Flow past a circular cylinder is investigated in the subcritical regime, below the onset of Bénard-von Kármán vortex shedding at Reynolds number ${\text{Re}}_c\simeq 47$. The transient response of infinitesimal perturbations is computed. The domain requirements for obtaining converged results is discussed at length. It is shown that energy amplification occurs as low as $\text{Re}=2.2$. Throughout much of the subcritical regime the maximum energy amplification increases approximately exponentially in the square of Re reaching 6800 at ${\text{Re}}_c$. The spatiotemporal structure of the optimal transient dynamics is shown to be transitory Bénard-von Kármán vortex streets. At $\text{Re}\simeq 42$ the long-time structure switches from exponentially increasing downstream to exponentially decaying downstream. Three-dimensional computations show that two-dimensional structures dominate the energy growth except at short times.

• Received 19 May 2010

DOI:https://doi.org/10.1103/PhysRevE.82.026315