Linear instability of plane Couette and Poiseuille flows

• Published in: Journal of experimental and theoretical physics Vol. 122; no. 5; pp. 925 - 931
• Main Authors: Chefranov, S. G., Chefranov, A. G.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.05.2016; Springer
• Subjects: Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COUETTE FLOW; DISTURBANCES; Elementary Particles; HYDRODYNAMICS; INSTABILITY; LAMINAR FLOW; Nonlinear; Particle and Nuclear Physics; PERIODICITY; Physics; Physics and Astronomy; Quantum Field Theory; Relativity Theory; REYNOLDS NUMBER; Soft Matter Physics; Solid State Physics; STABILITY; Statistical
• ISSN: 1063-7761; 1090-6509
• DOI: 10.1134/S1063776116050034

It is shown that linear instability of plane Couette flow can take place even at finite Reynolds numbers Re > Re th ≈ 139, which agrees with the experimental value of Re th ≈ 150 ± 5 [16, 17]. This new result of the linear theory of hydrodynamic stability is obtained by abandoning traditional assumption of the longitudinal periodicity of disturbances in the flow direction. It is established that previous notions about linear stability of this flow at arbitrarily large Reynolds numbers relied directly upon the assumed separation of spatial variables of the field of disturbances and their longitudinal periodicity in the linear theory. By also abandoning these assumptions for plane Poiseuille flow, a new threshold Reynolds number Re th ≈ 1035 is obtained, which agrees to within 4% with experiment—in contrast to 500% discrepancy for the previous estimate of Re th ≈ 5772 obtained in the framework of the linear theory under assumption of the “normal” shape of disturbances [2].