Coupled waves of linear velocity, angular velocity, and temperature in a liquid with internal rotation

Equations of motion for a locally nonequilibrium liquid with internal rotation are derived, and the thermospin effect is considered. It is demonstrated that high-frequency transverse coupled waves of linear velocity, angular velocity of internal rotation, and temperature may propagate a liquid with internal rotation. A dispersion relation and a frequency dependence of the damping ratio are deduced. Comparison between theoretical and experimental values of the transverse sound velocity dispersion shows their satisfactory agreement. Low-frequency transverse waves do not penetrate into the liquid: they decay over a distance on the order of the wavelength. It is shown that frequencies and their corresponding wavenumbers exist in a liquid with internal rotation at which either waves do not decay or a phase shift in the skin layer is absent. It is found that the excitation spectrum may contain a cutoff frequency or an energy gap due to interaction between the linear and angular velocity fields. The dispersion and damping ratio for the coupled waves near synchronism points, where uncoupled waves resonantly interact with each other, are determined.