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The Note presents an alternative derivation and interpretation of the Germanoidentity and its error, showing that the Germano identity error directlyestimates the residual of the LES equation, i.e., the misfit when evaluatingthe inexact equation for the exact solution, and therefore represents thesource of errors in LES. This has many applications, including for optimaloutput-based grid/filter-adaptation and uncertainty quantification in LES.

An alternative derivation of the Germano identity as the residual of the LES equation