Interfacial Wave Motions Due to Marangoni Instability: III. Solitary Waves and (Periodic) Wave Trains and Their Collisions and Reflections Leading to Dynamic Network (Cellular) Patterns in Large Containers

Abstract

Collisions and reflections of solitary waves and (periodic) wave trains driven by surface tension gradients (Marangoni stresses) exhibit a wealth of astonishing features. Depending on the angle between the incoming wave crests, the outgoing waves show in their trajectories after collision negative phase shift for small enough angles, no phase shift at about π/2 and hence no appreciable change in their trajectories, or positive phase shift, accompanied by the appearance of a phase-locked third wave or Mach–Russell stem at wider crossing angles. Synchronous wave collisions exhibit regular but complex dynamic network patterns whose formation and dependence on the size and the shape of the container are discussed. Although wave reflections share some of these features, corresponding apparently to the outcome of the virtual collision of a wave with its mirror image, there are significant differences that are described here.