THE LEAKAGE PROBLEM OF ORTHONORMAL WAVELET TRANSFORMS WHEN APPLIED TOATMOSPHERIC-TURBULENCE

Orthonormal wavelet transforms are becoming common in the study of tur bulence phenomena. Although they are powerful tools in representing a signal, their use as tools to study the characteristics of turbulent s tructures can create appreciable errors in interpretation. It is shown here that although the orthonormal wavelet transform is computational ly economical by taking advantage of multiresolution analysis, it has insufficient resolution in both scale and location to resolve detailed information of turbulence structures. Lacking in resolution, the ener gy at a particular frequency (or wavelength) may leak into neighboring frequencies and may pass down to smaller scales to produce an artific ial ''cascade'' of energy (with a slope close to -2/3). The choice of wavelet basis function is important to the wavelet spectrum, especiall y in the study of turbulence flows dominated by coherent structures, s ince the method most accurately senses energy contained in pulses that have a similar pattern to the wavelet function. To use the method as a filter can be problematic owing to the low resolution of the orthono rmal wavelet transform; nonorthonormal wavelet analysis should be empl oyed when high resolution is important. When orthonormal wavelet trans forms have to be used for signal analysis, segmented averaging should be employed.