Potentialtheoretische Behandlung des Wehneltzylinders

Wendt, Georg

doi:10.1002/andp.19334090408

Cited by 6 publications

(6 citation statements)

References 3 publications

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“…On the other hand, due to the extremely low molecular viscosity in astrophysical disks Reynolds number can reach the value of Re ∼ 10 10 . In addition subcritical turbulence observed in flows of cyclonic type (about cyclonic and anticyclonic flows see, for example, Lesur and Longaretti (2005)) at the high but finite Reynolds numbers (see Taylor (1936), Wendt (1933)). Moreover, the negative results obtained in numerical simulations, can be explained by insufficient numerical resolution (see Longaretti (2002)).…”

Section: Discussionmentioning

confidence: 99%

Transient dynamics of large scale vortices in Keplerian disk

Razdoburdin

2016

Preprint

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The mechanism of transition from laminar state to turbulent state in Keplerian disks is still unknown. The most popular version today is generation of turbulence due to magnetorotational instability (MRI). However magnetohydrodynamic simulations give the value of Shakura-Sunyaev parameter more then an order of magnitude smaller rather than that found from observations. One way to solve this problem is the existence of an alternative or additional mechanism for generating turbulence. It can be the bypass mechanism, which is responsible for transition to turbulence in Couette and Poiseuille flows. This mechanism is based on the transient growth of linear perturbations in the flow with the subsequent transition to the nonlinear stage.In order to clarify the role of this mechanism in astrophysical disks first of all it is necessary to calculate the maximal possible growth factor of linear perturbations in the flow. In this paper the results of such calculations are presented for perturbations on different scales compared with the disk thickness. Qualitative description of mechanisms responsible for the growth will also be presented. It was found that the most rapidly growing shear harmonics have azimuthal wavelength of the order of the disk thickness. In addition, their initial form is always similar to the vortex perturbations with the same potential vorticity. It was shown that the vortices with azimuthal wavelength more than an order of magnitude in excess of the disc thickness, are still able to grow by dozens of times.

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Section: Discussionmentioning

confidence: 99%

Transient dynamics of large scale vortices in Keplerian disk

Razdoburdin

2016

Preprint

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“…On the other hand, in a cyclonic flow the subcritical turbulence is observed at finite, although large values Re T , see papers [30], [31] on experiments with spectrally stable Taylor-Couette flow, as well as their analysis in astrophysical context in Zel'dovich's paper [32] and later in paper [33]. In addition, negative results obtained in numerical experiments mentioned above can be explained by insufficient numerical resolution, as discussed in paper [34].…”

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confidence: 90%

“…Expression (42) shows that SFH initially taken as a leading spiral with k x < 0 increases in amplitude until the time (31), and at the swing moment, wheñ k x = 0, reaches maximum in the norm and then decays. The energy transfer from the background flow to perturbations is described in detail in terms of fluid particles in [107] (see Fig.…”

Section: Vortex Amplification Factormentioning

confidence: 99%

Transient dynamics of perturbations in astrophysical disks

Razdoburdin

Zhuravlev

2015

Phys.-Usp.

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This paper reviews some aspects of one of the major unsolved problems in understanding astrophysical (in particular, accretion) disks: whether the disk interiors may be effectively viscous in spite of the absence of marnetorotational instability? In this case a rotational homogeneous inviscid flow with a Keplerian angular velocity profile is spectrally stable, making the transient growth of perturbations a candidate mechanism for energy transfer from the regular motion to perturbations. Transient perturbations differ qualitatively from perturbation modes and can grow substantially in shear flows due to the nonnormality of their dynamical evolution operator. Since the eigenvectors of this operator, alias perturbation modes, are mutually nonorthogonal, they can mutually interfere, resulting in the transient growth of their linear combinations. Physically, a growing transient perturbation is a leading spiral whose branches are shrunk as a result of the differential rotation of the flow. This paper discusses in detail the transient growth of vortex shear harmonics in the spatially local limit as well as methods for identifying the optimal (fastest growth) perturbations. Special attention is given to obtaining such solutions variationally, by integrating the direct and adjoint equations forward and backward in time, respectively. The material is presented in a newcomer-friendly style. *

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“…which is the result obtained in [56] (see also formula 4 in [61]). Expression (42) shows that SFH initially taken as a leading spiral with k x < 0 increases in amplitude until the time (31), and at the swing moment, wheñ k x = 0, reaches maximum in the norm and then decays. The energy transfer from the background flow to perturbations is described in detail in terms of fluid particles in [107] (see Fig.…”

Section: Vortex Amplification Factormentioning

confidence: 99%

“…Here we assume the quasi-Keplerian flow to be the so-called anticyclonic flow (see, for example, the definition in [29]), where the specific angular momentum increases, while the angular velocity itself, in contrast, decreases towards the periphery. 1 On the other hand, in a cyclonic flow the subcritical turbulence is observed at finite, although large values Re T , see papers [30], [31] on experiments with spectrally stable Taylor-Couette flow, as well as their analysis in astrophysical context in Zel'dovich's paper [32] and later in paper [33]. In addition, negative results obtained in numerical experiments mentioned above can be explained by insufficient numerical resolution, as discussed in paper [34].…”

Section: Introductionmentioning

confidence: 99%

Transient dynamics of perturbations in astrophysical disks

Razdoburdin¹,

Zhuravlev²

2015

Usp. Fiz. Nauk

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Potentialtheoretische Behandlung des Wehneltzylinders

Cited by 6 publications

References 3 publications

Transient dynamics of large scale vortices in Keplerian disk

Transient dynamics of large scale vortices in Keplerian disk

Transient dynamics of perturbations in astrophysical disks

Transient dynamics of perturbations in astrophysical disks

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