A New Wavelet : RI-Spline Wavelet and its Application to Unsteady Turbulence Analysis

Abstract

In this paper, we propose a new complex-type wavelet which we call the RI-Spline wavelet. We show that the RI-Spline wavelet satisfies the admissibility condition and bi-orthogonal condition. That is, the RI-Spline wavelet can be used for continuous and discrete wavelet transform as mother wavelet. We confirm the effectiveness of this wavelet in continuous and discrete cases by using a model signal and applying it to unsteady turbulence analysis. The main results obtained can be summarized as follows : the eddy structure and the energy transportation process of the turbulence can be shown very well. The unsteady turbulence intensity, which is derived from the discrete wavelet transform, is also effective for examining quantitatively the change of the unsteady turbulence energy in terms of time. Our results demonstrate the advantages of our approach.