A gauge identity for interscale transfer in inhomogeneous turbulence

In inhomogeneous turbulence, local interscale energy transfer is commonly diagnosed in Large Eddy Simulation (LES) using the subgrid-scale (SGS) production Π^{SGS}=-τ_{ij}S_{ij}, although its physical meaning is unclear near boundaries. An exact gauge identity is derived showing that Π^{SGS}=Π^{inc}+nabla!cdot!J, where Π^{inc} is a kernel-integrated increment-based transfer consistent with Kármán--Howarth--Monin--Hill formulations and J is a spatial transport current. The identity is verified using the exact Womersley solution and evaluated with DNS of turbulent channel flow. It is found that near walls nabla!cdot!J can dominate Π^{SGS}, implying that SGS production is not a unique proxy for local cascade in inhomogeneous LES diagnostics.