Observations of Breathers in Soliton-Cnoidal Wave Interaction in a Viscous Fluid Conduit - Part II

Conduits generated by the buoyant injection of a miscible, Stokes fluid into another Stokes fluid with high viscosity contrast have been studied due to their remarkable nonlinear wave behavior. Applications in geological and geophysical contexts include the dynamics of channelized flows in magmatic and glacial systems. Breathers, localized disturbances to nonlinear periodic wavetrains, have been theoretically studied in the strongly nonlinear regime of a viscous fluid conduit using the so-called conduit equation. The present work utilizes a laboratory setup for fluid interfacial waves that can reliably generate solitons and nonlinear periodic waves by varying the flow rate of dyed, diluted glycerin injected into the bottom of a pure glycerin reservoir. The generated cnoidal-type waves quantitatively agree with exact conduit equation periodic traveling wave solutions. Breathers of the elevation and depression types are observed to be the result of the nonlinear superposition of solitons and cnoidal waves. In this study, the first experimental results exhibiting the complex, coherent, nonlinear structures of breathers in a fluid conduit are presented, motivating future investigations in other fluid dynamic contexts such as shallow water waves and internal waves.