CRPC-TR99807-S						September 1999

Title: Bifurcations in Kolmogorov and Taylor-Vortex Flows

Authors: Philip Love

Submitted November 1999

Abstract:

     The bifurcation structure of Kolmogorov and Taylor-Vortex flows was
computed with the aid of the Recursive Projection Method; see Schroff and
Keller [32].  It was shown that RPM significantly imnproves the
convergence of our numerical mehtod while calculationg steady state
solutions.  Moreover we use RPM to detect bifurcation points while
continuing along solution branches, and to provide the required
augmentation when continuing around a fold, or along a travelling wave
branch.
     The bifurcations to two and three-dimensional solutions from the
shear flow solution of Kolmogorov flow are calculated both numerically, by
solving an ordinary differential equation, and analytically, using an
approximation method.  Our results for the two-dimensional bifurcations
agree with the work of Meshalkin and Sinai [26].
     We also explain how the branches of Kolmogorov flows observed by
Platt and Sirovich [29] are connected together, and observe that our
solutions have worm like structures even at relatively low Reynolds
numbers.  Various statistics of our flows are calculated and compare with
those from isotropic trubulence calculations.
     Additionally various solutions branches of the Taylor Vortex flow
were computed, including spiral vortices.  Furthermore, it was discovered
that the Wavy Taylor Vortex branches arise from sub-critical Hopf
bifurcaations, and they undergo a fold colse to their bifurcation point.

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Philip Love
California Institute of Technology