Diffuse wavefields in cylindrical coordinates

A diffuse wavefield is normally defined in terms of plane waves--to quote one textbook definition "plane waves are incident from all directions with equal probability and random phase." In some vibro-acoustic problems the response of a two-dimensional component such as a plate is more conveniently expressed in terms of cylindrical waves, and it is not immediately obvious what properties should be assigned to the cylindrical waves to constitute a diffuse field. It is shown here that a diffuse wavefield can be modeled as a summation of statistically independent cylindrical waves, apart from the fact that each outgoing wave of a particular order is fully correlated to an incoming wave of the same order. A simple relationship is derived between the energy flow P in each wave component and the energy density e of the wavefield: P = ec(g)/k, where c(g) is the group velocity and k is the wavenumber. This result is shown to hold true for both bending waves and in-plane waves (longitudinal and shear) in a plate. The work has application to the calculation of coupling loss factors in statistical energy analysis.