Coherent structures and two-dimensionalization in rotating turbulent flow
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We study laboratory-produced fluid turbulence under the influence of rapid rotation. Three-dimensional (3D) turbulence is generated by strong pumping through sources and sinks at the bottom of a rotating tank (48.4 cm high, 39.4 cm diameter) filled with water. This flow evolves toward quasi-two-dimensional (quasi-2D) turbulence with increasing height in the tank. Digital Particle Image Velocimetry (DPIV) measurements were taken using tracer particles illuminated by a horizontal laser light-sheet. The quasi-2D flow near the top of the tank contains many long-lived coherent vortices and jets with a wide range of sizes near the top of the tank. The vertical vorticity field exhibits complex dynamics such as vortex birth, merger, scattering, and destruction. Measurements using two synchronized cameras and vertically separated light sheets revealed coherent structures that were columnar and extended vertically throughout the tank. The effect of rotation greatly increased the vertical correlation of the flow, even for small rotation rates. A gradual decay in the correlation of increasingly vertically separated vii planes was observed, rather than a sharp transition. The discrete wavelet packet transform (DWPT) and discrete wavelet transform (DWT) were used to extract and study the dynamics of the localized coherent structures near the top of our tank. We separated the flow into a low-entropy “coherent” and a highentropy “incoherent” component by thresholding the coefficients of the DWPT and DWT of the vorticity field. Similar thresholdings using the Fourier transform and JPEG compression, the Okubo-Weiss criterion and Proper Orthogonal Decomposition (POD) were also tested. We found that the DWPT and DWT yield similar results and are much more efficient at representing the total flow than other methods. Only about 3% of the largeamplitude coefficients of the DWPT and DWT were necessary to represent the coherent component and preserve the vorticity probability density function, transport properties, and spatial and temporal correlations of the measured fields. 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 faithfully describe and simulate such turbulent flow using a relatively small number of wavelet or wavelet packet modes.