Solitary wave fission in a viscous fluid conduit

This talk presents a theoretical and experimental study of the long-standing fluid mechanics problem involving the temporal resolution of a large localised initial disturbance into a sequence of solitary waves. Of fundamental importance in a range of applications including tsunami and internal ocean wave modelling, this problem is studied in the context of the viscous fluid conduit system–the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Owing to buoyancy-induced nonlinear self-steepening balanced by stress-induced interfacial dispersion, the disturbance evolves into a slowly modulated wavetrain and further into a sequence of solitary waves. An extension of Whitham modulation theory is used to resolve the fission of an initial disturbance into solitary waves. The developed theory predicts the relationship between the initial disturbance's profile, the number of emergent solitary waves and their amplitude distribution. The theoretical predictions for the fluid conduit system are confirmed both numerically and experimentally. The number of observed solitary waves is consistently within one to two waves of the prediction, and the amplitude distribution shows remarkable agreement.