Characterising the energy cascade using the zero-crossings of the longitudinal velocity fluctuations

Abstract

It is well known that the zero-crossings of the longitudinal velocity fluctuations can be used to estimate the Taylor length scale of turbulence via the Rice theorem. Furthermore, it has recently been shown that they can also be used to compute the turbulence integral length scale. We show how these two findings can be combined to study single-point statistics in turbulent flows. This approach is advantageous, as it makes possible the characterization of turbulent flows in extremely challenging situations, i.e. statistically unsteady flows or conditions when adequate instrument calibration cannot be maintained. Using experimental data for a wide range of Reλ from different flows (passiveand active-grid-generated turbulence and planar turbulent wakes), we show how energy cascade variables can be computed solely by using the zero-crossings of the longitudinal velocity fluctuations. Furthermore, using Voronoï tessellations, we study zero-crossing clustering properties. In particular, we discuss how its clusters and voids are related to the turbulence cascade.