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 ∂2 T ij /∂t 2 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.
This paper is based on an alternative analysis which does not neglect retarded times. It makes use of the Lighthill relationship, whereby the fourth-order T ij retarded-time covariance is evaluated from the square of a similar second-order covariance, which is assumed known. In this derivation no statistical assumptions are involved. This result, using distributions for the second-order space-time velocity squared covariance based on the Direct Numerical Simulation (DNS) results of both Sarkar and Hussaini (1993) and Dubois (1993), is compared with a re-evaluation of Proudman's original model. These results are then compared with the sound power derived from a phenomenological model based on simple approximations to the retarded-time/space covariance of T xx . Finally, the recent numerical solutions of Sarkar and Hussaini (1993) for the acoustic power are compared with the results obtained from the analytic solutions.
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Communicated by Jay C. Hardin and M.Y. Hussaini
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Lilley, G.M. The radiated noise from isotropic turbulence. Theoret. Comput. Fluid Dynamics 6, 281–301 (1994). https://doi.org/10.1007/BF00311842
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DOI: https://doi.org/10.1007/BF00311842