Computer Science
Scientific paper
Jun 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980pnas...77.3075p&link_type=abstract
Proceedings of the National Academy of Sciences of the United States of America, Volume 77, Issue 6, pp. 3075-3079
Computer Science
Scientific paper
It is shown that, in addition to the static Emden solution, a self-gravitating polytropic gas has a dynamic option in which there is stationary flow along spiral trajectories wound around the surfaces of concentric tori. The motion is obtained as a solution of a partial differential equation which is satisfied by the meridional stream function, coupled with Poisson's equation and a Bernoulli-type equation for the pressure (density). The pressure is affected by the whole of the Bernoulli term rather than by the centrifugal part only, which acts for a rotating model, and it may be reduced down to zero at the center. The spiral type of flow is illustrated for an incompressible fluid (n = 0), for which an exact solution is obtained. The features of the dynamic constant-density model are discussed as a basis for future comparison with the solution for compressible models.
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