Flow asymmetry over a body of revolution

This paper investigates the mean flow asymmetry about the meridional plane in crossflow over a 6 : 1 prolate spheroid using high-fidelity numerical simulations. A series of direct numerical simulations are performed at diameter-based Reynolds number $\textit{Re}_{\!D} = 3.0 \times 10^3$ over a range of angles of attack. We identify a critical angle of attack for the onset of mean flow asymmetry between $40^\circ$ and $42^\circ$ . In cases where asymmetry eventually develops, the flow initially remains symmetric for an extended period before turbulent fluctuations in the wake perturb the symmetry. As wake turbulence becomes more vigorous at higher Reynolds numbers, this observation suggests a reduced critical angle of attack – an expectation confirmed by simulations at $\textit{Re}_{\!D} = 6.0 \times 10^3$ . To investigate the mechanism responsible for the asymmetry, we propose a new measure of mean asymmetry and derive a corresponding transport equation from the Navier–Stokes equations. This formulation identifies the production and destruction terms governing the evolution of asymmetry. Our analysis of the equation reveals that the generation mechanism is primarily inviscid, suggesting that the findings at low Reynolds number may extend to higher Reynolds numbers. Finally, we present spectral analyses of the force and moment histories at $45^\circ$ angle of attack, revealing two dominant frequencies and their physical origin, and quantifying inter-scale interactions by applying amplitude modulation analysis to the force and moment signals.