Characterizing the spatiotemporal dynamics of turbulence

This paper introduces a new wavelet-based approach for characterizing the dynamics of turbulence. The proposed approach reduces the dynamics of turbulence into a number of time series, each at a different spatial scale. The effectiveness of the proposed method is illustrated by freely decaying two-dimensional turbulence, which shows three distinct dynamic stages in the present wavelet representation. Increase of the wavelet energies in the large scale subbands characterizes the inverse energy transfer. Moreover, an anomalous transfer of the subband energy and enstrophy among spatial scales is observed during the transient stage. The decaying of the subscale enstrophies exhibits power law scaling and, interestingly, the decay rates increase monotonically with the refinement of the scales.