TABLE OF CONTENTS Studying turbulence with wavelets is a controversial scientific program. This is not surprising, since we are attacking one of the most difficult and itself controversial problems in science with a rather simple tool. Criticism arose originally when a few scientists announced that spectacular results had been obtained by wavelet methods. It was highly unlikely, however, that one of the oldest fundamental problems of classical physics a problem whose solution has eluded some of the outstanding scientists of the twentieth century would suddenly be resolved by the mere introduction of a new tool.
Similar criticisms arose when wavelet methods were first applied to image processing. Today we have a much better understanding of how low-level processing can benefit from wavelet methods. We also understand that some aspects of image processing, such as pattern recognition, are not directly accessible through wavelet methods. In our report on wavelets and turbulence, we hope to draw similar balanced conclusions by indicating what is working and what is not.
Wavelets have been applied to at least three problems in fluid dynamics during the past 15 years. The first one concerns a line of research that was introduced by Beno t Mandelbrot and developed by Uriel Frisch and Giorgio Parisi; it is the program that has led to the recent results by Alain Arneodo and his coworkers in Bordeaux, France. These programs seek to unravel the intricate fine-scale geometrical structure of fully developed turbulence by analyzing time series obtained from wind tunnel experiments. One wishes to know if...
