Direct numerical simulation of rotating fluid flow in a closed cylinder

Abstract

Present numerical simulations of the transition scenario of a rotating fluid flow in a closed cylinder are presented, where the motion is created by a rotating lid. The numerical algorithm, which is based on a finite-difference discretization of the axisymmetric Navier-Stokes equations, is validated against experimental visualizations of both transient and stable periodic flows. The complexity of the flow problem is illuminated numerically by injecting flow tracers into the flow domain and following their evolution in time. The vortex dynamics appears as stretching, folding and squeezing of flow structures which wave along the contour of a central vortex core. The main purpose of the study is to clarify the mechanisms of the transition scenario and relate these to experiences known from other dynamical systems and bifurcation theory. The dynamical system was observed to exhibit up to three multiple solutions for the same Reynolds number, and to contain four discernible branches. The transition to strange attractor behavior was identified as a nontrivial Ruelle-Takens transition through a transient torus. The various solution branches of the rotating flow problem are illustrated by phase portraits and summarized on a frequency diagram.