Linear theory of gravity waves on a Voigt viscoelastic medium

Linear surface gravity waves on a semi-infinite incompressible Voigt medium are studied in this paper. Three dimensionless parameters, the dimensionle ss viscoelastic parameter Theta, the dimensionless wave number and the dime nsionless sur; face tension are introduced. A dimensionless characteristic equation describing the waves is derived. This is a sixth order complex alg ebraic equation which is solved to give the complex dispersion relation. Ba sed on the numerical solution, two critical values of Theta, Theta (A) = 0. 607 and Theta (B) = 2.380, which represent the appearance of the cutoff reg ion and the disappearance of the strong dispersion region, are found. The e ffects of Theta on the characteristic equation and the properties of the wa ves are discussed.