Germano identity-based subgrid-scale modeling: A brief survey of variations on a fertile theme

It has now been over 20 years since the introduction of the Germano identity. Mostly, the identity has been applied to closures for the subgrid-scale fluxes required in large eddy simulations in the bulk of turbulent flows. However, the basic ideas underlying the Germano identity can be applied in various other contexts. In recent years a number of such generalizations have been developed, and several of these are surveyed in this paper. The survey is based on an interpretation of the Germano identity stating that the sum of resolved and modeled contributions to basic quantities of intrinsic physical interest must be independent of filter scale. The focus of this survey is on the conceptual bases of the various generalizations and their common features, as a way of pointing to possible further extensions.

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