  We present a reduced system of 7 ordinary differential equations that
captures the time evolution of spatial gradients of the velocity and the
temperature in fluid elements of stratified turbulent flows. We show the
existence of invariant manifolds (further reducing the system dimensionality),
and compare the results with data stemming from direct numerical simulations of
the full incompressible Boussinesq equations in the stably stratified case.
Numerical results accumulate over the invariant anifolds of the reduced system,
indicating the system lives at the brink of an instability. Finally, we study
the stability of the reduced system, and show that it is compatible with recent
observations in stratified turbulence of non-monotonic dependence of
intermittency with stratification.
