A gauge identity for interscale transfer in inhomogeneous turbulence

Local interscale energy transfer in Large Eddy Simulation (LES) is typically diagnosed using the subgrid-scale (SGS) production, $\Pi^{SGS}$. In this work, an exact algebraic gauge identity is derived, demonstrating that $\Pi^{SGS}$ is composed of a kernel-integrated increment-based transfer, $\Pi^{inc}$, and the divergence of a spatial transport current, $\nabla \cdot J$. This identity was verified to machine precision ($10^{-16}$) using the analytical multi-harmonic Womersley solution. Further evaluation was conducted via Direct Numerical Simulation (DNS) of turbulent channel flow at $Re_\tau \approx 1000$. It was observed that $\nabla \cdot J$ dominates $\Pi^{SGS}$ in the near-wall region. The results suggest that $\Pi^{SGS}$ is not a unique proxy for the local cascade in inhomogeneous flows. A new framework is thus provided for the interpretation of interscale transfer diagnostics in wall-bounded transport phenomena.