The onset and spatial development of turbulence in flow systems

Aranson, Igor S.; Gaponov-Grekhov, Andrei V.; Rabinovich, M. I.

doi:10.1016/s0167-2789(98)90004-5

Cited by 41 publications

(13 citation statements)

References 11 publications

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“…В этой ситуации и представляется естественным использование размерности ν(x) (или функции размерно-сти ν(x,ε); см. [87]) в качестве одной из характеристик, описывающих пространственное развитие течения. Она не является универсальной в том смысле, что характеризует данное конкретное течение и становится универсальной для однотипных течений, преобладающим фактором в развитии которых являются абсолютные неустойчивости.…”

Section: размерность пот окаunclassified

“…Поэтому ис-следования скейлинговых свойств переходов в пространстве пока огра-ничены лишь теми моделями, которые в однородном приближении де-монстрируют те же свойства критического поведения, что и маломер-ные динамические системы. В частности, для двух типов критического поведения проведено ренормгрупповое описание пространственного раз-вития турбулентности в потоковых системах и построена теория пере-хода через перемежаемость в пространственно-однородных изотропных ансамблях структур [87,159].…”

Section: зарождениеunclassified

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The regular and chaotic dynamics of structures in fluid flows

Rabinovich¹,

Sushchik²

1990

Usp. Fiz. Nauk

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Section: размерность пот окаunclassified

Section: зарождениеunclassified

The regular and chaotic dynamics of structures in fluid flows

Rabinovich¹,

Sushchik²

1990

Usp. Fiz. Nauk

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“…Recently, efforts have been made to generalize the scaling results of period doubling for the 1D map to coupled 1D maps [5][6][7][8][9][10][11], which are used to simulate spatially extended systems with effectively many degrees of freedom [12]. It has been found that the critical scaling behaviors of period doubling for the coupled 1D maps are much richer than those for the uncoupled 1D map [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Intermittency in coupled maps

Kim

1999

Phys. Rev. E

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Using a renormalization method, we study the critical behavior for intermittency in two coupled one-dimensional (1D) maps. We find two fixed maps of the renormalization transformation. They all have common relevant eigenvalues associated with scaling of the control parameter of the uncoupled 1D map. However, the relevant "coupling eigenvalues" associated with coupling perturbations vary depending on the fixed maps. It is also found that the two fixed maps are associated with the critical behavior in the vicinity of a critical line segment. One fixed map with no relevant coupling eigenvalues governs the critical behavior at interior points of the critical line segment, while the other one with relevant coupling eigenvalues governs the critical behavior at both ends. The results of the two coupled 1D maps are also extended to many globally-coupled 1D maps, in which each 1D map is coupled to all the other ones with equal strength.

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“…On the problem of transition in the pipes there is a certain contradiction between the works ofAranson et al [2] and Huang and Huang [36], where a relatively small attractor dimension was obtained, and that of Sreenivasan and Ramshankar [60], where transition seemed to occur in a sudden shift to turbulence of high dimension. In boundary layers, interest lies above all in the instability mechanisms and the receptivity of the flow to outside disturbances: the initial results of an interesting study by Gaster [26] suggest that the transition to turbulence occurs by means of a nonlinear increase in the disturbances with low-dimension characteristics (see also [41 ]).…”

Section: Chaos and Near-wan Turbulencementioning

confidence: 96%

Nonlinear analysis of near-wall turbulence time series

Porporato

Ridolfi

1996

Appl. Sci. Res.

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Abstract. We present the results of the nonlinear analysis of a near-wall turbulence signal, measured using a Laser Doppler Anemometer. Despite being preliminary in part, the results highlight some interesting aspects of the dynamics of coherent structures. Careful reconstruction of the dynamics from the scalar time series highlight particular phases of the bursting cycle, corresponding to the VITA detections, immersed in the overall high-dimension dynamics: the possibility to distinguish these trajectories in the embedding space provides indications for conditional sampling techniques on the reconstructed attractor. The application of nonlinear prediction to a system of high-dimension produces forecasts of rapidly decreasing quality over time, with no consequences for practical applications. Much more interesting instead is the analysis of the forecast errors for very short forecast intervals, where we observed a greater difficulty to predict the beginning of coherent structure instability probably due to the quasi-random forcing of the outer flow.

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The onset and spatial development of turbulence in flow systems

Cited by 41 publications

References 11 publications

The regular and chaotic dynamics of structures in fluid flows

The regular and chaotic dynamics of structures in fluid flows

Intermittency in coupled maps

Nonlinear analysis of near-wall turbulence time series

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