Viscous sources in the Curle-Lighthill analogy

Although the Curle-Lighthill analogy for sound generation by unsteady flow past solid surfaces is formally exact, it has become accepted practice in aeroacoustics to use an approximate version in which viscous quadrupoles are neglected. In this paper we examine this approximation by comparing the predictions of the Curle-Lighthill analogy with an exact solution for the case of a cylinder vibrating in a viscous fluid. Results indicate that significant discrepancies can be observed when the cylinder radius is comparable with or smaller than the viscous penetration depth. In addition results differ significantly depending on the Green's function used to solved the acoustic analogy. The physical interpretation of the viscous quadrupoles is clarified by comparing the surface source terms Curle-Lighthill analogy with those found in an analogy based on the viscous wave equation. This also shows that the two formulations are indeed consistent.