The evolution of turbulence theories and the need for continuous wavelets

TL;DR

This paper reviews the history of turbulence research, discusses the potential of continuous wavelets for turbulence analysis, and presents results demonstrating their effectiveness in representing and filtering turbulent flows.

Contribution

It introduces the application of continuous wavelet transforms to turbulence analysis, highlighting their advantages and presenting new results in turbulent flow representation and filtering.

Findings

Continuous wavelets effectively represent turbulent flows.

Wavelet-based filtering isolates turbulence features.

The approach offers a non-linear analysis tool for turbulence.

Abstract

In the first part of this article, I summarise two centuries of research on turbulence. I also critically discuss some of the interpretations that are still in use, as turbulence remains an inherently non-linear problem that is still unsolved to this day. In the second part, I tell the story of how Alex Grossmann introduced me to the continuous wavelet representation in 1983, and how he instantly convinced me that this is the tool I was looking for to study turbulence. In the third part, I present a selection of results I obtained in collaboration with several students and colleagues to represent, analyse and filter different turbulent flows using the continuous wavelet transform. I have chosen to present both these theories and results without the use of equations, in the hope that the reading of this article will be more enjoyable.