Wake dynamics of permeable disks across the transition from steady to chaotic flow

We numerically investigate the steady and unsteady wakes of three-dimensional permeable disks over Reynolds number ( $\textit{Re}$ ) range 100–300 and Darcy number ( $Da$ ) range $10^{-9}$ – $10^{-3}$ . For disks with low permeability ( $Da\le 8\times 10^{-5}$ ), the dynamical transition route is the same as that of impervious disks, with the critical $\textit{Re}$ for all bifurcations increasing with decreasing permeability. In contrast, for disks with high permeability ( $Da\ge 2\times 10^{-4}$ ), all unsteady bifurcations are suppressed, and the wake remains in a steady regime throughout the $\textit{Re}$ range considered. Interestingly, at moderate $Da$ , permeability gives rise to two previously unreported flow regimes. The first is the ‘SVR breathing’ regime, occurring at $Da\approx 10^{-4}$ and $\textit{Re}\approx 200$ , and is attributed to the subharmonic lock-in between two distinct unsteady dynamics: the shedding of hairpin vortices and the low-frequency unsteadiness of the near-wake recirculation regions. The second is the ‘intermittency’ regime, which occurs at $Da\approx 1.5\times 10^{-4}$ , $\textit{Re}\approx 200$ ; the wake alternates irregularly between two periodic modes with orthogonal planes of symmetry. Future work might include verifying whether intermittency arises from the energy competition between two modes, as the vortices lack sufficient energy to sustain stable single-mode harmonic oscillations. These findings demonstrate that permeability can fundamentally alter wake dynamics and introduce new wake structures that do not occur on an impervious disk.