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The escape-probability technique of Sobolev for solving radiative transfer problems in moving atmospheres is extended to treat flows in which the line-of-sight component of the flow velocity is not monotonic. A completely general geometrical configuration and flow velocity field are considered; an integral equation is derived for configurations in which a surface is intersected an arbitrary number of times. For the case of just two intersections, it is shown that an iterative solution always converges rapidly. Numerical results for inverse power-law velocity fields demonstrate the magnitude of the radiative coupling between distant parts of the atmosphere.
Rybicki et al. (Sun,) studied this question.