Solitary Wave Formation and Dynamics on Falling Films

Abstract

Publisher Summary This chapter provides an overview of solitary wave formation and dynamics on falling films. The most dramatic solitary interfacial waves exist on a thin film falling down a plane under the force of gravity. The solitary waves, with their large amplitudes and broad Fourier content, cannot be described by weakly nonlinear theories with only a few Fourier modes. Their construction and dynamics can be discerned only with strongly (global) nonlinear techniques in dynamical systems theory. In this respect, the falling film is arguably the best hydrodynamics example of how modern dynamical systems theory, especially global theories associated with homoclinic bifurcations, can be applied to understand its complex spatio-temporal dynamics. Although the chaotic dynamics of solitary pulses occur at relatively low Reynolds numbers due to the presence of destabilizing inertia force at scales different from the stabilizing capillary force, the dynamics share many of the characteristics of high Reynolds number shear flow turbulence. Subharmonic secondary instabilities, broadband excitation, synchronization, and coherent structure interactions seem to occur in all these open flow systems. With its low Reynolds number, the falling film instability is relatively easy to study numerically, and its solitary waves are simpler to construct.