Publication Abstracts

Canuto 1989

Canuto, V.M., 1989: AMLT: Anisotropic mixing length theory. Astron. Astrophys., 217, 333-343.

The standard MLT assumed a) that the largest eddies are the only ones that contribute to convection and b) that they are isotropic. These two requirements are internally inconsistent since it is experimentally known that only small eddies are isotropic, while large eddies exhibit large degrees of anisotropy. In this paper we present a new model: anisotropic mixing length theory, AMLT, together with a model that relates the anisotropy to other quantities of the problem. The new AMLT equations are solved for two cases of interest in stellar structure calculations.

In the first case, the gradients ∇r and ∇ad are considered known, and the resulting expression for ∇ and ∇ derived. The basic AMLT relations are given in two equivalent representations: Eqs. (49)-(52) and/or Eqs. (53)-(54). It is shown that: 1) The value of ∇ - ∇ad from the AMLT is up to two orders of magnitude larger than the corresponding MLT value, Eq. (60). 2) In the physically important case of large degrees of anisotropy, the turbulent velocity in the AMLT is lower than the corresponding MLT value by a factor of 2, Eq. (67). This may help lessen the problem of overshooting.

In the second case, the gradients ∇ and ∇ad, are considered known and the resulting expressions for ∇r and ∇' are derived, together with the expressions for the convective flux and the turbulent velocity, Eqs. (71), (73), (74) and (75). For the case of large anisotropies, the AMLT can be solved analytically, Eqs. (79)-(83). The convective flux, the convective velocities, the temperature excess, and the radiative gradient, are smaller than the MLT relations by the factors x-1, x-1/2, x-1/2, and x-1, respectively, where x ≫ 1 is given in terms of known variables via Eq. (79).

The present formalism is valid only in the optically thick case.

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BibTeX Citation

@article{ca04810k,
  author={Canuto, V. M.},
  title={AMLT: Anisotropic mixing length theory},
  year={1989},
  journal={Astron. Astrophys.},
  volume={217},
  pages={333--343},
}

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RIS Citation

TY  - JOUR
ID  - ca04810k
AU  - Canuto, V. M.
PY  - 1989
TI  - AMLT: Anisotropic mixing length theory
JA  - Astron. Astrophys.
VL  - 217
SP  - 333
EP  - 343
ER  -

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