Statistics – Computation
Scientific paper
Apr 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...425..303c&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 425, no. 1, p. 303-325
Statistics
Computation
45
Boussinesq Approximation, Computational Astrophysics, Differential Equations, Mathematical Models, Reynolds Stress, Solar Convection (Astronomy), Stellar Rotation, Turbulent Flow, Anisotropy, Hydrodynamics, Kinetic Energy, Nonlinearity, Numerical Analysis
Scientific paper
In most hydrodynamic cases, the existence of a turbulent flow superimposed on a mean flow is caused by a shear instability in the latter. Boussinesq suggested the first model for the turbulent Reynolds stresses bar-(uiuj) in which the mean shear Sij is the cause (or source) of turbulence represented by the stress bar-(uiuj). In the case of solar differential rotation, exactly the reverse physical process occurs: turbulence (which must pre-exist) generates a mean flow which manifests itself in the form of differential rotation. Thus, the Boussinesq model is wholly inadequate because in the solar case, cause and effect are reversed. Since the Boussinesq model is inadequate, one needs an alternative model for the Reynolds stresses. We present a new dynamical model for the Reynolds stresses, convective fluxes, turbulent kinetic energy, and temperature fluctuations. The complete model requires the solution of 11 differential equations. We then introduce a set of simplifying assumptions which reduce the full dynamical model to a set of algebraic Reynolds stress models. We explicitly solve one of these models that entails only one differential equation. The overall agreement with the data is obtained with a model that is neither phenomenological nor one that requires a full numerical simulation, since it is algebraic in nature. The new model can play an important role in understanding the complex physics underlying the interplay between solar differential rotation and convection, as many physical processes can naturally be incorporated into the model.
Canuto Vittorio M.
Minotti Fernando O.
Schilling O.
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