A doubly localized equilibrium solution of plane Couette flow
نویسندگان
چکیده
منابع مشابه
Snakes and ladders: localized solutions of plane Couette flow.
We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in one spatial dimension. Solutions of different size are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations. These new solutions are a step towards ...
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We survey equilibria and traveling waves of plane Couette flow in small periodic cells at moderate Reynolds number Re, adding in the process eight new equilibrium and two new traveling wave solutions to the four solutions previously known. Bifurcations under changes of Re and spanwise period are examined. These non-trivial solutions can only be computed numerically, but they are 'exact' in the ...
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The energy gradient theory has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this theory, it is suggested that the transition to turbulence depends on the relative magnitudes of the energy gradient amplifying the disturbance and the viscous friction damping that disturbance. For a given flow geometry and fluid propert...
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The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it reproduces the globally sub-critical behavior typical of this flow. In particular, the statistics of turbulent transients at decay from turbulent to laminar fl...
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Plane Couette ow perturbed by a spanwise oriented ribbon, similar to a con guration investigated experimentally at CEA-Saclay, is investigated numerically using a spectral-element code. 2D steady states are computed for the perturbed con guration; these di er from the unperturbed ows mainly by a region of counter-circulation surrounding the ribbon. The 2D steady ow loses stability to 3D eigenmo...
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ژورنال
عنوان ژورنال: Journal of Fluid Mechanics
سال: 2014
ISSN: 0022-1120,1469-7645
DOI: 10.1017/jfm.2014.285