Recent analysis of horizontally driven stratified turbulence has, for the first time, connected nonlinear exact coherent states with stratified linear instabilities which organise the turbulence into horizontal layers. These unstable steady states show progressively more inclined shear layers as the stratification is increased and the turbulence organised about these underlying states then forms well defined layers of mixed fluid and stronger density gradients. The linear theory provides a scaling for the layers in the limit of strong stratification which is found to carry through to the turbulence; l ~ U/N where U is a typical horizontal velocity scale and N the buoyancy frequency.
We investigate the mixing properties of this flow by attempting a "recurrent flow analysis"; via a Newton-GMRES-hookstep algorithm we converge unstable periodic orbits (UPOs) and compare their mixing efficiency to that of the turbulent simulation in which they are embedded. In this way we develop a reduced description of the mixing in terms of these UPOs and can examine in detail the processes involved in rearranging the buoyancy field. We find the mixing efficiency of the turbulence follows a familiar trend in terms of the buoyancy Reynolds number, saturating at a value equivalent to the eponymous Osborn model value of 1/6. In light of this we tackle the recurrent flow analysis at parameters where the mixing efficiency is low and where it is near optimal. This enables us to make a robust comparison between the dynamical loops of processes which give rise to each case.