On the continuum theory of the one-fluid solar wind for small Prandtl number
On the continuum theory of the one-fluid solar wind for small Prandtl number
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小普朗特数下单流体太阳风的连续介质理论
DOI：
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
R. S. Johnson
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文献类型：
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作者：
R. S. Johnson
考虑了单组分气体膨胀到真空（或近真空）的连续介质理论。假设气体是可压缩的、粘性的和导热的，具有恒定的普朗特数和与（温度）ω成比例的粘度，ω > 1。气体受到以太阳为中心的引力场的影响。对于小的普朗特数（这对于单流体太阳风是现实的），采用匹配渐近展开的方法构造了一个描述从太阳表面到无穷远的完整流场的解。前两个区域对应于Roberts & Soward（1972）发现的大导热系数区域;下一个区域涉及粘性项，第四个区域主要是粘性项。从第四个区域可以看出，要么流动保持超音速但终止于有限点，要么流动通过扩散激波层变为亚音速并在无穷远处接近非零压力。可以看出，临界点（亚音速/超音速过渡）的存在以及无穷远处的已知压力可以唯一地确定完整的解决方案。然而，为了与太阳附近和地球轨道上的典型结果相对应，我们发现无穷远处的压力比一般公认的要大得多。
The continuum theory for a single-species 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 one-fluid 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 non-zero 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.