Dispersion of linear gravity waves on a viscoelastic fluid in an horizontal canal

A characteristic equation is derived that describes the spatial decay of linear surface gravity waves on Maxwell fluids. Except at small frequencies, the derived dispersion relation is different from the temporal decay dispersion relation which is normally studied within fluid mechanics. The implications for waves on viscous Newtonian fluids using the two different dispersion relations is briefly discussed. The wave number is measured experimentally as function of the frequency in a horizontal canal. Seven Newtonian fluids and four viscoelastic liquids with constant viscosity have been used in the experiments. The spatial decay theory for Newtonian fluids fits well to the experimental data. The model and experiments are used to determine limits for the Maxwell fluid time numbers for the four viscoelastic liquids. As a result of low viscosity it was not possible within this study to obtain these time numbers from oscillatory experiments. Therefore, a comparison of surface gravity wave experiments with theory is applicable as a method to evaluate memory times of low viscosity viscoelastic fluids.