Anelastic Mixing:  Transport by Weakly Compressible Flow:

                         by
 
              Rich McLaughlin, Univ. of Utah

             JTB 120, 3:20pm  Monday, March 2, 1998


                          Abstract
 
  Many studies to date have focused upon the turbulent diffusion 
of a passive scalar in the presence of an incompressible fluid 
flow.  This is quite natural as a means for understanding 
mixing in turbulent environments for which the fluid in question 
satisfies a zero divergence constraint.  However, for many physical 
environments, the fluid density is not constant, and may admit 
a non-trivial adiabatic steady-state density profile leading to non-zero 
flow divergence constraints.  Such is the case when considering 
the atmosphere over moderately large vertical scales.  
 
  Here, we discuss a simplified model aimed at describing 
fluid flow in the presence of large-scale density variation.  We 
then derive effective equations governing the large-scale, 
long-time renormalized dynamics of a passive tracer diffusing 
in the presence of this weakly compressible fluid flow.  We 
compare the predictions of this theory with the analogous 
theory of homogenized enhanced diffusivities for the constant 
density case and demonstrate some interesting differences 
in the effective bulk transport of the scalar quantity specifically 
due to the combined effects of the variable density profile and 
small-scale fluid motion. 

Requests for preprints and reprints to: rmm@math.utah.edu
This source can be found at http://www.math.utah.edu/applied-math/