Publication Abstracts
Canuto 1992
, 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 Fc = cp*ρ*ave(w*θ) is not given simply by (κt is the turbulent velocity)
Fc = FcMLT ≃ κt(∇-∇ad).
2. Inclusion of the diffusion terms related to ave(w2*θ) and ave(w*θ2) contributes a countergradient term Γc, which may carry heat from cold to hot regions,
Fc ≃ κt(∇-∇ad+Γc).
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)
Fc ≃ κt(∇-∇ad+Γc)+Fcdiff,
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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BibTeX Citation
@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}, }
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RIS Citation
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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