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Analytical formulas are derived for the propagation of a partially coherent twisted anisotropic Gaussian Schell-model (TAGSM) beam in a turbulent atmosphere. Propagation properties of a TAGSM beam in a turbulent atmosphere are investigated in detail. It is found that a TAGSM beam will become a circular beam in a turbulent atmosphere, and low coherence and larger twist have an effect of anticircularization of the beam spot. The beam spot spreads more rapidly for lower coherence, larger twist, or stronger turbulence.
Cai et al. (Mon,) studied this question.