Geodesic
On a model equation that reflects some of the shear flow hydrodynamic stability properties
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1.

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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 ađusted 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. 
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     author = {V. D. {\DJ}or{\dj}evi\'c},
     title = {On a model equation that reflects some of the shear flow hydrodynamic stability properties},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {29 - 40},
     publisher = {mathdoc},
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}
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V. D. Đorđević. On a model equation that reflects some of the shear flow hydrodynamic stability properties. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 31 (2006) no. 1. http://geodesic.mathdoc.fr/item/BASS_2006_31_1_a2/