ON THE TRANSITIONAL CHARACTERISTICS OF MIRROR SYMMETRIC LID-DRIVEN CAVITY FLOW

The transitional critical characteristics refer to the change of physical properties of flow field caused by the change of different flow states, which is amid the transitional stages. For instance, when flow evolves from steady to unsteady periodic. It fundamentally determines physical laws, like evolution mode and flow characteristics, deep inside the corresponding flow field, which is of great importance and necessity to understand the formation mechanism of flow phenomena. In this paper, the numerical simulations and flow stability analysis are carried out for the mirror symmetric lid driven cavity flow. The flow bifurcations, such as Hopf bifurcation and Neimark-Sacker bifurcation, are captured and their influence on the flow characteristics is discussed. The flow evolution mode is analyzed as well, it is found that with the increase of Reynolds numbers, the flow evolves from a steady state to a unsteady periodic state, then to a quasi-periodic state and finally into chaos. It is explained that the formation mechanism of various flow phenomena, for example, flow hysteresis, symmetry loss, energy cascade, etc. The flow topology is analyzed and the relation between mirror symmetry and stability is clarified. The conclusions of the present study is helpful to better understand the physics of this internal flow field, further completing the corresponding research of on this research direction, such as the classic lid driven cavity flow. Based on the findings of present study, we have found that the unsteadiness of flow field always starts as the Hopf bifurcation appears, the flow symmetry breaks as soon as the flow unsteadiness shows up. It is found that the flow evolves as the classic Ruelle-Takens mode and the flow hysteresis is observed when flow evolves from a steady state to an unsteady periodic state.