Periodically forced centrifugally unstable flows

                                   by

                               John Lopez
           Department of Mathematics, Arizona State University

               INSCC 110, 3:30pm  Monday, October 5, 1998


                                Abstract

                           
Recent experiments (Weisberg, Kevrekidis & Smits J. Fluid Mechanics 1997) 
have demonstrated that the centrifugal instability leading to
Taylor vortex flow can be controlled by harmonic oscillations of the inner
cylinder in the axial direction. Marques & Lopez (J. Fluid Mechanics 1997) 
used (linear) Floquet analysis to describe the observed control of the
instability over a wide range of frequencies and amplitudes of this 
oscillation; the dynamics remained axisymmetric and the response
to the applied periodic control mechanism was synchronous. However, 
for large amplitudes of oscillations with small frequencies, the response
is neither axisymmetric nor synchronous, and competition between
different azimuthal and axial modes is important. Here, we
present some further Floquet analysis in the parameter regime where
experimentally the onset is to ``wobbly'' Taylor cells, i.e. the
bifurcated flow is quasiperiodic and not axisymmetric. We also
implement an accurate and  efficient spectral-projection scheme
for solving the fully nonlinear axisymmetric Navier-Stokes equations
to examine the effects of endwalls and the breaking of space-time
symmetries.  


Request for preprints and reprints to lopez@math.la.asu.edu
This information can be found at http://www.math.utah.edu/research/