The purpose of the present work is to investigate time-dependent flow properties in doubly periodic and weakly turbulent wavy vortex flows in a Taylor-Couette flow system with the aid of a wavelet analysis. Time series data of fluctuating tangential velocity were obtained with a fiberoptic laser-Doppler velocimeter. To clarify the dependence of time-fluctuation flow properties on spatial location, the velocity was measured at many positions within each vortex. In order to estimate wavelet correlation patterns, logarithmic expectation and information entropy were calculated at each time scale. The wavelet patterns revealed that the time-fluctuation properties depend not only on the spatial location but also on time. The continuous wavelet transform analysis can provide a promising technique to reveal the fractal structure of a chaotic wavy vortex now.