Lighthill's mechanism and vorticity cascade in the logarithmic layer of wall turbulence
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915486780882944 |
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| author | Kumar, Samvit Toedtli, Simon Zaki, Tamer A. Eyink, Gregory |
| author_facet | Kumar, Samvit Toedtli, Simon Zaki, Tamer A. Eyink, Gregory |
| contents | We investigate Lighthill's proposed turbulent mechanism for near-wall concentration of spanwise vorticity by calculating mean flows conditioned on motion away from or toward the wall in an $Re_τ=1000$ database of plane-parallel channel flow. Our results corroborate Lighthill's proposal throughout the entire logarithmic layer, but extended by counterflows that help explain anti-correlation of vorticity transport by advection and by stretching/tilting. We present evidence also for Lighthill's hypothesis that the vorticity transport in the log-layer is a ``cascade process'' through a scale-hierarchy of eddies, with intense competition between transport outward from and inward to the wall. Townsend's model of attached eddies of hairpin-vortex type accounts for half of the vorticity cascade, whereas we identify necklace-type or ``shawl vortices'' that envelop turbulent sweeps as supplying the other half. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07746 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lighthill's mechanism and vorticity cascade in the logarithmic layer of wall turbulence Kumar, Samvit Toedtli, Simon Zaki, Tamer A. Eyink, Gregory Fluid Dynamics We investigate Lighthill's proposed turbulent mechanism for near-wall concentration of spanwise vorticity by calculating mean flows conditioned on motion away from or toward the wall in an $Re_τ=1000$ database of plane-parallel channel flow. Our results corroborate Lighthill's proposal throughout the entire logarithmic layer, but extended by counterflows that help explain anti-correlation of vorticity transport by advection and by stretching/tilting. We present evidence also for Lighthill's hypothesis that the vorticity transport in the log-layer is a ``cascade process'' through a scale-hierarchy of eddies, with intense competition between transport outward from and inward to the wall. Townsend's model of attached eddies of hairpin-vortex type accounts for half of the vorticity cascade, whereas we identify necklace-type or ``shawl vortices'' that envelop turbulent sweeps as supplying the other half. |
| title | Lighthill's mechanism and vorticity cascade in the logarithmic layer of wall turbulence |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2509.07746 |