Linear gravity waves on Maxwell fluids of finite depth

Linear surface gravity waves on Maxwell viscoelastic fluids with finite depth are studied in this paper. A dispersion equation describing the spatial decay of the gravity wave in finite depth is derived. A dimensionless memory (time) number θ is introduced. The dispersion equation for the pure viscous fluid will be a specific case of the dispersion equation for the viscoelastic fluid as θ=0. The complex dispersion equation is numerically solved to investigate the dispersion relation. The influences of θ and water depth on the dispersion characteristics and wave decay are discussed. It is found that the role of elasticity for the Maxwell fluid is to make the surface gravity wave on the Maxwell fluid behave more like the surface gravity wave on the inviscid fluid.