Modal analysis of bluff body wakes

TL;DR

This study uses spectral proper orthogonal decomposition to analyze the dominant flow modes in unstratified and stratified wakes behind a circular disk at high Reynolds numbers, revealing different dominant modes and their roles in wake dynamics and wave generation.

Contribution

It provides a detailed comparison of flow structures in stratified and unstratified wakes at high Reynolds numbers using SPOD, highlighting the role of vortex shedding and double helix modes.

Findings

Vortex shedding mode dominates near the wake in unstratified flows.

Double helix mode becomes dominant at far downstream in unstratified wakes.

Vortex shedding mode is responsible for internal gravity wave generation in stratified 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.