Abstract
A number of works have been done on statistical theoretical analyses of turbulence since the presentation of the direct-interaction approximation (DIA) method that is explained in Sec. 3.5. It is not too much, however, to say that most of them focus attention on homogeneous isotropic turbulence. In this course, one of a handful of theoretical works on turbulent shear flow was also done by Kraichnan (1964), the advocate of the DIA, and the formal expressions for the Reynolds stress and the turbulent scalar flux were derived with the aid of the DIA.
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Yoshizawa, A. (1998). Two-Scale Direct-Interaction Approximation. In: Hydrodynamic and Magnetohydrodynamic Turbulent Flows. Fluid Mechanics and Its Applications, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1810-3_6
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DOI: https://doi.org/10.1007/978-94-017-1810-3_6
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