Construction of circle bifurcations of a two-dimensional spatially periodic flow

[摘要] The study by Yudovich [V.I. Yudovich, Example of the generation of a secondary stationary or periodic flow when there is loss of stability of the laminar flow of a viscous incompressible fluid, J. Math. Mech. 29 (1965) 587-603] on spatially periodic flows forced by a single Fourier mode proved the existence of two-dimensional spectral spaces and each space gives rise to a bifurcating steady-state solution. The investigation discussed herein provides a structure of secondary steady-state flows. It is constructed explicitly by an expansion that when the Reynolds number increases across each of its critical values, a unique steady-state solution bifurcates from the basic flow along each normal vector of the two-dimensional spectral space. Thus, at a single Reynolds number supercritical value, the bifurcating steady-state solutions arising from the basic solution form a circle. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01

[关键词] steady-state bifurcation;pitchfork bifurcation;Navier-Stokes equation;Kolmogorov flow