Rational subgrid-scale modelling: a short survey

We review the previous attempts of rational subgrid-scale (SGS) modelling by employing the Kolmogorov equation of filtered quantities. Aiming at explaining and solving the underlying problems in these models, we also introduce the recent methodological investigations for the rational SGS modelling technique by defining the terms of assumption and restriction. These methodological works are expected to provide instructive criterions for not only the rational SGS modelling, but also other types of SGS modelling practices.