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Bifurcations of a steady-state solution to the two-dimensional Navier-Stokes equations

Bifurcations of a steady-state solution to the two-dimensional Navier-Stokes equations
Bifurcations of a steady-state solution to the two-dimensional Navier-Stokes equations
This paper studies the spatially periodic Navier-Stokes flows in R2 driven by a unidirectional external force. This dynamical system admits a steady-state solution u0 for all Reynolds numbers. u0 is the basic flow in our consideration, and primary bifurcations of u0 are investigated. In particular, it is found that there exists a flow invariant subspace containing cos(mx+ny) or sin(mx+ny), and the occurrence of stability and bifurcations of u0 in such a subspace essentially depends on the choice of the integers m and n. Our findings are obtained by analysis together with numerical computation.
0010-3616
117-138
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f

Chen, Zhi-Min (1999) Bifurcations of a steady-state solution to the two-dimensional Navier-Stokes equations. Communications in Mathematical Physics, 201 (1), 117-138. (doi:10.1007/s002200050551).

Record type: Article

Abstract

This paper studies the spatially periodic Navier-Stokes flows in R2 driven by a unidirectional external force. This dynamical system admits a steady-state solution u0 for all Reynolds numbers. u0 is the basic flow in our consideration, and primary bifurcations of u0 are investigated. In particular, it is found that there exists a flow invariant subspace containing cos(mx+ny) or sin(mx+ny), and the occurrence of stability and bifurcations of u0 in such a subspace essentially depends on the choice of the integers m and n. Our findings are obtained by analysis together with numerical computation.

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More information

Published date: 1999
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 204453
URI: http://eprints.soton.ac.uk/id/eprint/204453
ISSN: 0010-3616
PURE UUID: 4c903355-6623-4fa6-9f04-e9d015ed8d0f

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Date deposited: 29 Nov 2011 15:38
Last modified: 16 Jul 2019 23:17

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