Modal analysis of bluff body wakes

Abstract: Spectral proper orthogonal decomposition (SPOD) analyses are performed for unstratified and stratified wakes of a circular disk at Reynolds number, $U_\infty D/\nu = 50,000$, where $U_\infty$ is the freestream velocity and $D$ is the diameter of the circular disk. At $Re= 50,000$, three diameter-based Froude numbers, $\Fro = U_\infty/ND = \infty$, $2$ and $10$ are analyzed. We find that in the unstratified configuration, two modes: (i) the vortex shedding (VS) mode ($m=1, \Str = 0.135$) and (ii) the double helix (DH) mode ($m=2, \Str \rightarrow 0$) are the most dominant features. At far-downstream distances, DH mode is dominant while at near and intermediate locations, VS mode dominates the energetics. Reconstruction of TKE and Reynolds shear stresses are also explored at near and far wake locations. In the stratified cases ($\Fro = 2$ and $10$), the vortex shedding mode (at $\Str \approx 0.13-0.14$) dominates the wake. At intermediate to late streamwise locations ($x/D$), we establish through pressure wave flux reconstruction that the VS mode is responsible for the internal gravity wave (IGW) generation. A comparison between the SPOD decomposition analyses between $Re =5000$ and $Re = 50,000$ is also performed at $\Fro =2$. Preliminary results show that the low-$Re$ wake is also dominated by the VS mode but exhibits more coherence, namely higher contribution of leading SPOD modes, than the high-$Re$ wake.