Level-crossings reveal organized coherent structures in a turbulent time series

In turbulent flows, energy production is associated with highly organized structures, known as coherent structures. Since these structures are three-dimensional, their detection remains challenging in the most common situation, when single-point temporal measurements are considered. While previous research on coherent structure detection from time series employs a thresholding approach, the thresholds are ad-hoc and vary significantly from one study to another. To eliminate this subjective bias, we introduce the level-crossing method and show how specific features of a turbulent time series associated with coherent structures can be objectively identified, without assigning a prior any arbitrary threshold. By using two wall-bounded turbulence time series datasets, we successfully extract through level-crossing analysis the impacts of coherent structures on turbulent dynamics, and therefore, open an alternative avenue in experimental turbulence research. By utilizing this framework further we identify a new metric, characterized by a statistical asymmetry between peaks and troughs of a turbulent signal, to quantify inner-outer interaction in wall turbulence. Moreover, a connection is established between extreme value statistics and level-crossing analysis, thereby allowing additional possibilities to study extreme events in other dynamical systems.
Comment: This manuscript has 9 figures and 3 supplementary figures