Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Welander, Pierre

doi:10.3402/tellusa.v7i2.8797

Cited by 116 publications

(45 citation statements)

References 4 publications

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“…A good historical review is given by Pierrehumbert (1991a). Earliest examples of such studies are papers by Rossby et al (1937) and Welander (1955), in which deformation and mixing of a fluid element were discussed with serological data and experimental results, respectively. Both of the papers treat basic and important properties of the Lagrangian motion and are still worth referring to.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Lagrangian Motion and Heat Transport in a Steady, Baroclinic Annulus Wave

Sugata

Yoden

1994

Journal of the Meteorological Society of Japan

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Lagrangian motion in a steady, Baroclinic annulus wave is investigated numerically by following a tracer particle trajectory for a long period. Even for the regular Eulerian flow field of steady waves, the trajectory shows a chaotic nature, which is an example of "Lagrangian turbulence". However, the chaotic trajectory has some organized structures depending on its position in the annulus. Based on the structure, the annulus of fluid is divided into the following regions: the upper-level and lower-level jets, the cyclonically and anticyclonically trapped regions, and the inner, outer and lower boundary layers. Some isolated regions in which the marked particle has never stayed for that period are also found inside the cyclonically trapped region and around the anticyclonically trapped region. Statistics over the long period show a preferred cyclic route of the region transitions: the outer boundary layer-the upper-level jet -the inner boundary layer-the lower-level jet or the lower boundary layer-the outer boundary layer. The number of dwell periods of the particle in the trapped regions is much smaller than that in the cyclic route, but the average time of one stay in the trapped regions is longer.A Lagrangian view of the heat transport in the steady annulus wave is obtained: The fluid particle absorbs a large amount of heat in the outer boundary layer and releases it in the inner boundary layer, while it nearly conserves its temperature in the interior regions. Inward heat transport is small in every one cycle of the meander of the jets.

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Section: Introductionmentioning

confidence: 99%

Chaotic Lagrangian Motion and Heat Transport in a Steady, Baroclinic Annulus Wave

Sugata

Yoden

1994

Journal of the Meteorological Society of Japan

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“…This paper is notable also because of its discussion of the importance of coarse-grained averages. Figues 9,10 and 11 reproduced from Welander (1955) show that simple velocity fields produce spectacular distortion of passive scalars.…”

Section: A Welander Scrapbookmentioning

confidence: 99%

“…Thus, the displacement r produced by a single pulse is Xn+l -Xn = 7"* sincpn, and r = IXn+l -xnl. (15) The PDF of the random variable r can be obtained from the PDF of cP, that is P(cp) = Ij2-r, using the rule for transforming probabilties: P(r) = LP(cp)I~~I, == P(r) = 2 H(7"* -r) .…”

Section: The Averaged Green's Function Of the Rw Modelmentioning

confidence: 99%

“…As an example of this notation, the average velocity of the N particles is 1 N (u) == N L un(t). n=l (15) 4 A time series of Lagrangian velocity Because of the stationarity assumption, (u) is independent of time, and we can refer all displacements relative to the position of the center of mass by writing Xl = X -(u)t and u~ = Un -(u). To save decorating all our subsequent x's and u's with primes we now assume that (u) = O.…”

Section: This Procedures Introduces the Additional Assumptions That Thmentioning

confidence: 99%

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Stirring and Mixing: 1999 Program of Summer Study in Geophysical Fluid Dynamics

Balmforth¹,

Young²,

Fields³

et al. 2000

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“…For this type of flows many of these problems are overcome by using the mapping method. This versatile method, similar to the approach proposed by Welander 5 and Spencer and Wiley, 6 was first used for studying concentration distributions, Kruijt et al 7 and Galaktionov et al, 8 and recently extended to stretching distributions in mixing flows by Galaktionov et al,9 enabling the analysis of the dynamics of the microstructure and, for the first time, optimizing mixing procedures. The flow domain is divided into ͑a large number of͒ subdomains and for a given quantity ͑for example, concentration͒ the transport from one subdomain to others after a characteristic period of time is calculated.…”

Section: Introductionmentioning

confidence: 99%

Structure development during chaotic mixing in the journal bearing flow

2002

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Laminar mixing in the two-dimensional time-periodic Stokes flows between eccentric cylinders ͓journal bearing flow ͑JBF͔͒ is studied using the extended mapping method ͓Galaktionov et al., Int. J. Multiphase Flows 28, 497 ͑2002͔͒ with the emphasis on the material stretching, e.g., the interface generation abilities, of the flow. With this flexible and computational advantageous method both, the macroscopic material transport and the evolution of the microstructure can be described. It enables a convenient way for studying the material stretching in the flow and moreover, it provides spatial distribution of locally averaged stretching values instead of pointwise statistics, which was typical for previous studies ͓Liu et al., AIChE J. 40, 1273 ͑1994͒; Muzzio et al., Phys. Fluids A 3, 822 ͑1991͔͒. The results clearly indicate how the total amount of stretching generated by the flow depends on the parameters of the flow protocol, and that this is not just proportional to the work done on the system, as was suggested earlier in Muzzio et al., Phys. Fluids A 3, 822 ͑1991͒. It was found that when self-similar patterns are established, distinctive zones in the flow, which we call ''microstructural demixing zones,'' are observed, where interfaces are contracted during a typical period of the mixing process. Spatial nonuniformity of stretching in chaotic flows calls for additional mixing measures that reflect the nonuniformity of self-similar stretching patterns, created by time-periodic mixing flows.

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Studies on the General Development of Motion in a Two-Dimensional, Ideal Fluid

Cited by 116 publications

References 4 publications

Chaotic Lagrangian Motion and Heat Transport in a Steady, Baroclinic Annulus Wave

Chaotic Lagrangian Motion and Heat Transport in a Steady, Baroclinic Annulus Wave

Stirring and Mixing: 1999 Program of Summer Study in Geophysical Fluid Dynamics

Structure development during chaotic mixing in the journal bearing flow

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