Computational study of subcritical response in flow past a circular cylinder

TL;DR

This study analyzes the transient response of flow past a circular cylinder in the subcritical regime, revealing energy amplification phenomena and vortex structures, with implications for flow stability and transition prediction.

Contribution

It provides a detailed computational analysis of subcritical flow response, including energy amplification and vortex dynamics, extending understanding below the vortex shedding threshold.

Findings

Energy amplification occurs as low as Re=2.2.

Maximum energy amplification reaches 6800 at Re_c.

Transient vortex streets are observed in optimal dynamics.

Abstract

Flow past a circular cylinder is investigated in the subcritical regime, below the onset of Benard-von Karman vortex shedding at Re_c ~ 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 Re=2.2. Throughout much of the subcritical regime the maximum energy amplification increases approximately exponentially in the square of Re reaching 6800 at Re_c$. The spatiotemporal structure of the optimal transient dynamics is shown to be transitory Benard-von Karman vortex streets. At Re ~ 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.