The Search for Exact Coherent Structures in a Quasi-Two-Dimensional Flow

Abstract

Recent theoretical advances suggest that turbulence can be characterized using unstable solutions of the Navier-Stokes equations having regular temporal behavior, called Exact Coherent Structures (ECS). Due to their experimental accessibility and theoretical tractability, two-dimensional flows provide an ideal setting for the exploration of turbulence from a dynamical systems perspective. In our talk, we present a combined numerical and experimental study of electromagnetically driven flows in a shallow layer of electrolyte. On the numerical front we present our research concerning the search for ECS in a two-dimensional Kolmogorov-like flow. We discuss the change in the dynamics of the flow as the Reynolds number is varied. For a weakly turbulent flow, we show that the turbulent trajectory explores a region of state space which contains a number of ECS. We then discuss the occurrence of states similar to these numerically computed ECS in an experimental quasi-two-dimensional Kolmogorov-like flow.