A methodology for turbulence constitutive modeling is discussed on the basis of the square-root tensor of the Reynolds stress. The present methodology can satisfy the realizability condition for the Reynolds stress proposed by Schumann [Phys. Fluids 20, 721 (1977)] in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root tensor have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds stress. Examples of possible constitutive models of both tensor-expansion and transport-equation types have been proposed.
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