text: The Eulerian approach to turbulent diffusion focuses on an infinitesimal volume at a specific space and time in a fixed frame of reference, at which physical properties such as mass, momentum, and temperature are measured. The model is useful because Eulerian statistics are consistently measurable and offer great application to chemical reactions.  Similarly to molecular models, it must satisfy the same principles as the continuity equation below (where the advection of an element or species is balanced by its diffusion, generation by reaction, and addition from other sources or points) and the Navier–Stokes equations:
  where  = species concentration of interest,  = velocity
  t= time, = direction,  = molecular diffusion constant,  = rate of  generated reaction,  = rate of  generated by source.
    Note that   is concentration per unit volume, and is not mixing ratio () in a background fluid.
  If we consider an inert species (no reaction) with no sources and assume molecular diffusion to be negligible, only the advection terms on the left hand side of the equation survive. The solution to this model seems trivial at first, however we have ignored the random component of the velocity plus the average velocity in u= ū + u’ that is typically associated with turbulent behavior.  In turn, the concentration solution for the Eulerian model must also have a random component c= + c’. This results in a closure problem of infinite variables and equations and makes it impossible to solve for a definite c on the assumptions stated.
  Fortunately there exists a closure approximation in introducing the concept of eddy diffusivity and its statistical approximations for the random concentration and velocity components from turbulent mixing:
  where K is the eddy diffusivity.
  Substituting into the first continuity equation and ignoring reactions, sources, and molecular diffusion results in the following differential equation considering only the turbulent diffusion approximation in eddy diffusion:
  Unlike the molecular diffusion constant D, the eddy diffusivity is a matrix expression that may vary in space, and thus may not be taken outside the outer derivative.