Exact Coherent Structures in Viscoelastic Turbulence

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Viscoelasticity, which is the presence of both elasticity and viscosity, is increasingly realised to be an important feature of many common liquids in today's world (e.g. blood, shampoo, paints, DNA suspensions etc). However, due to the complexity of the mathematical models currently used to describe them, viscoelastic fluids remain poorly understand despite a wealth of interesting properties (e.g. it has been known for over 70 years that only a minute amount of elasticity is enough to at least halve the viscous drag on a surface exerted by a turbulent flow). In particular, it has only relatively recently been realised that there are possibly three forms of turbulence which can occur: (classical) Newtonian turbulence (NT) which exists in the absence of elasticity, Elastic turbulence (ET) which exists in the absence of inertia, and a third, apparently intermediate, form of turbulence called Elasto-inertial turbulence (EIT) which requires a balance of inertia and elasticity to exist. This proposal is directed at trying to identify the dynamical origins of EIT by building upon a recently discovered instability of unidirectional viscoelastic flows. Finite-amplitude states already found by us to emerge from this instability resemble what is seen in EIT suggesting that they are proxy which can be used to understand the underlying physics of EIT as well as mapped out to see when EIT exists in parameter space. Outstanding questions to be also addressed include trying to establish connections between these states and both ET and NT. Establishing connections here would help untangle whether there really are 3 distinct types of turbulence or more different limits of the same turbulence. Ultimately, the proposed work will improve our understanding of what type of viscoelastic flow (laminar, turbulent or something else in between) will be realised at a given set of parameters which will help engineers design industrial processes or design products.