Influence of viscosity on the diffraction of sound by a circular aperture in a plane screen

The linearized equations of viscous fluid flow are used to analyze the diffraction of a time-harmonic acoustic plane wave by a circular aperture in a rigid plane screen. Arbitrary aperture size and arbitrary angle of incidence are considered. Sets of dual integral equations are derived for the diffracted velocity and pressure fields, and are solved by analytic reduction to sets of linear algebraic equations. In the case of normal incidence, numerical results are presented for the fluid velocity in the aperture and the power absorption due to viscous dissipation. The theoretical results for power absorption are compared to previously obtained results from high amplitude acoustic experiments in air. The conditions under which the dissipation predicted by linear theory becomes significantare quantified in terms of the fluid viscosity and sound speed, the acoustic frequency, and the aperture radius.