Bifurcation phenomena in a finite-length Taylor-Couette flow system have been observed by an electrochemical technique. The axial wavelength was varied as the characteristic parameter of vortex cell structure by varying the aspect ratio of the annular flow space and controlling the inner cylinder acceleration up to a steady rotation speed. Multi-resolution analysis in wavelets was used not only for noise reduction, but also for extraction of low frequency components from the experimental time-series data. When the dimensionless axial wavelength lambda/d < 1, the first fundamental frequency f(1)/f(r) of singly periodic wavy vortex flow was fixed at a unique value independent of the magnitude of lambda/d. When lambda/d greater than or equal to 1, on the other hand, f(1) was not fixed uniquely but showed some variation, depending on the magnitude of lambda/d. In the transition to doubly periodic wavy vortex flow, not only Hopf bifurcation but also two-cycle period doubling bifurcation occurred in some cases when lambda/d < 1, The first and second fundamental frequencies, f(1) and f(2) have tendencies to increase with increasing lambda/d in spite of some exceptions. In the process of a transition to weakly turbulent wavy vortex flow, two-torus motion in phase space broke up at all wavelengths without frequency locking.