# Solitary wave fission of a large disturbance in a viscous fluid conduit

## TL;DR

This study combines theory, numerical simulations, and experiments to analyze how large disturbances in viscous fluid conduits break into sequences of solitary waves, extending soliton resolution concepts to non-integrable systems.

## Contribution

It introduces the solitary wave resolution method for non-integrable systems and validates its predictions through experiments and simulations in viscous fluid conduits.

## Key findings

- Predicted number of solitary waves matches experimental observations within 1-2 waves.
- Amplitude distribution of waves shows strong agreement with theoretical predictions.
- Universal properties of solitary wave fission are identified across fluid dynamics problems.

## Abstract

This paper 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. This problem is of fundamental importance in a range of applications including tsunami and internal ocean wave modelling. This study is performed in the context of the viscous fluid conduit system-the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Due 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, termed the solitary wave resolution method, 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, quantifying an extension of the well-known soliton resolution conjecture from integrable systems to non-integrable systems that often provide a more accurate modelling of physical systems. The theoretical predictions for the fluid conduit system are confirmed both numerically and experimentally. The number of observed solitary waves is consistently within 1-2 waves of the prediction, and the amplitude distribution shows remarkable agreement. Universal properties of solitary wave fission in other fluid dynamics problems are identified.