The three-dimensional transition in the flow around a rotating cylinder

The flow around a circular cylinder rotating with a constant angular velocity, placed in a uniform stream, is investigated by means of two- and three-dimensional direct numerical simulations. The successive changes in the flow pattern are studied as a function of the rotation rate. Suppression of vortex shedding occurs as the rotation rate increases (> 2). A second kind of instabilty appears for higher rotation speed where a series of counter-clockwise vortices is shed in the upper shear layer. Three-dimensional computations are carried out to analyse the three-dimensional transition under the effect of rotation for low rotation rates. The rotation attenuates the secondary instability and increases the critical Reynolds number for the appearance of this instability. The linear and nonlinear parts of the three-dimensional transition have been quantified by means of the amplitude evolution versus time, using the Landau global oscillator model. Proper orthogonal decomposition of the three-dimensional fields allowed identification of the most energetic modes and three-dimensional flow reconstruction involving a reduced number of modes.