Dynamical Mechanism and Energy Conversion of the Couette–Taylor Flow

Abstract

In this paper, we study the dynamical mechanism and energy conversion of the Couette–Taylor flow. The Couette–Taylor flow chaotic system is transformed into the Kolmogorov type system, which is decomposed into four types of torques. Combining different torques, the key factors of chaos generation and the physical interpretation of the Couette–Taylor flow are studied. We further investigate the conversion among Hamiltonian, kinetic and potential energies, as well as the correlation between the energies and the Reynolds number. It is concluded that the combination of the four torques is necessary to produce chaos, and the system can produce chaos only when the dissipative torques match the driving (external) torques. Any combination of three types of torques cannot produce chaos. Moreover, we introduce the Casimir function to analyze the system dynamics, and choose its derivation to formulate the energy conversion. The bound of chaotic attractor is obtained by the Casimir function and Lagrange multiplier. It is found that the Casimir function reflects the energy conversion and the distance between the orbit and the equilibria.