LINEAR-THEORY OF GRAVITY-WAVES ON A MAXWELL FLUID

Surface gravity waves on a semi-infinite incompressible Maxwell fluid are studied by means of linear theory. A dimensionless (memory) time-number (Θ), different from the Deborah number, is introduced, together with a dimensionless wave-number and a dimensionless surface tension. A characteristic equation describing the waves is derived. This is an 8-degree complex polynomial which is solved to give the complex dispersion relation. Two critical time-numbers are found, ΘA = 0.321 and Θc = 0.906. These are important for the number of pure decay solutions and propagating waves. The dispersion relation is shown for Θ in the range from 0 to 2. A similarity to gravity waves on inviscid fluids is seen for small wave numbers. For large wave numbers these are solutions of the Rayleigh wave type. © 1990.