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 dimensionless viscoelastic parameter ϑ, the dimensionless wave number and the dimensionless surface tension are introduced. A dimensionless characteristic equation describing the waves is derived. This is a sixth order complex algebraic equation which is solved to give the complex dispersion relation. Based on the numerical solution, two critical values of ϑ, ϑ _A =0.607 and ϑ _B =2.380, which represent the appearance of the cutoff region and the disappearance of the strong dispersion region, are found. The effects of ϑ on the characteristic equation and the properties of the waves are discussed. The project supported by the National Natural Science Foundation of China (59709006)