Nonlinear dynamics and transition in rectilinear viscoelastic flows

Abstract: Many liquids in the modern world possess both elastic and viscous properties (e.g. paints, saliva and DNA suspensions among many others polymers). Understanding their behaviour is paramount in many industrial processes where turbulence is commonplace but may be highly undesirable (e.g. pharmaceutical, chemical, and plastic). Little is known about how and why this viscoelastic turbulence occurs, mainly due to the complexity and variety of the mathematical models used to describe it. In particular, it has only recently been realised that there may be three distinct types: a polymer-adjusted Newtonian turbulence (NT) which predominantly exists due to inertial effects, Elastic turbulence (ET) which exists in the absence of inertia and is entirely driven by the elasticity, and a third form called Elasto-inertial turbulence (EIT) which requires a balance of 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. In this talk, I will attempt to review recent work seeking some answers largely stimulated by a recently-discovered viscoelastic centre mode instability [1] and a newly-discovered ``polymer diffusive instability'' [2]. I will also explore the transition to viscoelastic turbulence when transition is triggered by finite amplitude perturbations and introduce some of its challenges.

Refs: [1] Garg et al. Phys. Rev. Lett., 121, 024502, 2018 [2] Beneitez et al. Phys. Rev. Fluids 8, L101901, 2023.