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The invariance of second moment turbulent closure under a change of frame is examined. It is shown that the Reynolds stresses and the higher turbulence correlations based on an ensemble mean are frame-indifferent while the Reynolds stress transport equations are frame dependent. As a result of this incompatibility, second moment closure cannot form a general foundation for the study of turbulence. Alternative approaches that are properly invariant are discussed.
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Charles G. Speziale (1979) studied this question.
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