A gauge identity for interscale transfer in inhomogeneous turbulence
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910259524665344 |
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| author | Saqr, Khalid M. |
| author_facet | Saqr, Khalid M. |
| contents | Local interscale energy transfer in Large Eddy Simulation (LES) is typically diagnosed using the subgrid-scale (SGS) production, $Π^{SGS}$. In this work, an exact algebraic gauge identity is derived, demonstrating that $Π^{SGS}$ is composed of a kernel-integrated increment-based transfer, $Π^{inc}$, 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 $Re_τ\approx 1000$. It was observed that $\nabla \cdot J$ dominates $Π^{SGS}$ in the near-wall region. The results suggest that $Π^{SGS}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20653 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A gauge identity for interscale transfer in inhomogeneous turbulence Saqr, Khalid M. Fluid Dynamics 76F02, 76F65, 35Q30, 76Z05 Local interscale energy transfer in Large Eddy Simulation (LES) is typically diagnosed using the subgrid-scale (SGS) production, $Π^{SGS}$. In this work, an exact algebraic gauge identity is derived, demonstrating that $Π^{SGS}$ is composed of a kernel-integrated increment-based transfer, $Π^{inc}$, 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 $Re_τ\approx 1000$. It was observed that $\nabla \cdot J$ dominates $Π^{SGS}$ in the near-wall region. The results suggest that $Π^{SGS}$ 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. |
| title | A gauge identity for interscale transfer in inhomogeneous turbulence |
| topic | Fluid Dynamics 76F02, 76F65, 35Q30, 76Z05 |
| url | https://arxiv.org/abs/2512.20653 |