  We show that the phase space of stratified turbulence mainly consists of two
slow invariant manifolds with rich physics, embedded on a larger basin with
fast evolution. A local invariant manifold in the vicinity of the fluid at
equilibrium corresponds to waves, while a global invariant manifold corresponds
to the onset of local convection. Using a reduced model derived from the
Boussinesq equations, we propose that waves accumulate energy nonlinearly up to
a point such that fluid elements escape from the local manifold and evolve fast
to the global manifold, where kinetic energy can be more efficiently
dissipated. After this, fluid elements return to the first manifold. As the
stratification increases, the volume of the first manifold increases, and the
second manifold becomes harder to access. This explains recent observations of
enhanced intermittency and marginal instability in these flows. The reduced
model also allows us to study structure formation, alignment of field gradients
in the flow, and to identify balance relations that hold for each fluid
element.
