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

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. As these parameters are shaped by particular averaged properties of the turbulence cascade, they can be used to deduce some aspects of it. This approach is advantageous, as it makes possible the characterisation 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 Taylor-scale-based Reynolds numbers from different flows (passive- and active-grid-generated turbulence and planar turbulent wakes), we show how, by solely using the zero-crossings of the longitudinal velocity fluctuations, some aspects of the energy cascade can be studied. Furthermore, using Voronoï tessellations, we study zero-crossing clustering properties. In particular, we discuss how its clusters and voids are related to the separation of scales in turbulent flows.