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The wake flow past an axisymmetric body of revolution at a diameter-based Reynolds number$$Re=u_{\infty }D/\nu =5000$$is investigated via a direct numerical simulation. The study is focused on identification of coherent vortical motions and the dominant frequencies in this flow. Three dominant coherent motions are identified in the wake: the vortex shedding motion with the frequency of$$St=fD/u_{\infty }=0.27$$, the bubble pumping motion with$$St=0.02$$, and the very-low-frequency (VLF) motion originated in the very near wake of the body with the frequency$$St=0.002$$–$$0.005$$. The vortex shedding pattern is demonstrated to follow a reflectional symmetry breaking mode, whereas the vortex loops are shed alternatingly from each side of the vortex shedding plane, but are subsequently twisted and tangled, giving the resulting wake structure a helical spiraling pattern. The bubble pumping motion is confined to the recirculation region and is a result of a Görtler instability. The VLF motion is related to a stochastic destabilisation of a steady symmetric mode in the near wake and manifests itself as a slow, precessional motion of the wake barycentre. The VLF mode with$$St=0.005$$is also detectable in the intermediate wake and may be associated with a low-frequency radial flapping of the shear layer.
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Characterization of energy transfer and triadic interactions of coherent structures in turbulent wakes
Turbulent wakes are often characterized by dominant coherent structures over disparate scales. Dynamics of their behaviour can be attributed to interscale energy dynamics and triadic interactions. We develop a methodology to quantify the dynamics of kinetic energy of specific scales. Coherent motions are characterized by the triple decomposition and used to define mean, coherent and random velocity. Specific scales of coherent structures are identified through dynamic mode decomposition, whereby the total coherent velocity is separated into a set of velocities classified by frequency. The coherent kinetic energy of a specific scale is defined by a frequency triad of scale-specific velocities. Equations for the balance of scale-specific coherent kinetic energy are derived to interpret interscale dynamics. The methodology is demonstrated on three wake flows: (i)$${Re}=175$$flow over a cylinder; (ii) a direct numerical simulation of$${Re}=3900$$flow over a cylinder; and (iii) a large-eddy simulation of a utility-scale wind turbine. The cylinder wake cases show that energy transfer starts with vortex shedding and redistributes energy through resonance of higher harmonics. The scale-specific coherent kinetic energy balance quantifies the distribution of transport and transfer among coherent, mean and random scales. The coherent kinetic energy in the rotor scales and the hub vortex scale in the wind turbine interact to produce new scales. The analysis reveals that vortices at the blade root interact with the hub vortex formed behind the nacelle, which has implications for the proliferation of scales in the downwind near wake.
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- Award ID(s):
- 2136371
- PAR ID:
- 10487171
- Publisher / Repository:
- Journal of Fluid Mechanics
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 971
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.641
