On the nature of turbulence in a problem on the motion of a fluid behind a ledge

Abstract

In the present paper, we suggest a numerical method for the analysis of the motion of a viscous incompressible fluid under the transition to the turbulent mode for an example of the numerical solution of a three-dimensional space problem on the fluid flow behind a ledge for various values of the Reynolds number. We show that, at the initial stages, the turbulence in the problem is developed via successive bifurcations of generation of a stable cycle, two-dimensional tori, and then three-dimensional tori in the infinite-dimensional phase space of the system.