EDP Sciences
Free access
Volume 422, Number 3, August II 2004
Page(s) 793 - 816
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:20035874

A&A 422, 793-816 (2004)
DOI: 10.1051/0004-6361:20035874

Local models of stellar convection:

Reynolds stresses and turbulent heat transport
P. J. Käpylä1, 2, M. J. Korpi1, 3 and I. Tuominen1

1  Astronomy Division, Department of Physical Sciences, University of Oulu, PO Box 3000, 90014 University of Oulu, Finland
    e-mail: petri.kapyla@oulu.fi
2  Kiepenheuer-Institut für Sonnenphysik, Schöneckstrasse 6, 79104 Freiburg, Germany
3  Laboratoire d'Astrophysique, Observatoire Midi-Pyr $\acute{\rm e}$n $\acute{\rm e}$es, 14 Av. E. Belin, 31400 Toulouse, France

(Received 16 December 2003 / Accepted 14 March 2004 )

We study stellar convection using a local three-dimensional MHD model, with which we investigate the influence of rotation and large-scale magnetic fields on the turbulent momentum and heat transport and their role in generating large-scale flows in stellar convection zones. The former is studied by computing the turbulent velocity correlations, known as Reynolds stresses, the latter by calculating the correlation of velocity and temperature fluctuations, both as functions of rotation and latitude. We find that the horizontal correlation, $Q_{\theta \phi}$, capable of generating horizontal differential rotation, attains significant values and is mostly negative in the southern hemisphere for Coriolis numbers exceeding unity, corresponding to equatorward flux of angular momentum. This result is also in accordance with solar observations. The radial component  $Q_{r \phi}$ is negative for slow and intermediate rotation indicating inward transport of angular momentum, while for rapid rotation, the transport occurs outwards. Parametrisation in terms of the mean-field $\Lambda$-effect shows qualitative agreement with the turbulence model of Kichatinov & Rüdiger (1993) for the horizontal part $H \propto \frac{Q_{\theta \phi}}{\cos \theta}$, whereas for the vertical $\Lambda$-effect, $V \propto \frac{Q_{r \phi}}{\sin \theta}$, agreement only for intermediate rotation exists. The $\Lambda$-coefficients become suppressed in the limit of rapid rotation, this rotational quenching being stronger and occurring with slower rotation for the V component than for  H. We have also studied the behaviour of the Reynolds stresses under the influence of a large-scale azimuthal magnetic field of varying strength. We find that the stresses are enhanced by the presence of the magnetic field for field strengths up to and above the equipartition value, without significant quenching. Concerning the turbulent heat transport, our calculations show that the transport in the radial direction is most efficient at the equatorial regions, obtains a minimum at midlatitudes, and shows a slight increase towards the poles. The latitudinal heat transport does not show a systematic trend as a function of latitude or rotation.

Key words: convection -- hydrodynamics -- Sun: rotation

© ESO 2004