Rotational acoustic resonances in cylindrical waveguides

An investigation is made into the existence of rotational acoustic resonances in a circular cylindrical waveguide, and their frequencies of oscillation are calculated numerically. The guide is assumed to contain a number of radial fins which have finite extent, and which are distributed at equal azimuthal angles around the guide. A variational principle is used to prove the existence of different types of localised, rotational motion, and the frequencies of these spinning modes are computed. The numerical method is based on the use of a Galerkin technique to solve the integral equation which arises in the solution of the governing Helmholtz equation. The variation of the spinning mode frequencies with the number of fins and type of mode is discussed, and a comparison with non-rotational resonances is made.