RESUME / ABSTRACT
A fundamental problem in fluid dynamics that remains a mystery, even after
half a century of dedicated research, is turbulence. It is a central
feature of atmospheric and oceanic dynamics, within which the effects of
rotation and stratification are paramount. These effects, however, have
not been properly accounted for in previous research. In particular, it
is well known in meteorology and oceanography that the distribution of
`potential vorticity' (representing the `balanced motions') has the
greatest influence on the observed fluid motion, whereas higher-frequency
`inertia-gravity waves' (representing the `imbalanced motions') are of
secondary importance. Previous studies and numerical simulations have
considered these two types of motion to be of comparable importance ---
this is not the regime relevant to atmospheric and oceanic turbulence.
Here, we address this regime in detail, using arguably the most advanced
numerical method available, together with a revolutionary new procedure
which optimally distinguishes the balanced and imbalanced motions. This
approach is novel in two major respects: it addresses directly and with an
unprecedentedly accurate numerical method the dominantly balanced regime
of turbulence, and it offers a very new and surprisingly straightforward
way forward to cleanly separate balanced and imbalanced motions even in
highly-complex flows like turbulence.