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A Formalism for Differential Rotation

Published online by Cambridge University Press:  30 March 2016

B. R. Durney  and
H. C. Spruit
B. R. Durney
Affiliation:
Sacramento Peak Observatory, Sunspot, New Mexico
H. C. Spruit
Affiliation:
High Altitude Observatory, Boulder, Colorado

Extract

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One of the approaches for dealing with the differential rotation of the Sun is to separate the flow in the convection zone into an axisymmetric steady part (differential rotation plus meridional circulation) and a “turbulent” part comprising all smaller scales of motion. In the equations of motion and energy the effect of the small scales is then represented by a turbulent viscosity and conductivity. Theories of this type at present belong to either of two categories:

  1. a) Theories stressing the role of an anisotropic turbulent viscosity. Due to the presence of gravity as a preferred direction the velocity distribution in the turbulent flow is different in the horizontal and vertical directions. This implies that the turbulent viscosity is also anisotropic. Biermann (1951) showed that as a result, the convection zone cannot rotate as a solid body. Theories based on this idea were developed by Kippenhahn (1963) and Köhler (1970).

  2. b) Theories using a latitude dependence of the efficiency of turbulent transport of heat. In the deeper layers of the convection zone the influence of rotation on convection is strong because the convective turnover time is comparable to the rotation period. Since the angle between gravity and the rotation axis varies with latitude, this influence must also vary with latitude. This produces a temperature variation between the pole and the equator which drives a meridional circulation. Since the Coriolis force dominates over the viscous force in most of the convection zone, there is a strong differential rotation associated with this circulation (quasi geostrophic flow). This type of theory has been developed by Weiss (1965), Durney and Roxburgh (1971) and Belvedere and Paterno (1977).

Type
Joint Discussion
Information
Highlights of Astronomy , Volume 5: Highlights of Astronomy. As presented at the XVIIth General Assembly of the IAU, 1979 , 1980 , pp. 121 - 127
Copyright
Copyright © Cambridge University Press 1980

References

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