The mixing length theory of convection is generalized for use in the envelopes of nonrotating, radially pulsating stars by the methods proposed by Gough (1965) and Unno (1967). The essential differences between the physical assumptions made in the two approaches are explained. The detailed formulas required for a linear pulsational-stability analysis of a static star are derived.
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D. O. Gough (1977) studied this question.