Irreversible mixing by unstable periodic orbits in stratified turbulence

This page accompanies research into unstable periodic orbits (UPOs) controlling mixing in body-forced stably-stratified turbulence. Joint work with C. P. Caulfield as part of the MUST program.

The published paper is in JFM here:

A preprint of the paper is available here.

UPOo1 u UPOo1 rho_tot

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.

 

UPOo1 u UPOo1 rho_totUPOo1 rho_tot
 

 

 

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.