Astronomy and Astrophysics – Astrophysics
Scientific paper
Nov 1972
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972ap%26ss..19..189l&link_type=abstract
Astrophysics and Space Science, Volume 19, Issue 1, pp.189-193
Astronomy and Astrophysics
Astrophysics
1
Scientific paper
In the theory of homogeneous, stationary, axisymmetric, incompressible velocity turbulence there arise four scalar functions. The incompressibility condition provides two relations between these four functions. We will demonstrate here that application of Cramér's theorem imposes two additional constraints on the four functions. These constraints do not uniquely define the allowed functional form but they do provide very powerful criteria for limiting the class of functions which are permitted. In view of the growing use of velocity turbulence in kinematic dynamo theory and its importance in astrophysical situations (e.g., Earth, Sun, Galaxy) to maintain or regenerate a large scale magnetic field, we believe that the present constraints are of more than academic interest. In particular, application of the constraints to a form of velocity turbulence used by Steenbeck, Krause and Rädler when computing kinematic dynamo action, shows that their assumed turbulence is not physically realizable in nature.
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