Geodesic
Evolution of three-dimensional picture of disturbances imposed on~a~rotational-axial flow in a cylindrical clearance
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 345-354

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This work deals with stability relative to three-dimensional disturbances of a compound rotational-axial shear flow of Newtonian viscous fluid inside a cylindrical clearance. The corresponding linearized problem on stability is stated with the sticking conditions. On the basis of the integral relation method permitting to obtain sufficient estimates of stability as well as lower estimates for critical Reynolds numbers, the general upper estimate of real part of a spectral parameter (responding to stability) is derived. This estimate is defined more exactly for cases of both three-dimensional axially symmetric disturbances and two-dimensional non-axially symmetric ones.
Keywords: Newtonian fluid, cylindrical clearance, shear flow, the integral relation method, quadratic functional, variational inequality, stability, critical Reynolds number.
Mots-clés : rotation 
@article{ND_2014_10_3_a7,
     author = {Dmitrii V. Georgievskii},
     title = {Evolution of three-dimensional picture of disturbances imposed on~a~rotational-axial flow in a cylindrical clearance},
     journal = {Russian journal of nonlinear dynamics},
     pages = {345--354},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_3_a7/}
}
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Dmitrii V. Georgievskii. Evolution of three-dimensional picture of disturbances imposed on~a~rotational-axial flow in a cylindrical clearance. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 3, pp. 345-354. http://geodesic.mathdoc.fr/item/ND_2014_10_3_a7/