  Conduits generated by the buoyant dynamics between two miscible, Stokes
fluids with high viscosity contrast exhibit rich nonlinear wave dynamics.
However, little is known about the fundamental wave dispersion properties of
the medium. In the present work, a pump is used to inject a time-periodic flow
that results in the excitation of propagating small and large amplitude
periodic traveling waves along the conduit interface. This wavemaker problem is
used as a means to measure the linear and nonlinear dispersion relations and
corresponding periodic traveling wave profiles. Measurements are favorably
compared with predictions from a fully nonlinear, long-wave model (the conduit
equation) and the analytically computed linear dispersion relation for
two-Stokes flow. A critical frequency is observed, marking the threshold
between propagating and non-propagating (spatially decaying) waves.
Measurements of wave profiles and the wavenumber-frequency dispersion relation
quantitatively agree with wave solutions of the conduit equation. An upshift
from the conduit equation's predicted critical frequency is observed and is
hypothesized to be explained by incorporating a weak recirculating flow into
the full two-Stokes flow model which we observe to be operable in the
experiment. When the boundary condition corresponds to the temporal profile of
a nonlinear periodic traveling wave solution of the conduit equation, weakly
nonlinear and strongly nonlinear, cnoidal-type waves are observed that
quantitatively agree with the conduit nonlinear dispersion relation and wave
profiles. This wavemaker problem is an important precursor to the experimental
investigation of more general boundary value problems in viscous fluid conduit
nonlinear wave dynamics.
