Abstract

The energy cascade found in fully developed fluid turbulence is believed to originate as large-scale organized motions called coherent structures. The process of detecting, locating, and tracking these coherent structures is therefore of central importance to the continued study of turbulence. A number of researchers have applied wavelet-based methods to the problem of coherent structure detection, and significant performance improvements over other existing methods have already been reported.

In this paper, we compare the performance of various conventional as well as wavelet-based detector algorithms for cylinder wake flow data. The resulting ROC curves quantitatively demonstrate the effectiveness of wavelet methods. The detections are then used to form conditional averages of the velocity time-series, revealing their underlying physical structure.

Introduction

Recently, advances in the theoretical understanding and implementation of wavelets have led to their increased use in analysis and signal processing. Wavelet methods can be very effective in the study of non-stationary phenomena [7], and have thus sparked a concerted interest in applying them to the analysis of turbulent flows in general, and to the detection of coherent structures in particular [8].

It is possible that some coherent structure detectors are better suited for certain types of turbulent flows, or operate most effectively under specific conditions. As the numbers and types of detectors grow, it becomes increasingly important to measure their relative performance in quantitatively meaningful ways. In this chapter, we describe an approach to the comparison of detector algorithms by means of the Receiver Operating Characteristic (ROC) curves, and demonstrate the utility of this method for the case of cylinder wake flow.