Flow past a rotating cylinder translating at different gap heights along a wall

The flow past a rotating circular cylinder translating parallel to a wall at different heights is investigated for Reynolds numbers up to 400 for three discrete rotation rates. In particular, the various wake transitions that occur as a function of gap height are quantified for the three cases examined: non-rotation, and forward and reverse rotations. At low gap heights, only a single steady three-dimensional mode is found to become unstable on the steady base flow. As the gap height is increased, several new three-dimensional modes are observed, of which one attains large amplitudes in the near wake and another preferentially in the far wake. At still larger gap heights, the transition sequence resembles that observed in a rotating cylinder wake, for which the wake first undergoes transition to a periodic state, prior to the onset of three-dimensional flow. Parameter space maps showing the neutral stability curves and regions of instability for each mode are presented for each rotation rate, together with a discussion of the spatio-temporal characteristics and spatial distributions of the new modes. Finally, the force coefficients for the steady and periodic two-dimensional base flows are presented