame moving with the vortex, the flow is azimuthal. A suitable model for the flow field is given by (6) (Lamb's vortex)-this is also the similarity solution studied by Marcu et al [37] for dense particles moving near a Burgers vortex (where there is an external irrotational straining flow). The streamfunction corresponding to a fixed Rankine vortex (6) is…”

Section: Particles Outside the Vortex Corementioning

confidence: 98%

Vortices, Complex Flows and Inertial Particles

Hunt

Delfos

Eames

et al. 2007

Flow Turbulence Combust

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The properties of vortical structures at high Reynolds number in uniform flows and near rigid boundaries are reviewed. New properties are derived by analysing the dynamics of the main flow features and the related integral constraints, including the relations between mean swirl and bulk speed, the relative level of internal fluctuations to bulk properties, and connections between the steadiness and topology of the structures. A crucial property that determines energy dissipation and the transport of inertial particles (with finite fall speed) is the variation across the structure of the ratio of the mean strain rate ( ) to the mean vorticity ( ). It is shown how, once such particles are entrained into the vortical regions of a coherent structure, they can be transported over significant distances even as the vortices grow and their internal structure is distorted by internal turbulence, swirling motions and the presence of rigid boundaries. However if the vortex is strongly distorted by a straining motion so that is greater than , the entrained particles are ejected quite rapidly. These mechanisms are consistent with previous studies of entrained and sedimenting particles in disperse two phase flows over flat surfaces, and over bluff obstacles and dunes. They are also tested in more detail here through laboratory observations and measurements of 50-200-μm particles entrained into circular and non-circular vortices moving first into still air and then onto rigid surfaces placed parallel and perpendicular to the direction of motion of the vortices.

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“…In an influential paper by Lundgren [3], a three-dimensional spiral vortex model is introduced in which vorticity is not axially symmetric as in the Burger's vortex (see Marcu, Meiburg, and Newton [4]), but has a characteristic spiral structure. In this model, these structures arise dynamically from the interaction of two regions of constant vorticity.…”

Section: Introductionmentioning

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Vortex Motion and the Geometric Phase. Part II. Slowly Varying Spiral Structures

Shashikanth

Newton

1999

J. Nonlinear Sci.

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Summary.We derive formulas for the long time evolution of passive interfaces in three "canonical" incompressible, inviscid, two-dimensional flow models. The point vortex models, introduced in Part 1 [1] are (i) a "restricted" three-vortex problem, (ii) a vortex and a particle in a closed circular domain, and (iii) a particle in the flowfield of a mixing layer model undergoing a vortex pairing instability. In each configuration, it was shown in Part 1 that the passive particle exhibits a geometric or Hannay-Berry phase over long time periods induced by the slowly varying periodic background field. In this paper we show how the formula for the evolution of a passive interface driven by the dynamics of the vortices inherits this geometric phase effect. The interface wraps into a spiral formation around the "parent" vortex, with a slowly varying component induced by the farfield vorticity. The length formula for the long time growth of the slowly rotating spiral decomposes into a "dynamic" part and a "geometric" part. The dynamic part is the length in the "unperturbed" system-i.e., in the absence of the background field-and the geometric part is the contribution of the geometric phase θ g for a passive particle in the flow. We derive the following simple formula for an interface along a smooth curve joining two arbitrary particles labelled A and B. Define L(T ) as the difference in interface lengths between the "unperturbed" system and the "perturbed" slowly varying system at the end of the long time period T . In each case,where ξ is the radial coordinate parametrizing the interface at t = 0. * Current address: Control and Dynamical Systems,

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Dynamics of heavy particles in a Burgers vortex

Cited by 12 publications

References 0 publications

On the measurement of vortex filament lifetime statistics in turbulence

On the measurement of vortex filament lifetime statistics in turbulence

Vortices, Complex Flows and Inertial Particles

Vortex Motion and the Geometric Phase. Part II. Slowly Varying Spiral Structures

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