  Journal of Applied Mathematics and Mechanics Russian Academy of Sciences   Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 00218928 (print version) 
Archive of Issues
Total articles in the database:   1729 
In Russian (ÏÌÌ):   951

In English (J. Appl. Math. Mech.):   778 

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D.V. Georgiyevskii, "New estimates of the stability of onedimensional planeparallel flows of a viscous incompressible fluid," J. Appl. Math. Mech. 74 (4), 452459 (2010) 
Year 
2010 
Volume 
74 
Issue 
4 
Pages 
452459 
Title 
New estimates of the stability of onedimensional planeparallel flows of a viscous incompressible fluid 
Author(s) 
D.V. Georgiyevskii (Moscow, Russia, georgiev@mech.math.msu.ru) 
Abstract 
The stability of a number of onedimensional planeparallel steady flows of a viscous incompressible fluid is investigated analytically using the method of integral relations. The mathematical formulation is reduced to eigenvalue problems for the OrrSommerfeld equation. One of three versions is chosen as the boundary conditions: all the components of the velocity perturbation are equal to zero on both boundaries of the layer (in this case we have the classical OrrSommerfeld problem), all the components of the velocity perturbation on one of the boundaries are equal to zero and the perturbations of the shear component of the stress vector and of the normal component of the velocity are equal to zero on the other, and all the components of the velocity perturbation are equal to zero on one boundary and the other boundary should be free. The boundary conditions derived in the latter case, are characterized by the occurrence of a spectral parameter in them. For kinematic conditions the lower estimates of the critical Reynolds number  the JosephYih estimates, are improved. In the remaining cases the technique of the integralrelations method is developed, leading to new estimates of the stability. Analogs of Squire's theorem are derived for the boundary conditions of all the types mentioned above. Upper estimates of the increment of the increase in perturbations in eigenvalue problems for the Rayleigh equation with two types of boundary conditions are given. 
Received 
10 July 2008 
Link to Fulltext 
http://www.sciencedirect.com/science/journal/00218928 
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