Multifractal Analysis of Vortex Pair Formation of Modified Taylor-Couette Flow in Laminar and Turbulent Regimes*

For sufficiently large effective Reynolds Numbers the formation of Taylor Vortex Pairs in Modified Taylor-Couette flow with hourglass geometry becomes irregular in time. At higher effective Reynolds Numbers the flow becomes turbulent, but Taylor Vortices may still be discerned. Again, for sufficiently high effective Reynolds Numbers, the formation of these vortex pairs becomes chaotic. Previously we have demonstrated that each process may be characterized as low dimensional chaos.\footnote{A. Kowalski, T. Olsen, \& R. Wiener, Bull. Am. Phys. Soc. \textbf{50-9}, P1.00030 (2006).} We now present a multifractal analysis\footnote{J. A. Glazier \& A. Libchaber, IEEE Trans. On Circuits and Systems \textbf{35-7}, 790 (1988).}$^,$\footnote{T. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, \& B. I. Shraiman, Phys. Rev. A \textbf{33}, 1141 (1986).} of these processes.