WANG He-yuan, CUI Jin. Low-Dimensional Analysis and Numerical Simulation of Rotating Flow[J]. Applied Mathematics and Mechanics, 2017, 38(7): 794-806. doi: 10.21656/1000-0887.360342
Citation: WANG He-yuan, CUI Jin. Low-Dimensional Analysis and Numerical Simulation of Rotating Flow[J]. Applied Mathematics and Mechanics, 2017, 38(7): 794-806. doi: 10.21656/1000-0887.360342

Low-Dimensional Analysis and Numerical Simulation of Rotating Flow

doi: 10.21656/1000-0887.360342
Funds:  The National Natural Science Foundation of China(11572146;11526105)
  • Received Date: 2015-12-10
  • Rev Recd Date: 2017-05-24
  • Publish Date: 2017-07-15
  • In order to explore the transition way of the Couette-Taylor flow from laminar flow to turbulence and the characteristics of chaotic attractors in turbulence, dynamic behaviors and numerical simulation of the Couette-Taylor flow were studied by means of the low-dimensional analysis method. The dynamic properties of the 3-model Lorenz-type system of the Couette-Taylor flow were discussed, including the stability of equilibrium points, the occurence of limit cycles, the evolution of bifurcation and chaos, as well as the global stability etc. Through linear stability analysis and numerical simulation, the dynamic behavior and evolution history of bifurcation and chaos of this low-dimensional model were presented. Consequently, successive transitions of the Couette-Taylor flow from laminar flow to turbulence in the experiment were explained. The numerical simulation results of bifurcation diagrams, Lyapunov exponent spectra, Poincaré sections, power spectra and return mappings of the system reveal the general features of the system chaos behaviors.
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