Abstract:

There have been a lot of investigations which concern with rotating flow between two concentric cylinders (abbreviate frequently as Couette-Taylor Flow), Couette-Taylor flow is the typical rotation flow problems, It provides a paradigm from laminar to turbulent transition. Dynamical mechanism and energy conversion of Couette-Taylor flow are investigated in this paper, the Couette-Taylor flow chaotic system is transformed into Kolmogorov type system, which is decomposed into four types of torques:inertial torque, internal torque, dissipation and external torque. By the combinations of different torques, key factors of chaos generation and the physical meaning of Couette-Taylor Flow are studied. The conversion among Hamiltonian energy, kinetic energy and potential energy is investigated. The relationship between the energies and the Reynolds number is discussed. It concludes that the combination of the four torques is necessary conditions to produce chaos, and only when the dissipative torques matches the driving (external) torques can the system produce chaos, any combination of three types of torques cannot produce chaos. The external torque, which is provided by the rotation of the cylinder, supply the energy of the system, and that leads to Taylor vortex and chaos, the physical meaning and energy conversion of Couette-Taylor flow system are investigated. The Casimir function is introduced to analyze the system dynamics, and its derivation is chosen to formulate energy conversion. The bound of chaotic attractor is obtained by the Casimir function and Lagrange multiplier. The Casimir function reflects the energy conversion and the distance between the orbit and the equilibria. These relationships are illustrated by numerical simulations.

Key words: Couette-Taylor flow, Dynamical Mechanism, Kolmogorov system, Chaos