Abstract
Turbulence structures of most practical flows are little understood, and involved calculations of their sound field are prohibited by our severely restricted knowledge of a complicated turbulence stress tensor. Proudman [Proc. Roy. Soc. (London) A211, 564 (1952)] computed the noise radiated by decaying isotropic turbulence on the basis of the theory developed by Lighthill [Proc. Roy. Soc. (London) A214, 119 (1952)], but this work is probably the only detailed quantitative application of noise theory that is feasible with our present limited understanding of turbulence. Recent developments in statistical mechanics may lead to better understanding of the complicated structure of the turbulence stress tensor in an anisotropic turbulence. It is shown how spectral and correlation tensors are evaluated with the aid of various irreversible thermodynamic derivatives and the sum formulas recently discussed by Onsager, Kubo, and others, in connection with transport phenomena in many body theory and in irreversible statistical mechanics.
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