Nonlinear theory of hydrodynamic stability and bifurcations of solutions of the Navier-Stokes equations

DOI10.1007/BF01051290zbMath0711.76039MaRDI QIDQ922870

B. Yu. Skobelev

Publication date: 1990

Published in: Fluid Dynamics (Search for Journal in Brave)

zbMATH Keywords

Navier-Stokes equationsplane Poiseuille flowfinite-dimensional invariant manifoldsnonlinear development of disturbancestheory of invariant manifoldstwo- dimensional invariant projection

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Nonlinear effects in hydrodynamic stability (76E30) Navier-Stokes equations (35Q30)

Cites Work

• Unnamed Item
• Subcritical autooscillations and nonlinear neutral curve for Poiseuille flow
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• The onset of auto-oscillations in a fluid
• On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow
• On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow
• On Itoh's finite amplitude stability theory for pipe flow
• Finite-amplitude instability of parallel shear flows
• A non-linear instability theory for a wave system in plane Poiseuille flow
• Non-linear resonant instability in boundary layers

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