Analysis of inertial-range intermittency in forward and inverse cascade regions in isotropic turbulence

Abstract

In order to test the hypothesis that inverse cascade regions in turbulent flows might exhibit more Gaussian noise-like and less intermittent small-scale statistics compared to the overall statistics, in this work we measure degrees of small-scale intermittency separately in regions of forward and inverse cascade. The local energy cascade rate $(Φ_\ell)$ at length scale $(\ell)$ is defined using the scale-integrated Kolmogorov-Hill (KH) equation. To characterize intermittency, we analyze the probability density functions (PDFs) of longitudinal and transverse velocity increments at scale $\ell$, conditioned on positive and negative $Φ_\ell$ (local forward and inverse cascades). Our findings reveal that transverse velocity increments display approximately the same degree of non-Gaussianity and intermittency, in both forward or inverse cascade regions. The only noticeable difference is observed for longitudinal velocity increments that display strong negative skewness in regions of forward cascade compared to small positive skewness in regions of inverse cascade. We repeat the analysis for filtered velocity gradient tensor elements at scale $\ell$ and obtain similar results, except that the skewness of its longitudinal elements is slightly negative even in regions of inverse cascade. The analysis is based on isotropic turbulence data ($Re_λ\sim 1{,}250$) available from the public Johns Hopkins Turbulence Databases, JHTDB v2.0. This refactored system is based on the Zarr storage format, while data access is based on the ``virtual sensor'' approach, enabled by a Python backend package (Giverny) that replaces the legacy SQL storage and SOAP Web Services-based approaches. Information about the new system as well as sample Python notebooks are described and illustrated. (Matlab, C, and Fortran access methods are also provided).