Vortex models based on similarity solutions of the two-dimensional diffusion equation

Satijn, MP Maurice; Buren, Van; Clercx, Hjh Herman; Heijst, van Gjf Gert-Jan

doi:10.1063/1.1804548

Cited by 8 publications

(12 citation statements)

References 23 publications

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“…Self-similar solutions are generally associated with the long-time behavior of dynamic processes [1] and found in nearly all disciplines, from astrophysics and fluid dynamics to condensed matter and optics [2][3][4][5][6][7]. In most dissipative systems, similarity solutions decay with a characteristic rate, indicating the asymptotic evolution of a given initial condition [6,8].…”

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confidence: 99%

Self-Similar Modes of Coherent Diffusion

et al. 2010

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Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical diffraction. In an experiment of light storage in a gas of diffusing atoms, a complex initial condition is imprinted, and its diffusion dynamics is monitored.The self-similarity of both the amplitude and the phase pattern is demonstrated, and an algebraic decay associated with the mode order is measured. Notably, as opposed to a regular diffusion spreading, a self-similar contraction of a special subset of the solutions is predicted and observed.Typeset by REVT E X 1

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confidence: 99%

Self-Similar Modes of Coherent Diffusion

et al. 2010

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“…Нарешті, заслуговує на увагу стат-тя М. Сатіжина та ін. [34], де увага зосереджена на моделях вихорів, побудованих на автомодель-них розв'язках.…”

Section: моделі генерації компактного турбулентного вихоруunclassified

Analytical Models Development of Compact Monopole Vortex Flows

Lukianov

Turick

2017

Research Bulletin of the National Technical University of Ukraine "Kyiv Politechnic Institute"

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Background. Mathematical description of vortex flows as a part of basic fundamental concepts of continuum mechanics, hydro-and gas dynamics, thermal physics, theoretical basics of chemical engineering, geophysics, meteorology. Objective. Replenishment of existing information in traditional scientific, technical and educational publications about vortices and their analytical models by new data for scientists, teachers, post-graduates and students with the purpose of using in further investigations of fluids and gas vortex motion. Methods. Analytical review of existing vortex current models, including monopole compact vortices, on a basis of the latest data from scientific articles and specialized monographs and their comparison with traditional data containing in the known textbooks and educational materials. Results. The lack of modern compact vortices models was revealed in traditional scientific, technical and educational literary sources. They include the compact analogs of the point vortex and Rankine vortex: quasi-point vortex and compact compensated vortex. On basis of these ones and similar to them solutions (circular vortex, vortex with triad constant vorticity zones) the models of compact helical flows and vortices with helical symmetry were elaborated. The solutions of such tasks were analyzed: diffusion of compact vortices (Taylor vortex, Kloosterziel solution), turbulent diffusion of compact vortex, solutions for quasi-compact (laminar and turbulent) vortex-source, vortex-sink and also solution of the problem about compact turbulent vortex generation by rotating cylinder. All considered models are consistent with the energy conservation law and have advantages in their use. Conclusions. The article contains series of the latest analytical models that describe both laminar and turbulent dynamics of monopole vortex flows which have not been reflected in traditional publications up to the present. The further research must be directed to search of analytical models for the coherent vortical structures in flows of viscous fluids, particularly near curved surfaces, where known in hydromechanics "wall law" is disturbed and heat and mass transfer anomalies take place.

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“…We introduce a class of functions which is well adapted to the application of the Galerkin method as well as to the representation of localized vorticity fields, as used by Kloosterziel 24 and followed by Satijn et al 25 We define the one-dimensional function h n of variable x and for some integer n by…”

Section: Appendix B: Symmetries Of the Pdes Modelmentioning

confidence: 99%

A comprehensible low-order model for wall turbulence dynamics

Lagha

2014

Physics of Fluids

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Streamwise vortices play an important role in the sustainment of wall turbulence. They are associated with regions with strong Reynolds shear stress production. In turbulent plane Couette flow at low Reynolds numbers, these streamwise vortices fill the whole gap between the plates. Using a low-order model obtained from the Navier-Stokes equations through a two-step Galerkin projection, the dynamics of these streamwise vortices is shown to be similar to the dynamics observed in the near-wall region of turbulent boundary layers [M. Lagha, J. Kim, J. D. Eldredge, and X. Zhong, "Near-wall dynamics of compressible boundary layer," Phys. Fluids 23, 065109 (2011)]. A spanwise vortex filling the whole gap between the plates and with vorticity opposite in sign to that of the base flow, is tilted in the streamwise direction by the spanwise shear of the streaks. The resultant vortex has a crescent shape and its legs are two streamwise vortices. They regenerate the streaks by the lift-up effect. Through its ability to generate periodic spatio-temporal flow patterns, this model is shown to provide an ideal tool for studying the different mechanisms at work. C 2014 AIP Publishing LLC. [http://dx.

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Vortex models based on similarity solutions of the two-dimensional diffusion equation

Cited by 8 publications

References 23 publications

Self-Similar Modes of Coherent Diffusion

Self-Similar Modes of Coherent Diffusion

Analytical Models Development of Compact Monopole Vortex Flows

A comprehensible low-order model for wall turbulence dynamics

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