Comparing local energy cascade rates in isotropic turbulence using structure function and filtering formulations

Two common definitions of the spatially local energy cascade rate at some scale $ell$ in turbulent flows are (i) the cubic velocity difference term appearing in the generalized Kolmogorov-Hill equation (structure function approach), and (ii) the subfilter-scale energy flux term in the transport equation for subgrid-scale kinetic energy (filtering approach). We perform a comparative study of both quantities based on direct numerical simulation data of isotropic turbulence at Taylor-scale Reynolds number of 1250. Conditional averaging is used to explore the relationship between the local cascade rate and the local filtered dissipation rate as well as filtered velocity gradient tensor properties such as its invariants. By conditioning on the local dissipation, we confirm Kolmogorov's second refined similarity hypothesis with both quantities. Conditioning on velocity gradients invariants, we find statistically robust evidence of inverse cascade when both the large-scale rotation rate is strong and the large-scale strain rate is weak. Even stronger net inverse cascading is observed in the ``vortex compression'' $R>0$, $Q>0$ quadrant where $R$ and $Q$ are velocity gradient invariants. Qualitatively similar, but quantitatively much weaker trends are observed for the conditionally averaged subfilter scale energy flux.