Velocity phase-transitions in the wake of a wavy cylinder at low Reynolds numbers

Wake behind a sinusoidal wavy cylinder is investigated in the range of Reynolds number (Re) up to 350. Detailed direct numerical simulations show that the wake is featured with significant three-dimensional (3D) effects. In the wake transition regime, the onset of mode A at Re= 190 and mode B at Re= 280 is well identified. In the laminar regime, the wake is in a spanwise-periodic wavy fashion rather than two-dimensional one of the straight circular cylinders. The critical Re for the onset of 3D effects is approximately 50. Regarding mean wake dynamics, different routes from the initial in-phase waviness in the very near-wake to the ultimate spanwise homogeneity in the far wake are observed for the first time. Accordingly, laminar flows past the wavy cylinder are classified into three phase transition regimes with three underlying mean velocity patterns. No phase transition occurs below 60, one phase transition exists at 60 ≤Re< 88, and wake undergoes two phase transitions when Re≥ 88. The transition location has been derived to be dependent on a combination of Re^−1/2 and Re^-1. Mean velocity patterns are further explored to account for the phase transition regimes. Finally, the phase transition phenomenon is found to modulate wake structures with an alternation of vortex-shedding frequency.