| Two key ideas stand out as crucial to understanding atmosphere-ocean
dynamics, and the dynamics of other planets including the gas giants.
The first key idea is the invertibility principle for potential
vorticity (PV). Without it, one can hardly give a coherent account
of even so important and elementary a process as Rossby-wave
propagation, going beyond the simplest textbook cases. Still less
can one fully understand nonlinear processes like the self-sharpening
or narrowing of jets – the once-mysterious "negative viscosity"
phenomenon. The second key idea, also crucial to understanding jets,
might be summarized in the phrase "there is no such thing as
turbulence without waves", meaning Rossby waves especially. Without
this idea one cannot begin to make sense of, for instance, momentum
budgets and eddy momentum transports in complex large-scale flows.
Like the invertibility principle the idea has long been recognized,
or at least adumbrated. However, it is worth articulating explicitly
if only because it can be forgotten when, in the usual way, we speak
of "turbulence" and "turbulence theory" as if they were
autonomous concepts. In many cases of interest, such as the
well-studied terrestrial stratosphere, reality is more accurately
described as a highly inhomogeneous "wave-turbulence jigsaw
puzzle" in which wavelike and turbulent regions fit together and
crucially affect each other's evolution. This modifies, for
instance, formulae for the Rhines scale interpreted as indicating the
comparable importance of wavelike and turbulent dynamics. Also,
weakly inhomogeneous turbulence theory is altogether inapplicable.
For instance there is no scale separation. Eddy scales are not much
smaller than the sizes of the individual turbulent regions in the
jigsaw. Here I review some recent progress in clarifying these ideas
and their implications. |