The published paper is in JFM here:
A preprint of the paper is available here.
Movies here show streamwise velocity (red/yellow, left) and total density (blue, below) for the UPO-o1 orbit. Re=20, B=1.
This UPO exhibits clear overturning motions and has larger irreversible mixing efficiency and gradient Richardson number is correlated to mixing efficiency.
The following movies show total density (left), perturbation density (bottom) and streamwise velocity (red/yellow, below) for the UPO-l1 orbit. Re=50, B=1.
This UPO exhibits more anisotropic layered motions and has lower irreversible mixing efficiency.
Here the gradient Richardson number is not correlated to mixing efficiency but rather the straining or scouring of density variations into thin sheets is responsible for the weak mixing.