Wake dynamics and transition of the flow around a square cylinder sliding along a wall

Abstract

The dynamics and transitions of the flow past a square cylinder sliding along a wall are investigated numerically for Reynolds numbers (Re) between 20 and 300, and gap distances (G) between 0.05 and 1.0 side length of the square (D). The presence of the wall is found to fundamentally alter the wake dynamics and three-dimensional transitions of the wake. The two-dimensional computations show that, for G/D≥0.2, the onset of vortex shedding is delayed to higher Reynolds number with decreasing gap ratio. A period-doubling shedding regime is identified for G/D≥0.8 at higher Re, driven by a feedback mechanism where the vortex formed by the shear layer from the top of the cylinder modulates subsequent shedding. The transition from two-dimensional to three-dimensional flow using linear stability analysis is studied. Results show that the wake initially undergoes a regular bifurcation from a steady two-dimensional flow to a steady three-dimensional wake for G/D≤0.35. In this regime, Floquet stability analysis of the periodic base flow reveals the complex behavior of three-dimensional instabilities. For G/D≥0.36, five separate instability modes (two subharmonic modes, two synchronous modes, and one periodic mode) bifurcating from the unsteady base flow are identified. Curves of marginal stability for all of the modes are presented in a parameter space map, and the associated characteristics of each mode are analyzed in detail.