Instabilities in rectilinear, sheared polymer flows and their relationship with elastic and elasto-inertial turbulence*

Adding polymers to a Newtonian solvent introduces elasticity to the solution and it is now known can give rise to new forms of turbulence. `Elastic Turbulence’ (ET) arises when the elastic forces are large enough in the absence of inertia, and `Elasto-Inertial Turbulence’ (EIT) appears to need both inertia and elasticity to exist. Many questions exist about these two forms of viscoelastic turbulence: in particular, whether they are dynamically connected, what triggers them and how EIT interacts with the presence of Newtonian turbulence at low levels of elasticity (e.g. Datta et al. Phys. Rev Fluids, 7, 080701, 2022). I will attempt to review recent work seeking some answers largely stimulated by a recently-discovered viscoelastic centre mode instability (Garg et al. Phys. Rev. Lett., 121, 024502, 2018) and a newly-discovered `polymeric diffusive instability’ (Beneitez et al. arXiv:2210.09961, 2022).