Mechanisms of the asymmetric-to-symmetric transition in the near wake of a wall-proximity sphere

Symmetry-breaking in the near-wake of a wall-proximity sphere is a claussic problem. Yet a clear understanding of how the gap ratio (

) governs the evolution and suppression of spanwise flow asymmetry across different Reynolds numbers (

upper R e R e $Re$

) is still lacking. Here, direct numerical simulations combined with proper orthogonal decomposition and vorticity transport analysis are employed over

420 less than or slanted equals upper R e less than or slanted equals 600 420 ⩽ R e ⩽ 600 $420 \leqslant Re \leqslant 600$

and

0.1 less than or slanted equals upper G divided by upper D less than or slanted equals 1.5 0.1 ⩽ G / D ⩽ 1.5 $0.1 \leqslant G/D \leqslant 1.5$

to elucidate the wall-induced suppression of spanwise asymmetry. As

upper G divided by upper D G / D $G/D$

decreases, four regimes are identified: asymmetric unsteady II, asymmetric unsteady I, symmetric unsteady and symmetric steady. Notably, the spanwise wake deflection reverses direction between the two asymmetric regimes, signalling a structural transition regulated by vortical competition. This corresponds to the transition from the alternating shedding of upper and lower hairpin vortices to the formation of longitudinal vortices (LV) that interact with wall-secondary vortices (WSV). Symmetry restoration is associated with merging and the emergence of the second harmonic of the dominant shedding frequency. Crucially, the wall effect homogenises the streamwise pressure gradient and velocity-gradients in the spanwise direction. This gradient homogenisation attenuates the asymmetric tilting of spanwise vorticity, thereby reducing the feedback that maintains the spanwise asymmetry of the shear layer. In asymmetric regimes, wake deflection is sustained by dominant spanwise-asymmetric vorticity tilting into streamwise and wall-normal components. In the symmetric regime, suppression of the spanwise deflection of the shear layer supports wake-symmetry recovery. These findings provide insights into symmetry-breaking in wall-proximity bluff-body wakes, and offer guidance for active flow control.