Wavelets and turbulence



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Texas Tech University


In this thesis, the issue of estimating intermittency rates in localized phenomena using wavelets will be addressed. This problem was earlier addressed by Gamage and Hagelberg in [6,8,9]. Here we present an approached based on coherent structure detection. The statistical problem is different from detecting single events, in which the false alarm rate (concluding the signal is coherent when it is actually not) or the size of the test must be controlled for the entire time series. Our new statistical technique controls the false alarm rate for each scale at each time sample, thereby controlling the total false alarm intermittency rate. This is done with a scale-dependent threshold for the wavelet coefficients, which allows two conclusions: that a signal contains intermittent localized phenomena, and that these phenomena are localized to specific time intervals in the signal. The algorithm is statistically rigorous and appropriate for long time series.