Nonlinear Sciences – Cellular Automata and Lattice Gases
Scientific paper
1995-02-10
Nonlinear Sciences
Cellular Automata and Lattice Gases
latex file; 4 Figures will be sent, on request, by airmail or by fax (e-mail address: rauh at beta.physik.uni-oldenburg.de)
Scientific paper
In the subcritical interval of the Reynolds number 4320\leq R\leq R_c\equiv 5772, the Navier--Stokes equations of the two--dimensional plane Poiseuille flow are approximated by a 22--dimensional Galerkin representation formed from eigenfunctions of the Orr--Sommerfeld equation. The resulting dynamical system is brought into a generalized normal form which is characterized by a disposable parameter controlling the magnitude of denominators of the normal form transformation. As rigorously proved, the generalized normal form decouples into a low--dimensional dominant and a slaved subsystem. {}From the dominant system the critical amplitude is calculated as a function of the Reynolds number. As compared with the Landau method, which works down to R=5300, the phase velocity of the critical mode agrees within 1 per cent; the critical amplitude is reproduced similarly well except close to the critical point, where the maximal error is about 16 per cent. We also examine boundary conditions which partly differ from the usual ones.
Rauh Alexander
Zachrau T.
Zoller J.
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