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Turbulent-laminar patterns in shear flows without walls
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Chantry, Matthew, Tuckermann, Laurette S. and Barkley, Dwight (2016) Turbulent-laminar patterns in shear flows without walls. Journal of Fluid Mechanics, 791 . doi:10.1017/jfm.2016.92
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Official URL: http://dx.doi.org/10.1017/jfm.2016.92
Abstract
Turbulent–laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow – the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatiotemporal phenomena observed in transition, from spot growth to turbulent bands and uniform turbulence. The model substantially reduces the cost of simulating intermittent turbulent structures while maintaining the essential physics and a direct connection to the Navier–Stokes equations. We demonstrate the generic nature of this process by introducing stress-free equivalent flows for plane Poiseuille and pipe flows that again capture the turbulent–laminar structures seen in transition.
| Item Type: | Journal Article | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||||
| Divisions: | Faculty of Science > Mathematics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Turbulence -- Mathematical models, Fluid dynamics | ||||||||||
| Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||||
| Publisher: | Cambridge University Press | ||||||||||
| ISSN: | 0022-1120 | ||||||||||
| Official Date: | March 2016 | ||||||||||
| Dates: |
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| Date of first compliant deposit: | 25 August 2016 | ||||||||||
| Volume: | 791 | ||||||||||
| Number of Pages: | 14 | ||||||||||
| DOI: | 10.1017/jfm.2016.92 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Funder: | France. Agence nationale de la recherche (ANR) | ||||||||||
| Grant number: | Grant TRANSFLOW | ||||||||||
| Adapted As: | |||||||||||
| Open Access Version: |
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