Axisymmetric waves in compressible Newtonian liquids contained in rigid tubes: steady-periodic mode shapes and dispersion by the method of eigenvalleys

Abstract

In this paper the first thirty-two axisymmetric modes for steady-periodic waves in viscous compressible liquids contained in rigid, impermeable, circular tubes are calculated. These results end long speculation over the effects of viscosity on guided acoustic waves. Sixteen of the modes belong to a family of rotation-dominated modes whose existence was previously unknown. The thirty-two modes were computed for a wide range of frequencies, viscosities and wave-lengths.The modes were found through the use of the method of eigenvalleys, which also led to the discovery of backward-propagating waves, an exact analytical expression for the zeroth rotational mode eigenvalue, definitive boundaries between low and intermediate frequencies and between intermediate and high frequencies, and a new type of boundary layer, called a dilatational boundary layer.