DYNAMICAL BEHAVIORS AND NUMERICAL SIMULATION OF A LORENZ-TYPE SYSTEM FOR THE INCOMPRESSIBLE FLOW BETWEEN TWO CONCENTRIC ROTATING CYLINDERS

Abstract

In this paper, we investigate the problem of dynamical behaviors and numerical simulation of Lorenz systems for the incompressible flow between two concentric rotating cylinders. A spectral Galerkin method is used to derive a model system of axisymmetric Couette–Taylor flow, a three-mode system, which is structurally similar to the Lorenz system, is obtained by a suitable three-mode truncation of the Navier–Stokes equations for the incompressible flow between two concentric rotating cylinders. The stability of the three-mode system is discussed, the existence of its attractor is given. Moreover, numerical simulation results indicate that this low-dimensional model exhibits a route to chaos via a period doubling cascade. Using these numerical results we explain successive transitions of Couette–Taylor flow from Laminar flow to turbulence in the experiment.