Publication Abstracts

Canuto et al. 1988

Canuto, V.M., I. Goldman, and J. Chasnov, 1988: Turbulent viscosity. Astron. Astrophys., 200, 291-300.

A key quantity needed to model the physics of accretion disks is the turbulent viscosity nuT. Most disks calculations have thus far used an expression for nuT that contains an unknown, quantity, the Shakura-Sunyaev α-parameter. This precludes the possibility of making theoretical predictions. Astrophysical data are often used to fix α, which should be calculated by a model of turbulence.

A successful model to treat fully developed turbulence (the Direct Interaxtion Approximation, DIA) was derived from first principles by Kraichnan in the early 60's and yet it has not been used in astrophyical problems like accretion disks or turbulent convection in stars.

This paradoxical situation may perhaps be explained by the fact that the DIA equations are rather more complex in structure and time consuming to solve, a difficulty which becomes all the more serious when turbulence is just one component of a larger problem.

To bridge the gap between the fully predictive but hard to use DIA and the phenomenological, easy to use, but non-predictive α-model, we propose a model for fully developed turbulence whose predictions compare favorably with those of the DIA and whose main equations are easy to handle.

Using this model, we derive four different expressions for nuT, Eqs. (50) and (56). The four expressions contain no free parameters. Two of the expressions are given in terms of properties of the turbulent fluid itself; the other two are given in terms of the instability that generated the turbulence and of the properties of the mean flow (shear). The numerical coefficients entering these relations are evaluated and found to be in good agreement with previous theoretical estimates based on a) Kraichnan's DIA, b) the Renormalization Group Method, and c) Turbulence Modeling. In the case of shear in the mean flow, we show that α < 10-2.

The four expressions can be generalized to include the effect of rotation and/or magnetic fields.

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BibTeX Citation

  author={Canuto, V. M. and Goldman, I. and Chasnov, J.},
  title={Turbulent viscosity},
  journal={Astronomy and Astrophysics},

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RIS Citation

ID  - ca03000u
AU  - Canuto, V. M.
AU  - Goldman, I.
AU  - Chasnov, J.
PY  - 1988
TI  - Turbulent viscosity
JA  - Astron. Astrophys.
JO  - Astronomy and Astrophysics
VL  - 200
SP  - 291
EP  - 300
ER  -

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