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Subgrid variance

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The subgrid variance of a passive scalar is defined as

\widetilde{Z_{sgs}''^2} = \widetilde{Z^2}- \widetilde{Z}^2

The scalar subgrid variance is also known as the subgrid scalar energy in analogy to the kinetic subgrid energy. An equation for the subgrid variance is

Instead of solving the above equation, algebraic models are often used. For dimensional analysis

\widetilde{Z_{sgs}''^2} =
C_Z \Delta^2 \frac{\partial \widetilde{Z} }{\partial x_i} \frac{\partial \widetilde{Z} }{\partial x_i}

where  C_Z can be obtained from the scalar spectra and its value is 0.1-0.2.

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