  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.
