On the Use of 2D Wavelets for the Analysis of Coherent Structures

Abstract

A common difficulty of experimental and numerical works is the complete exploitation of hude amount of data. With the improvement of experimental techniques, a lot of time dependent data are now available in fluid dynamics studies, and efficient tools are required to examine the physics. In this paper we consider two flow configurations. The first is the interaction between a shock wave and a fluid interface and the second is the naturally unsteady compressible turbulent shear layer. Since the precursor work of TOWNSEND [1], the existence of two kinds of turbulence is now well accepted. Indeed, in turbulent shear flows, coherent large scale structures are observed whereas smaller scales are more random. Experiments of PAPAMOSCHOU and ROSHKO[2] have shown that these structures exist also in compressible flows. Thus, the turbulence can be splitted into coherent vortices which are dynamically active, and advected by the mean flow and the “random” turbulence. Various tools have been developped to study these particular flows such as, the proper orthogonal decomposition, the pattern recognition, and the wavelet transform. The latter has been used in the present work. This technique is well adapted to capture a lot of flow features. For example, in image processing the mexican hat wavelet is well adapted to detect positions and characteristic scales, but directions are not well resolved. The Morlet wavelet is more suitable to detect directional information. In the first part of this article, the wavelet transform is summarized. Then the second part will describe the flows and analyze the results.