Abstract
Subgrid scale (SGS) variance of a scalar field in large eddy simulations is only properly defined in relation to a probability density function. This solves a reported problem in the variance definition [Cook and Riley, Phys. Fluids 6, 2868 (1994); Cook, Riley, and Kosály, Combust. Flame 109, 332 (1997)] and allows to write a simple evolution equation for the scalar variance. This equation shows that a recently proposed model for scalar dissipation in terms of the large-scale gradients [Pierce and Moin, Phys. Fluids 10, 3041 (1998)] implies dissipation and production canceling out, preventing variance decay and complete mixing at SGS level. An alternative simple model for dissipation in terms of a SGS mixing characteristic time is proposed and tested here.
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