Dynamics and stability of the wake behind a circular cylinder in the vicinity of a plane moving wall

Abstract This paper identifies and characterizes modes of the three-dimensional instability of the flow over a circular cylinder of diameter D near a plane moving wall with a gap height of G = 0 . 1 D beyond the onset of vortex shedding through the Floquet stability analysis. The associated effects of the transitions on the hydrodynamic forces of the cylinder are examined by performing direct numerical simulations. Six distinct three-dimensional modes are identified and their characteristics are discussed in detail. It is found that the physical mechanism responsible for the synchronous mode 1 appears to be associated to an elliptic instability. The quasi-periodic mode 4 is observed to transform to a synchronous mode (mode 6) on increasing the Reynolds number, indicating that they are likely to be resulted from the same physical mechanism. For mode 6, its physical nature seems to be a hyperbolic instability. Fully three-dimensional simulations show that the wake undergoes a rapid transition to complex chaotic flow state after the most dominant mode starts to saturate, due to the strongly nonlinear interactions of many modes with different spanwise wavelengths.