Publication Abstracts

Canuto 1996

Canuto, V.M., 1996: Turbulent convection: Old and new models. Astrophys. J., 467, 385-396, doi:10.1086/177613.

This paper contains (1) a physical argument to show that the one-eddy MLT model underestimates the convective flux Fc in the high-efficiency regime, while it overestimates Fc in the low-efficiency regime, and (2) a new derivation of the Fc(MLT) using a turbulence model in the one-eddy approximation. (3) We forsake the one-eddy approximation and adopt the Kolmogorov spectrum to represent the turbulent energy spectrum. The resulting Fc > Fc(MLT) in the high-efficiency regime, and Fc < Fc(MLT) in the low-efficiency case, are in agreement with the physical arguments concerning the one-eddy MLT model. (4) By forsaking the Kolmogorov model and solving a two-point closure model, one obtains the CM model. The Fc(CM) corresponds to a "tilt" in efficiency space of Fc(MLT), an effect that cannot be achieved by changing α. We discuss the astrophysical tests of the CM model.

(5) Concerning the laboratory turbulent convection, we show that the CM model provides a better fit than the MLT to recent high Rayleigh number (Ra) laboratory data on convection. (6) Concerning non-local convection, the most complete model available is the one-point closure model (Reynolds stress model), which entails five differential equations for the five second-order moments. We present the solution corresponding to the local, stationary case. The results are expressed analytically in terms of Ko (Kolmogorov constant), Pe (Peclet number), and S (convective efficiency).

(6) We find that the superadiabatic temperature is given by -dT/dr - gr/cp where the renormalized gr = g(1 + g-1ρ-1dPt/dz) and Pt is the turbulent pressure. This result, which follows naturally from the Reynolds stress approach, contrasts with previous empirical suggestions to include Pt. (8) We derive new expressions for the turbulence pressure using two different turbulence models and (9) we show that the often used Kolmogorov-Prandtl expression for the turbulent diffusivity is valid only in the high convective efficiency limit. We derive a new expression valid for arbitrary Peclet numbers. (10) We derive an expression for the flux conservation law, which includes F(KE), the flux of turbulent kinetic energy, a third-order moment for which we provide a news expression. (11) No model has thus far accounted for the influence on Fc due to the presence of a stable layer (radiative layer) bordering the convective zone. We work out the first such model, and (12) we discuss topics for future research.

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BibTeX Citation

@article{ca04900a,
  author={Canuto, V. M.},
  title={Turbulent convection: Old and new models},
  year={1996},
  journal={Astrophys. J.},
  volume={467},
  pages={385--396},
  doi={10.1086/177613},
}

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RIS Citation

TY  - JOUR
ID  - ca04900a
AU  - Canuto, V. M.
PY  - 1996
TI  - Turbulent convection: Old and new models
JA  - Astrophys. J.
VL  - 467
SP  - 385
EP  - 396
DO  - 10.1086/177613
ER  -

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