A gauge identity for interscale transfer in inhomogeneous turbulence

TL;DR

This paper derives an exact gauge identity for interscale energy transfer in inhomogeneous turbulence, clarifying the physical meaning of SGS production and its limitations near boundaries.

Contribution

It introduces a new gauge identity linking SGS production to an increment-based transfer and spatial transport, improving understanding of turbulence energy transfer.

Findings

Near walls, spatial transport dominates SGS production.

SGS production is not a unique indicator of local cascade in inhomogeneous flows.

The identity is validated with exact solutions and DNS data.

Abstract

In inhomogeneous turbulence, local interscale energy transfer is commonly diagnosed in Large Eddy Simulation (LES) using the subgrid-scale (SGS) production $\Pi^{\mathrm{SGS}}=-\tau_{ij}\bar{S}_{ij}$, although its physical meaning is unclear near boundaries. An exact gauge identity is derived showing that $\Pi^{\mathrm{SGS}}=\Pi^{\mathrm{inc}}+\nabla\!\cdot\!\boldsymbol{J}$, where $\Pi^{\mathrm{inc}}$ is a kernel-integrated increment-based transfer consistent with K\'arm\'an--Howarth--Monin--Hill formulations and $\boldsymbol{J}$ 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 $\nabla\!\cdot\!\boldsymbol{J}$ can dominate $\Pi^{\mathrm{SGS}}$, implying that SGS production is not a unique proxy for local cascade in inhomogeneous LES diagnostics.