When you hear on the weather forecast that there is a thermal inversion
it means that light (warm) air is sitting above heavier (cold)
air. The air is stratified.
Gravity impedes air moving vertically and traps pollution near
the ground. The stratosphere gets its name because the air in
that region is stratified all the time. This is why airplane
contrails persist for so long.
Large parts of the ocean are stratified as is the lowest region of the
atmosphere over land at night.
The renowned research meteorologist D.
K. Lilly coined the term Stratified
Turbulence for fully three-dimensional turbulence in which
turbulent motion in the vertical is constrained by gravity. A
question central to research into this flow regime is how much of
classical turbulence theory applies to stratified
predicting weather, for instance, we'd like to be able to use existing
turbulence models, but they are not always applicable.
Click on the thumbnails below to see the effect that buoyancy has on
turbulence. The stratified case has regions of intense turbulence and
regions of almost no turbulence that are particularly visible in the
plots of dissipation rate.
The images were generated by the direct numerical simulations reported
See Image Gallery for additional
velocity in unstratified
velocity in stratified turbulence
the dissipation rate in unstratified
the dissipation rate in stratified
Importance of High Buoyancy
Turbulence is inherently 3D, but gravity impedes vertical motion of
turbulent eddies larger than a given size called the Ozmidov
length. At very small lengths (smaller than the Kolmogorov
length), turbulent motion is suppressed by viscosity. So in
important ratio for stratified turbulence is the Ozmidov length /
Kolmogorov length, which is related to the buoyancy Reynolds number, Rb.
Rb must be above some value, typically taken to be 25 - 30, for
stratified turbulence to be in interesting. If the flow is
strongly stratified as it is in many geophysical flows, at least 500
billion grid points are needed for a 3D simulation at high enough Rb.