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Stability Analysis of Navier–Stokes Flows in Annuli
Author(s) -
Fujita H.,
Morimoto H.,
Okamoto H.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(19970725)20:11<959::aid-mma895>3.0.co;2-d
Subject(s) - mathematics , streamlines, streaklines, and pathlines , reynolds number , compressibility , perturbation (astronomy) , navier–stokes equations , hydrodynamic stability , stability (learning theory) , mathematical analysis , mechanics , physics , machine learning , computer science , quantum mechanics , turbulence
We study the linearized stability of planer flows of incompressible, viscous fluid in two‐dimensional annular domains. A certain family of steady, explicit solutions which have spiral streamlines are considered. The Navier–Stokes equations are linearized at these solutions and we show analytically or numerically that these solutions are stable to perturbation of steady states, whatever the Reynolds number or the aspect ratio of the annuli may be. Hopf bifurcations from them are also examined numerically. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.