Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiquesVol. CXXXIII, No. 31, pp. 29–40 (2006)
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Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques Vol. CXXXIII, No. 31, pp. 29–40 (2006) |
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On a model equation that reflects some of the shear flow hydrodynamic stability propertiesV. D. DjordjevicAbstract: A model equation is proposed in the paper that mimics some of the shear flow hydrodynamic stability properties. It contains the basic velocity profile, which can be arbitrarily chosen, and a nonlinear term, whose form can be appropriately adjusted to any particular problem. Full linear and weakly nonlinear theories for the Bickley jet velocity profile are elaborated. The solution of the linear problem is obtained in terms of associated Legendre functions. Within the weakly nonlinear theory a Landau equation is derived that describes the evolution of the perturbations near the critical wave number. The conditions for supercritical stability and subcritical instability are revealed. Keywords: model equation, shear flows, linear stability theory, weakly nonlinear stability theory, Landau equation Classification (MSC2000): 76E05, 76E30 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
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