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Publication Abstracts

Canuto 1992

Canuto, V.M., 1992: Turbulent convection with overshooting: Reynolds stress approach. Astrophys. J., 392, 218-232, doi:10.1086/171420.

Turbulent convection is a phenomenon relevant to both stellar structure and accretion disks. In the latter, a basic parameter such as the turbulent velocity nut is still treated phenomenologically; in the case of stellar structure, most of the work still relies on the mixing length theory (MLT) which assumes homogeneity and thus lacks diffusion terms (divergence of third-order moments like ave(w²*θ), ave(w*θ²)m ave(q²*w)). To include them, one needs a new formalism. We review and discuss the Reynolds stress approach (proven successful in other fields) which provides a set of coupled differential equations that yield all the turbulent quantities of interest. Although the system can only be solved numerically, some features can be listed:

1. The convective flux F_c = c_p*ρ*ave(w*θ) is not given simply by (κ_t is the turbulent velocity)

F_c = F_cMLT ≃ κ_t(∇-∇_ad).

2. Inclusion of the diffusion terms related to ave(w²*θ) and ave(w*θ²) contributes a countergradient term Γ_c, which may carry heat from cold to hot regions,

F_c ≃ κ_t(∇-∇_ad+Γ_c).

3. Inclusion of the diffusion term related to 0.5*ave(q²*w) (turbulent kinetic energy flux) contributes an additional term (first discussed in atmospheric turbulence by Tennekes)

F_c ≃ κ_t(∇-∇_ad+Γ_c)+F_cdiff,

which is responsible for overshooting.

In addition to the convective flux, we also derive a model expression for nut as a function of both shear and buoyancy: it is needed in the numerical simulation of stellar convection and in accretion disks to replace the phenomenological expressions used thus far.

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@article{ca06800b,
  author={Canuto, V. M.},
  title={Turbulent convection with overshooting: Reynolds stress approach},
  year={1992},
  journal={Astrophysical Journal},
  volume={392},
  pages={218--232},
  doi={10.1086/171420},
}

TY  - JOUR
ID  - ca06800b
AU  - Canuto, V. M.
PY  - 1992
TI  - Turbulent convection with overshooting: Reynolds stress approach
JA  - Astrophys. J.
JO  - Astrophysical Journal
VL  - 392
SP  - 218
EP  - 232
DO  - 10.1086/171420
ER  -

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