H. Linde

Evidence for solitary wave behavior in Marangoni–Bénard convection

Recent studies have elucidated the possibility of solitary wave behavior in Marangoni–Benard instability flows. The present paper takes a look at experiments in both heat‐transfer‐ and mass‐transfer‐driven Marangoni systems to discern nonlinear behavior of the type associated with solitary wave interactions. Direct observation of phase shifts incurred by two Marangoni waves having undergone a head‐on collision are reported. Analysis of experiments exhibiting wave reflection at a solid wall and obliquely interacting waves in Marangoni instability flows also show remarkable similarities with nonlinear behavior in Korteweg–de Vries systems.

Oblique and head‐on collisions of solitary waves in Marangoni–Bénard convection

In Marangoni–Benard convection with mass transfer from gas phase to liquid phase, it is found that solitary waves, excited and sustained by Marangoni stresses, are very stable during interactions with others, keeping their original shapes and celerities after interactions, thus experiencing at most a phase shift. Both positive and negative phase shifts have been observed for different types of oblique interaction. A ‘‘critical’’ angle, at which zero phase shift occurs as a result of the interaction, has been defined to delineate regions of negative and positive phase shifts.

Wall reflections of solitary waves in Marangoni-Bénard convection

In Marangoni–Benard convection with mass transfer from the air to the liquid, an experimental exploration of reflections of solitary waves at walls has been carried out. Mach stems are observed for small enough incident angles. Upon increasing the incident angle the stem disappears thus leading to regular reflections with, however, the angle of reflection being generally larger than the incident angle.

Marangoni-driven solitary waves

The analysis of wave interaction experiments in both heat-transfer-driven and mass-transfer-driven high supercritical Marangoni number convection flows provides strong evidence of solitary wave behavior. Wave reflections at a solid wall and oblique wave interactions are qualitatively similar to KdV type interactions in purely gravity-driven (free-surface and internal) solitary wave systems. It is anticipated that the results reported here will motivate new experiments designed to directly test for the existence of solitary waves and solitons in Marangoni-Benard systems.

Solitary waves driven by Marangoni stresses

Abstract Evidence is provided of solitary waves in Marangoni-Benard convection with mass transfer from gas-phase to liquid-phase. It has been found that solitary waves, excited and sustained by Marangoni stresses, are very stable during interactions with others, keeping their original shapes and celerities after interactions, thus experiencing at most a phase shift. Both positive and negative phase shifts appear according to the interaction angle.