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On the effects of viscosity in one-fluid solar wind theory

In order to examine the influence of small viscous effects on the in viscid solutions of Parker, Whang & Chang, and Durney the ideal, steady, one-fluid solar wind equations are examined in the limit: Reynolds number → ∞, Prandtl number → 0 (i. e. viscosity → 0, thermal conduction fixed). The method of matched asymptotic expansions is employed, and it is found that the inclusion of viscosity has considerable effect on the solutions far from the Sun. Small viscous terms cause the velocity to drop below the supersonic value of the Parker solution to subsonic values through a diffuse shock, the temperature still following the variation ∝ r-2/7 at large distances r. The result of small viscous effects on the Whang & Chang solution is that the temperature changes from a variation ∝ r-2/5 to follow the r-2/3 law of Whang, Liu & Chang, the velocity remaining supersonic, as r → ∞. The Durney solution is found to be the leading order part of a solution that is uniformly valid as r → ∞ in the limit considered.