On advection and diffusion in the mesosphere and lower thermosphere: The role of rotational fluxes

A formalism to describe the advective and diffusive eddy transport in terms of the mean tracer is presented. It is based on Eulerian averaging, the flux‐gradient relation, and the decomposition of the eddy flux of a tracer into advective, diffusive, and rotational components. The rotational (nondivergent) flux arises because the conservation equation for the mean tracer contains only a divergence of the eddy flux of the tracer. To provide a closure, a modification to the flux separation technique based on the eddy variance equation is introduced. The “eddy‐induced” advective velocity is represented as the sum of two velocities v1 and v2. Velocity v1 is similar to that in the Transformed Eulerian Mean (TEM) formulation but is generalized to account for both horizontal and vertical eddy fluxes and mean gradients. The velocity v2 depends on the flux of eddy variance of the tracer. The diffusion coefficient is represented as a sum of K1, which may serve as a diagnostic of an irreversible mixing, and K2, which describes up‐ or down‐gradient eddy fluxes of the tracer due to local transformations of the eddy variance. Both v2 and K2 arise from taking account of the rotational fluxes. The scheme is applied to output from a global circulation model of the middle atmosphere. It is shown that in the meridional plane the correction v2 to the TEM velocity is small in the mesosphere and lower thermosphere. For the diffusion coefficient, however, the correction K2 must be accounted for above approximately 110 km.