Characterizing 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 allow to estimate the Taylor length scale of turbulence thanks to the Rice theorem. Furthermore, it has recently been found (Mora \& Obligado, Exp. Fluids, 2020) that they can also be used to compute its integral length scale. In consequence, they can be exploited to study several one-point statistics from a turbulent flow.  Such approach presents several advantages as it enables to characterize a turbulent flow in extremely challenging situations, where the flow is unsteady or a proper calibration of the equipment cannot be guaranteed.  

Using experimental data from different flows (passive- and active-grid-generated turbulence, planar and axisymmetric turbulent wakes) for a wide range of $Re_\lambda$, we show how different aspects of the energy cascade can be described solely by using the zero-crossings of the longitudinal velocity fluctuations. Furthermore, using Voronoï tessellations we also studied the clustering properties of this quantity. In particular, we show how their voids are related to the characteristics of the cascade.