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Structural modeling

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Those that use the physical hypothesis of scale similarity

\tau_{ij} = L_{ij} = \widetilde{\bar{u}_i} \widetilde{\bar{u}_j} - \widetilde{\bar{u}_i \bar{u}_j}

Those derived by formal series expansions

\tau_{ij} = G_{ij} = \frac{\Delta^2}{12} \frac{\partial \bar{u}_i}{\partial x_{k}} \frac{\partial \bar{u}_j}{\partial x_{k}}

Mixed models, which are based on linear combinations of the eddy-viscosity and structural types

\tau_{ij} = G_{ij}-2\nu_{sgs} S_{ij}


\tau_{ij} = L_{ij}-2\nu_{sgs} S_{ij}

Dynamic structure models (non-viscosity version)

\tau_{ij} = 2k_{sgs} \left(\frac{L_{ij}}{L_{kk}}\right)


\tau_{ij} = 2k_{sgs} \left(\frac{G_{ij}}{G_{kk}}\right)
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