  Two common definitions of the spatially local rate of kinetic energy cascade
at some scale $\ell$ in turbulent flows are (i) the cubic velocity difference
term appearing in the generalized Kolmogorov-Hill equation (GKHE) (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. While observations of negative subfilter-scale energy flux (backscatter)
have in the past led to debates regarding interpretation and relevance of such
observations, we argue that the interpretation of the local structure
function-based cascade rate definition is unambiguous since it arises from a
divergence term in scale space. Conditional averaging is used to explore the
relationship between the local cascade rate and the local filtered viscous
dissipation rate as well as filtered velocity gradient tensor properties such
as its 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. Flow
visualizations show consistent trends, namely that spatially the inverse
cascade events appear to be located within large-scale vortices, specifically
in subregions when $R$ is large.
