The Note presents an alternative derivation and interpretation of the Germano identity and its error, showing that the Germano identity error directly estimates the residual of the LES equation (i.e., the misfit when evaluating the inexact equation for the exact solution) and therefore represents the source of errors in LES. The most prominent applications include a robust and easy to compute definition of the source of errors that can be used for grid/filter adaptation in LES or for estimating the coarse-graining related uncertainties, as well as offering a more robust explanation for the success of the dynamic procedure and the favorable characteristics that the dynamic models inherit.

注释提供了 Germano 恒等式及其误差的另一种推导和解释，表明 Germano 恒等式误差直接估计了 LES 方程的残差（即评估精确解的不精确方程时的失配），因此代表了来源LES 中的错误。最突出的应用包括一个稳健且易于计算的误差源定义，可用于 LES 中的网格/滤波器自适应或用于估计粗粒度相关的不确定性，以及为成功提供更可靠的解释动态过程和动态模型继承的有利特征。