dorsal/arxiv
View SchemaMean flow of turbulent-laminar patterns in plane Couette flow
| Authors | Dwight Barkley, Laurette S. Tuckerman |
|---|---|
| Categories | |
| ArXiv ID | physics/0701235 |
| URL | https://arxiv.org/abs/physics/0701235 |
| DOI | 10.1017/S002211200600454X |
| Journal | J. Fluid Mech. 576, 109-137 (2007) |
Abstract
A turbulent-laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasi-laminar region is not the linear Couette profile, but results from a non-trivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three cross-channel profiles as U(x,y,z) = U_0(y) + U_c(y) cos(kz) + U_s(y) sin(kz). A model is formulated which relates the cross-channel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic computational domain are presented. Observations of regular turbulent-laminar patterns in other shear flows -- Taylor-Couette, rotor-stator, and plane Poiseuille -- are compared.
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"abstract": "A turbulent-laminar banded pattern in plane Couette flow is studied\nnumerically. This pattern is statistically steady, is oriented obliquely to the\nstreamwise direction, and has a very large wavelength relative to the gap. The\nmean flow, averaged in time and in the homogeneous direction, is analysed. The\nflow in the quasi-laminar region is not the linear Couette profile, but results\nfrom a non-trivial balance between advection and diffusion. This force balance\nyields a first approximation to the relationship between the Reynolds number,\nangle, and wavelength of the pattern. Remarkably, the variation of the mean\nflow along the pattern wavevector is found to be almost exactly harmonic: the\nflow can be represented via only three cross-channel profiles as U(x,y,z) =\nU_0(y) + U_c(y) cos(kz) + U_s(y) sin(kz). A model is formulated which relates\nthe cross-channel profiles of the mean flow and of the Reynolds stress. Regimes\ncomputed for a full range of angle and Reynolds number in a tilted rectangular\nperiodic computational domain are presented. Observations of regular\nturbulent-laminar patterns in other shear flows -- Taylor-Couette,\nrotor-stator, and plane Poiseuille -- are compared.",
"arxiv_id": "physics/0701235",
"authors": [
"Dwight Barkley",
"Laurette S. Tuckerman"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1017/S002211200600454X",
"journal_ref": "J. Fluid Mech. 576, 109-137 (2007)",
"title": "Mean flow of turbulent-laminar patterns in plane Couette flow",
"url": "https://arxiv.org/abs/physics/0701235"
},
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