Subgrid scale variance and dissipation of a scalar field in large eddy simulations

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.