ABSTRACT
One unsatisfactory feature of the two dimensional vorticity equation is that it is, of course, incapable of modelling any three dimensional effects such as vortex tube stretching/compression. The dilation and compression of vortex tubes and filaments is a fundamental characteristic of turbulent three dimensional fluid flows. Another feature that the two dimensional vorticity equation (3.8) does not include, in the absence of a mean flow, is a term corresponding to a background vorticity gradient. The most important consequence of this property is that there are no nontrivial linear plane wave solutions to (3.8).
