Periodic waves in rotating plane Couette flow
Abstract
A class of nonlinear equations of NavierStokes type of the form (**) 33_2004_Article_BF00914350_TeX2GIFE1.gif {dw}/{dt} + L_0 w + (λ  λ _0 )L_1 w + γ λ (M_1 w + M_2 w) + γ ^2 L_3 (λ ,γ )w + B(w) = 0 is investigated, where λ is a “load” parameter (i.e., a Reynolds number), γ is a “structure” parameter, L _{o} L _{1}, M _{1}, M _{2} and L _{3}(λ, γ) are linear operators, and B is a quadratic operator. An equation of the form (**) describes a variety of spiral flow problems including rotating plane Couette flow which is studied here in detail. Under suitable hypotheses on the operators in (**), it is shown that Hopf bifurcation occurs for γ sufficiently small. In the problem of rotating plane Couette flow, by determining the sign of the real part of a certain “cubic” coefficient, it is shown, in addition, that the bifurcating periodic orbits are supercritical and asymptotically stable, and correspond to periodic waves.
 Publication:

Zeitschrift Angewandte Mathematik und Physik
 Pub Date:
 January 1993
 DOI:
 10.1007/BF00914350
 Bibcode:
 1993ZaMP...44....1K
 Keywords:

 Computational Fluid Dynamics;
 Couette Flow;
 Rotating Fluids;
 Boundary Conditions;
 Branching (Mathematics);
 Reynolds Number;
 Fluid Mechanics and Heat Transfer