A weakly viscous mean flow boundary layer is sandwiched between an inviscid outer flow and a viscous sublayer to form an asymptotic patchwork model for ducted acoustics in shear Sow over an acoustic lining. Analytical solutions are found for the acoustic mode shapes in the three regions and compared with solutions of the linearised compressible Navier-Stokes equations (LNSE). By asymptotically matching the analytical solutions, a closed-form effective impedance boundary condition is derived, applicable at the wall of an inviscid plug flow. Duct modes in the wavenumber and frequency domain are investigated and compared to the Myers boundary condition, its first order correction (the Modified Myers condition) and numerical solutions of the LNSE.
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