On the Continuum Theory of the OneFluid Solar Wind for Small Prandtl Number
Abstract
The continuum theory for a singlespecies gas expanding into a vacuum (or near vacuum) is considered. The gas is assumed compressible, viscous and heat conducting with a constant Prandtl number and viscosity proportional to (temperature)^{ω},ω >1. The gas is under the influence of a gravitational field centred on the Sun. For small Prandtl number (which is realistic for the onefluid solar wind), the method of matched asymptotic expansions is used to construct a solution describing the complete flow field from the surface of the Sun to infinity. The first two regions correspond to those found by Roberts & Soward (1972) for large thermal conductivity; the next involves the viscous terms, and in the fourth the viscous terms dominate. It is shown from the fourth region that either the flow remains supersonic but terminates at a finite point, or the flow becomes subsonic through a diffuse shock layer and approaches a nonzero pressure at infinity. It is seen that the existence of a critical point (subsonic/supersonic transition) together with a known pressure at infinity can uniquely determine the complete solution. However, to correspond with typical results near the Sun and at the Earth's orbit the pressure at infinity is found to be very much larger than that generally accepted.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 February 1976
 DOI:
 10.1098/rspa.1976.0028
 Bibcode:
 1976RSPSA.348..129J
 Keywords:

 Continuum Flow;
 Gas Expansion;
 Gravitational Effects;
 Magnetohydrodynamic Flow;
 Prandtl Number;
 Solar Wind;
 Astrophysics;
 Asymptotic Methods;
 Compressible Fluids;
 Flow Distribution;
 Flow Theory;
 Subsonic Flow;
 Supersonic Flow;
 Thermal Conductivity;
 Viscous Fluids;
 Solar Physics;
 CONTINUUM FLOW;
 GAS EXPANSION;
 GRAVITATIONAL EFFECTS;
 MAGNETOHYDRODYNAMIC FLOW;
 PRANDTL NUMBER;
 SOLAR WIND;
 ASTROPHYSICS;
 ASYMPTOTIC METHODS;
 COMPRESSIBLE FLUIDS;
 FLOW DISTRIBUTION;
 FLOW THEORY;
 SUBSONIC FLOW;
 SUPERSONIC FLOW;
 THERMAL CONDUCTIVITY;
 VISCOUS FLUIDS