Nonlocality in Turbulence

Tsinober, A.

doi:10.1007/978-94-017-0347-5_2

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…We remark that the viscous layer is usually defined as the region y + < 5 y + 0 . A condition for the annihilation of coherent structures produced by shear instabilities in the viscous layer -the seeds of bulk turbulence -can be put forward, therefore, as M (y + 0 ) > C, for some critical parameter C. This implies, due to the properties of (19), that M (y + ) > C for any y + , which indicates the damping action of the magnetic field over the boundary layer as a whole. We are led, then, to the conjecture that turbulence is suppressed if Using the standard definition of the friction factor f in terms of u τ and U [45],…”

Section: IImentioning

confidence: 99%

“…The original discussions presented in the seminal papers [5,[15][16][17] have proposed that M/Re should work as a controlling parameter for the laminar-turbulent transition -an educated guess that still percolates in much of the recent literature. However, broadly acknowledged and careful pipe flow experiments performed by Gardner and Lykoudis [18] almost fifty years ago, established that critical values of M/Re actually depend on the Reynolds numbers at the laminar-turbulent transition point, a fact emphasized by Tsinober [19] and further discussed by Branover [20], who proposed that a more accurate transition criterion would be given by M/Re α , where the exponent α is slightly smaller than unity. Narasimha pointed out, subsequently, that relaminarization could be related to flow regimes where magnetic forces dominate Reynolds stress gradients [21], an observation that is closely related to the arguments we address in this paper.…”

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Magnetic dissipation of near-wall turbulent coherent structures in magnetohydrodynamic pipe flows

Moriconi

2020

Phys. Rev. E

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Relaminarization of wall-bounded turbulent flows by means of external static magnetic fields is a long-known phenomenon in the physics of electrically conducting fluids at low magnetic Reynolds numbers. Despite the large literature on the subject, it is not yet completely clear what combination of the Hartmann (M ) and the Reynolds number has to be used to predict the laminar-turbulent transition in channel or pipe flows fed by upstream turbulent flows free of magnetic perturbations. Relying upon standard phenomenological approaches related to mixing length and structural concepts, we put forward that M/Rτ , where Rτ is the friction Reynolds number, is the appropriate controlling parameter for relaminarization, a proposal which finds good support from available experimental data.

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Section: IImentioning

confidence: 99%

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Magnetic dissipation of near-wall turbulent coherent structures in magnetohydrodynamic pipe flows

Moriconi

2020

Phys. Rev. E

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Local versus Nonlocal Processes in Turbulent Flows, Kinematic Coupling and General Stochastic Processes

Kholmyansky

Sabelnikov

Tsinober

2010

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Kolmogorov 4∕5 law, nonlocality, and sweeping decorrelation hypothesis

Kholmyansky

Tsinober

2008

Physics of Fluids

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We report results of experiments at large Reynolds numbers, confirming the equivalent form of the Kolmogorov 4 / 5 law obtained recently by Hosokawa ͓Prog. Theor. Phys. 118, 169 ͑2007͔͒. This, as well as purely kinematic exact relations, demonstrates one of the important aspects of nonlocality of turbulent flows in the inertial range and stands in contradiction with the sweeping decorrelation hypothesis understood as statistical independence between large and small scales. This letter is provoked by a short paper by Hosokawa 1 concerned mainly with the issues of refined similarity hypothesis. A starting point in his paper is that it is proven that the famous third-order structure function of the velocity in homogeneous isotropic turbulence derived by Kolmogorov implies the statistical interdependence of the difference and sum of the velocities at two points separated by a distance r. 1 In other words, contrary to frequent claims on locality of interactions and similar things, the 4 / 5 law points to an important aspect of nonlocality of turbulent flows understood as direct and bidirectional interaction of large and small scales. 2,3 Before proceeding, we quote the key relations obtained by Hosokawa.The first relation, the most important and equivalent ͑un-der the same assumptions of global isotropy͒ to the 4 / 5 law, reads ͗u + 2 u − ͘ = ͗⑀͘r/30. ͑1͒Here 2u + = u 1 ͑x + r͒ + u 1 ͑x͒, 2u − = u 1 ͑x + r͒ − u 1 ͑x͒; u 1 ͑x͒ is the longitudinal velocity component ͑in our case it will be just the streamwise velocity component͒ and ͗⑀͘ is the mean dissipation. It is noteworthy that though Eq. ͑1͒ contains velocity and not just its increments, it is readily checked that it is still Galilean invariant. We would like to emphasize that the relation ͑1͒-though formally equivalent to the Kolmogorov 4 / 5 law-has an important advantage from purely experimental point of view. Namely, it is linear in velocity increment u − , whereas the 4 / 5 law is cubic in u − . Therefore, the precision requirements for the verification of the relation ͑1͒ are far less stringent than those for the 4 / 5 law. We will return to this point below.The relation ͑1͒ is a consequence of the 4 / 5 law and a purely kinematic relation which is valid under isotropy assumptionwhich is a clear indication of the absence of statistical independence between u + and u − , i.e., between small and large scales.A similar purely kinematic relation is valid for secondorder quantities, 1Thus this is also-as stated by Hosokawa 1 -an elementary signature indicating the necessary statistical relationship between u + and u − , i.e., reflecting the nonlocality even at the level of second-order quantities. One more kinematic relation of third order was obtained by Sabelnikov in 1994,along with another set of kinematic relations involving a one-point quantity u 1 ͑x͒ ͓or u 1 ͑x + r͔͒ instead of u + , which is a two-point quantity. 5 The main purpose of this note is to present direct experimental evidence for the validity of the above relations ͑1͒-͑4͒ at very large Rey...

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Nonlocality in Turbulence

Cited by 3 publications

References 27 publications

Magnetic dissipation of near-wall turbulent coherent structures in magnetohydrodynamic pipe flows

Magnetic dissipation of near-wall turbulent coherent structures in magnetohydrodynamic pipe flows

Local versus Nonlocal Processes in Turbulent Flows, Kinematic Coupling and General Stochastic Processes

Kolmogorov 4∕5 law, nonlocality, and sweeping decorrelation hypothesis

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