Turbulence is defined as an eddy-like state of fluid motion where the inertial-vortex forces of the eddies are larger than any of the other forces that tend to damp the eddies out. Energy cascades of irrotational flows from large scales to small are non-turbulent, even if they supply energy to turbulence. Turbulent flows are rotational and cascade from small scales to large, with feedback. Viscous forces limit the smallest turbulent eddy size to the Kolmogorov scale. In stratified fluids, buoyancy forces limit large vertical overturns to the Ozmidov scale and convert the largest turbulent eddies into a unique class of saturated, non-propagating, internal waves, termed fossil-vorticity-turbulence. These waves have the same energy but different properties and spectral forms than the original turbulence patch. The Gibson (1980, 1986) theory of fossil turbulence applies universal similarity theories of turbulence and turbulent mixing to the vertical evolution of an isolated patch of turbulence in a stratified fluid as its growth is constrained and fossilized by buoyancy forces. These theories apply to the dynamics of atmospheric, astrophysical and cosmological turbulence.

31 pages, 11 figures, 2 tables, see http://www-acs.ucsd.edu/~ir118 Accepted for publication by the Chinese Journal of Oceanology and Limnology