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Linear and nonlinear instabilities of sliding Couette flow

  • K. DeguchiEmail author
  • M. Nagata
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 132)

Abstract

We consider an incompressible viscous fluid with the kinematic viscosity v between two infinitely long concentric cylinders with radii a and b (b > a). The fluid experiences a shear motion produced by pulling the inner cylinder with the axial speed U while keeping the outer cylinder at rest (see Fig.1). The axial basis flow at the radius r,
$$U_{B}(r) = R\frac{\ln(r(1 - \eta)/2)}{\ln(\eta)},$$
can be obtained as an exact solution of the Navier-Stokes equation, where \(R = U(b - a)/2v\) is the Reynolds number and \(\eta = a/b\) is the radius ratio.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Aeronautics and Astronautics, Graduate School of EngineeringKyoto UniversityKyotoJAPAN

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