Aerodynamic noise dependent on mean shear

Abstract

New factors illustrating the effect of convection on acoustic radiation are deduced from Lighthill's theory of aerodynamic noise. For sound dependent on mean velocity variations for its generation, that is shear noise, the new factors are (1 − M cos θ)⁻³ and (1 − M cos θ)⁻¹ in contrast with (1 − M cos θ)⁻⁵ for self noise.Comparison with the measured far-field directionality patterns reported by Howes (1960) shows that the factor (1 − M cos θ)⁻³ provides considerably better agreement with the experimental observations than the self noise factor.The source terms discussed by Lighthill (1954) when considering shear amplification are examined and shown to contain the terms produced by the analysis of Csanady (1966) as well as a new term dependent on the second derivative of the mean velocity.