Extraction of coherent structures in a rotating turbulent flow experiment

Jori E. Ruppert-Felsot*, Olivier Praud, Eran Sharon, Harry L. Swinney

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


The discrete wavelet transform (DWT) and discrete wavelet packet transform (DWPT) are used to extract and study the dynamics of coherent structures in a turbulent rotating fluid. Three-dimensional turbulence is generated by strong pumping through tubes at the bottom of a rotating tank (48.4cm high, 39.4cm diameter). This flow evolves toward two-dimensional (2D) turbulence with increasing height in the tank. Particle image velocimetry measurements on the quasi-2D flow reveal many long-lived coherent vortices with a wide range of sizes. The vorticity field exhibits vortex creation, merger, scattering, and destruction. We separate the flow into a low-entropy "coherent" and a high-entropy "incoherent" component by thresholding the coefficients of the DWT and DWPT of the vorticity field. Similar thresholdings using the Fourier transform and JPEG compression together with the Okubo-Weiss criterion are also tested for comparison. We find that the DWT and DWPT yield similar results and are much more efficient at representing the total flow than a Fourier-based method. Only about 3% of the large-amplitude coefficients of the DWT and DWPT are necessary to represent the coherent component and preserve the vorticity probability distribution function (PDF), transport properties, and spatial and temporal correlations. The remaining small-amplitude coefficients represent the incoherent component, which has near Gaussian vorticity PDF, contains no coherent structures, rapidly loses correlation in time, and does not contribute significantly to the transport properties of the flow. This suggests that one can describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.

Original languageAmerican English
Article number016311
JournalPhysical Review E
Issue number1
StatePublished - Jul 2005
Externally publishedYes


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