Differential diffusion spectral model

A spectral model similar to (3.82) can be derived from (3.75) for the joint scalar dissipation rate eap defined by (3.139), p. 90. We will use these models in Section 3.4 to understand the importance of spectral transport in determining differential-diffusion effects. As we shall see in the next section, the spectral interpretation of scalar energy transport has important ramifications on the transport equations for one-point scalar statistics for inhomogeneous turbulent mixing. 

The Lagrangian spectral relaxation model for differential diffusion in homogeneous turbulence. Physics of Fluids 11, 1550-1571. 

Sophisticated numerical techniques have been devised to study this standard model within mean field approximation. They exploit that the mean field problem of a Gaussian chain in an external field can be described by a modified diffusion equation in an external field [60]. The latter leads to a partial differential equation that can be solved by efficient computational techniques. Advanced real-space, spectral, and pseudospectral algorithms have been devised to this end [28, 78-80]. ... 

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