Three-dimensional hydrodynamic instability in a liquid film flow produced by the generalized Kuramoto-Sivashinsky equation

Abstract

We numerically study the three-dimensional hydrodynamic instability on spatiotemporal dynamics of a liquid film flow produced by the generalized two-dimensional Kuramoto-Sivashinsky (2D gKS) equation from a viewpoint of symbolic dynamics. The unstable liquid film flow gives rise to a rich variety of hydrodynamic instabilities such as three-dimensional hydrodynamic instability and spatiotemporal structures forming horseshoe-like and pointed structures. We study the wave dynamics by the estimating the dispersion entropy based on symbolic dynamics and statistics.