On attenuation of plane sound waves in turbulent mean flow

Plane sound waves in a smooth pipe turbulent boundary layer are known to be more strongly damped when the acoustic boundary layer becomes thicker than the viscous sublayer. The attenuation constants that govern this phenomenon are accurately predicted by the mathematical model proposed by M.S. Howe [The damping of sound by wall turbulent shear layers. Journal of the Acoustical Society of America 98(3) (1995) 1725–1730. Also in: Acoustics of Fluid–Structure Interactions, Cambridge University Press, Cambridge, 1998]. This model assumes uniform mean core flow. The present paper proposes a variant of this model which is based on the assumption of parallel sheared mean core flow. Predictions of the two approaches are compared.