Abstract
The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman (1952), was the first application of Lighthill's “Theory of Aerodynamic Noise” to a complete flow field. The theory presented by Proudman involves the assumption of the neglect of retarded-time differences and so replaces the second-order retarded-time and space covariance of Lighthill's stress tensor, T ij , and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the ∂2T ij /∂t2 covariance at low Mach numbers, but is not justified when that covariance is reduced to the sum of products of the time derivatives of equivalent second-order velocity covariances as required when Gaussian statistics are assumed. When these assumptions are removed the changes to the analysis are substantial, but the change in the numerical result for the total acoustic power is small.
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