Nature of Wave Modes in a Coupled Viscoelastic Layer over Water

Abstract

A theoretical study of wave modes in a system of layered materials is presented. The system consists of a floating linear viscoelastic layer over inviscid water. The viscoelastic cover is assumed to obey the Voigt constitutive law. As in many other layered systems, multiple wave modes are discovered. Guided by the roots under pure elastic and pure viscous conditions, the nature of all roots in the dispersion relation is identified for the viscoelastic case. Wave modes include the evanescent, gravity, shear, pressure, interfacial, and Rayleigh-Lamb. All of these previously known waves in elastic solid or fluid over fluid systems are found in the present system of a viscoelastic material floating over water. An analytic criterion for the presence of mode swap in cases with low viscosity is obtained, and the origin of this mode swap phenomenon is discussed. In the vicinity of mode swap, both wave modes are important. Away from this region, the gravity wave mode dominates the free-surface motion.