Observation of Linear Periodic Waves in a Viscous Fluid Conduit

Dispersion occurs when waves of different wavelengths propagate with various phase speeds such that an envelope of mixed wavelengths spreads out in space. The conduit equation which possesses a bounded, nonlocal dispersion relation is an accurate model of viscous fluid conduit interfacial waves. Laboratory measurements of glycerin viscous fluid conduits are compared with theoretical predictions from the linear theory for the conduit equation. Periodic interfacial waves are generated by periodically varying the flow rate of dyed, diluted glycerin injected into glycerin exterior fluid. To perform harmonic analysis on the experimental waves, Fourier transforms and the cosine fitting method are implemented to investigate wave properties such as amplitude, wavenumber and frequency. Periodic traveling wave solutions in the subcritical regime and spatial-decaying waves in the supercritical regime are obtained. Measurements of wave profiles and the wavenumber-frequency dispersion relation quantitatively agree with the conduit equation. A downshift of the critical frequency is observed which is explained by the full two Stokes fluid system. This study presents important linear wave features of the conduit system and provides a foundation for complex nonlinear wave dynamics.