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Surface waves on non-Newtonian viscoelastic liquids.

In the present work, we study the dynamics of thermally excited fluctuations on the surface of non-Newtonian viscoelastic liquids, which shows complex behaviors such as crossover between the capillary wave and the elastic wave, and the coexistence of several modes. We show that the power spectrum is separated into surface localized modes and the bulk shear modes, and they are decomposed further into several modes using the partial fraction expansion. The peak positions of these modes are characterized by roots of a polynomial equation. We calculate the decomposition of the surface wave spectra numerically, and discuss evolution of constituent peaks with liquid parameters.