Report on the IUTAM symposium: fundamental aspects of vortex motion

Aref, Hassan; Kambe, Tsutomu

doi:10.1017/s0022112088001466

Cited by 13 publications

(9 citation statements)

References 13 publications

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“…These comparisons have been reproduced in Aref & Kambe (1988, figure 8) and the reader is referred to them. In the idealized flow, the motion of the vortex rings and, therefore, the velocity field is periodic in time in a frame moving with the average speed of the rings.…”

Section: The Mixing Regionmentioning

confidence: 99%

“…Since the study of fluid particle motions involves only kinematical considerations, the application, and hence, results of dynamical systems theory are independent of Reynolds number. For example, Aref & Balachandar (1986) showed that unsteady Stokes flow between eccentric rotating cylinders, in which the rotation rate is modulated periodically in time, can exhibit chaotic particle motions of the Smale horseshoe type, Thus this particular Stokes flow is effectively non-reversible. This same flow has also been studied experimentally as well as theoretically by Chaiken et al (1986Chaiken et al ( , 1987.…”

Section: Introductionmentioning

confidence: 99%

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An analytical study of transport, mixing and chaos in an unsteady vortical flow

1990

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We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field induced by a vortex pair plus an oscillating strainrate field. I n the absence of the strain-rate field the vortex pair moves with a constant velocity and carries with it a constant body of fluid. When the strain-rate field is added the picture changes dramatically ; fluid is entrained and detrained from the neighbourhood of the vortices and chaotic particle motion occurs. We investigate the mechanism for this phenomenon and study the transport and mixing of fluid in this flow. Our work consists of both numerical and analytical studies. The analytical studies include the interpretation of the invariant manifolds as the underlying structure which govern the transport. For small values of strain-rate amplitude we use Melnikov's technique to investigate the behaviour of the manifolds as the parameters of the problem change and to prove the existence of a horseshoe map and thus the existence of chaotic particle paths in the flow. Using the Melnikov technique once more we develop an analytical estimate of the flux rate into and out of the vortex neighbourhood. We then develop a technique for determining the residence time distribution for fluid particles near the vortices that is valid for arbitrary strainrate amplitudes. The technique involves an understanding of the geometry of the tangling of the stable and unstable manifolds and results in a dramatic reduction in computational effort required for the determination of the residence time distributions. Additionally, we investigate the total stretch of material elements while they are in the vicinity of the vortex pair, using this quantity as a measure of the effect of the horseshoes on trajectories passing through this region. The numerical work verifies the analytical predictions regarding the structure of the invariant manifolds, the mechanism for entrainment and detrainment and the flux rate.

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Section: The Mixing Regionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An analytical study of transport, mixing and chaos in an unsteady vortical flow

1990

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“…In spite of the great number and variety of efforts as described by Foss & Wallace (1989), there are still many doubts as to the reliability of measurement methods of velocity fluctuation derivatives (e.g. Hussain 1986 ;Aref & Kambe 1988).…”

Section: Introductionmentioning

confidence: 99%

Experimental investigation of the field of velocity gradients in turbulent flows

1992

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We present results of experiments on a turbulent grid flow and a few results on measurements in the outer region of a boundary layer over a smooth plate. The air flow measurements included three velocity components and their nine gradients. This was done by a twelve-wire hot-wire probe (3 arrays × 4 wires), produced for this purpose using specially made equipment (micromanipulators and some other auxiliary special equipment), calibration unit and calibration procedure. The probe had no common prongs and the calibration procedure was based on constructing a calibration function for each combination of three wires in each array (total 12) as a three-dimensional Chebishev polynomial of fourth order. A variety of checks were made in order to estimate the reliability of the results.Among the results the most prominent are the experimental confirmation of the strong tendency for alignment between vorticity and the intermediate eigenvector of the rate-of-strain tensor, the positiveness of the total enstrophy-generating term ωiωjsij (sij = ½(∂ui/∂xj+∂uj/∂xi), ωi = εijk∂uj/∂xk) even for rather short records and the tendency for alignment in the strict sense between vorticity and the vortex stretching vector Wi = ωjsij. An emphasis is put on the necessity to measure invariant quantities, i.e. independent of the choice of the system of reference (e.g. sijsij and ωiωjsij) as the most appropriate to describe physical processes. From the methodological point of view the main result is that the multi-hot-wire technique can be successfully used for measurements of all the nine velocity derivatives in turbulent flows, at least at moderate Reynolds numbers.

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“…and vonex breakdown by Hall [112] and Leibovich [141]. A full discussion of the motion of few point vortices and vonex patches is given by Aref [9] and Aref and Kambe [13]. and more general perspectives by Aref[lO] and Zabusky [237].…”

Section: Outlinementioning

confidence: 99%

1. A Brief Overview of Vortex Methods

Sethian¹

1991

Vortex Methods and Vortex Motion

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Report on the IUTAM symposium: fundamental aspects of vortex motion

Cited by 13 publications

References 13 publications

An analytical study of transport, mixing and chaos in an unsteady vortical flow

An analytical study of transport, mixing and chaos in an unsteady vortical flow

Experimental investigation of the field of velocity gradients in turbulent flows

1. A Brief Overview of Vortex Methods

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