Chaotic flow in rotating lid cavities

Numerical computations are performed to investigate the structure and evolution of flow in a two-dimensional axisymmetric rotating lid cavity. Frequency decompositions, phase diagrams, and flow visualization are used to monitor the changing kinematics of the flow as the speed of the rotating side wall is increased. For the flow regimes investigated, the approach to steady state is characterized by oscillatory instabilities, quasiperiodic flow, and chaotic flow leading to turbulence. A detailed study of the physical mechanisms involved in the computed flow field indicates the existence of at least two independent frequencies at a rotational Reynolds number Re in the range of 8×105 to 9×105. At Re≳106, a multiple of independent frequencies appear in the spectrum that indicate a transition to turbulence. This seems to be consistent with the experiments of Daily and Nece [ASME J. Basic Eng. 82, 217 (1960)] for the Reynolds number at which transition to weak turbulence is observed and with the theoretical scenario of Ruelle and Takens [Commun. Math. Phys. 20, 167 (1967)] for the transition to turbulence.