A possibility of realizing the Landau—Hopf scenario in the problem of tube oscillations under the action of a fluid flow

We consider a boundary-value problem for a quasilinear partial differential equation describing tube oscillations under the action of a fluid flow. We show that the well-known Landau—Hopf scenario of transition to turbulence is realized in the considered evolution boundary-value problem with a suita...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2020-04, Vol.203 (1), p.501-511
Main Authors: Kulikov, A. N., Kulikov, D. A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Asymptotic methods
Boundary value problems
Canonical forms
Fluid dynamics
Fluid flow
Mathematical analysis
Mathematical and Computational Physics
Oscillations
Partial differential equations
Physics
Physics and Astronomy
Theoretical
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Summary:We consider a boundary-value problem for a quasilinear partial differential equation describing tube oscillations under the action of a fluid flow. We show that the well-known Landau—Hopf scenario of transition to turbulence is realized in the considered evolution boundary-value problem with a suitable choice of the governing parameter. To study the problem, we use the theory of infinite-dimensional dynamical systems. In particular, we use the method of integral manifolds, normal forms, and also asymptotic methods of analysis.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577920040066