Orthonormal Polynomial Wavelets on the Interval and Applications to the Analysis of Turbulent Flow Fields

We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomials. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind. The one-dimensional transform is applied to analytical data and appropriate definitions of a scalogram as well as local and global spectra are presented. The transform is then extended to the multi-dimensional case. Analyses of oneand twodimensional data from a direct numerical simulation of turbulent channel flow demonstrate the potential of the method.