New polynomial wavelets and their use for the analysis of wall–bounded flows

The first part of the paper presents a construction of orthonormal polynomial wavelets on the interval by means of a Malvar–type decomposition in polynomial coefficient space. With this approach the localization of the wavelets could be improved substantially compared to an earlier construction by the authors. The new basis is then applied to the analysis of turbulence in the presence of walls. In particular, it allows to define local spectra in wall– normal direction. As an example, DNS data of the flow in a plane channel are considered. The extension to higher dimensions is performed as well.