On the effect of viscosity in scattering from partially coated infinite cylinders

This paper considers the two-dimensional problem of scattering of a plane wave incident on an infinite cylinder that is coated with strips of pressure-release material extending over quadrants on the illuminated and shadowed sides, with the remainder of the surface considered to be rigid. Transitions from soft to rigid surfaces correspond to discontinuous boundary conditions. Ideal fluid theory predicts an infinite pressure gradient at these transitions, which suggests that viscous effects may be significant. The present work is a quantitative analysis of the global effect on acoustic scattering of viscosity effects arising in the vicinity of the discontinuity. The analysis represents the scattered field in terms of acoustic and vortical contributions. Both contributions are represented by series expansions in terms of azimuthal harmonics and associated cylindrical wave functions. The amplitudes of these harmonics are determined by satisfying a pair of discontinuous boundary conditions. Results obtained by using the method of weighted residuals are shown to be less accurate than those obtained from a collocation procedure. The results for surface pressure and farfield directivity indicate that viscous effects are important only if the Reynolds number is extremely small.