Transient energy growth in flow past a rotating cylinder

Abstract

After devoting to asymptotical instability for decades, the hydrodynamic community noticed that non-normality of the evolution operator for perturbations may have dominant effects over limited time horizons by inducing significant transient energy growth, especially in linearly stable/weakly unstable flows. In flow past a rotating cylinder, it has been observed that the unsteadiness and asymptotical instability associated with vortex shedding are suppressed over a wide range of the ratio between the rotating velocity and free stream velocity. In this work, we investigate the transient energy growth of initial perturbations in this stabilized flow and the physical relevance of the optimal initial perturbation. The nonlinear development of the initial perturbations is further studied by evolving the base flow initially perturbed by the optimal initial perturbation in DNS (Direct Numerical Simulation). As the initial perturbation is convected downstream, it is observed that the vortex shedding reassumes transiently.