A criterion of orthogonality on the assumption and restrictions in subgrid-scale modelling of turbulence

In order to shed light on understanding the subgrid-scale (SGS) modelling methodology, we analyze and define the concepts of assumption and restriction in the modelling procedure, then show by a generalized derivation that if there are multiple stationary restrictions in a modelling, the corresponding assumption function must satisfy a criterion of orthogonality. Numerical tests using one-dimensional nonlinear advection equation are performed to validate this criterion. This study is expected to inspire future research on generally guiding the SGS modelling methodology.