EMIS ELibM Electronic Journals 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 properties

V. D. Djordjevic

Abstract: 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

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Electronic fulltext finalized on: 10 Jun 2006. This page was last modified: 20 Jun 2011.

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