ENERGY FLUX FOR DAMPED INHOMOGENEOUS PLANE-WAVES IN VISCOELASTIC FLUIDS

The propagation of inhomogeneous plane waves in the context of the lin earized theory of incompressible viscoelastic fluids is considered. Th e angular frequency and the slowness vector are both assumed to be com plex. As in incompressible purely viscous fluids, two kinds of waves m ay propagate: A ''zero pressure wave'' for which the increment in pres sure due to the wave is zero, and a ''universal wave'' which is indepe ndent of the viscoelastic relaxation modulus. The balance of energy is written using a decomposition of the stress power into a reversible c omponent and a dissipative component proposed namely by P.W. Buchen [J . R. Astr. Sec. 23 (1971) 531-542]. For the inhomogeneous waves, a ''w eighted mean'' energy flux vector, ''weighted mean'' energy density an d ''weighted mean'' energy dissipation are introduced. It is shown tha t they satisfy two modulus independent relations. These generalize to the case of viscoelasticity relations previously obtained in other con texts. (C) 1998 Elsevier Science B.V. All rights reserved.