# Exact Coherent Structures in Viscoelastic Turbulence

Lead Research Organisation:
University of Cambridge

Department Name: Applied Maths and Theoretical Physics

### Abstract

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.

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.

### Publications

Beneitez M
(2023)

*Polymer diffusive instability leading to elastic turbulence in plane Couette flow*in Physical Review Fluids
Beneitez M
(2024)

*Multistability of elasto-inertial two-dimensional channel flow*in Journal of Fluid Mechanics
Buza G
(2022)

*Finite-amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number*in Journal of Fluid Mechanics
Buza G
(2022)

*Weakly nonlinear analysis of the viscoelastic instability in channel flow for finite and vanishing Reynolds numbers*in Journal of Fluid Mechanics
Couchman M
(2024)

*Inertial enhancement of the polymer diffusive instability*in Journal of Fluid Mechanics
Dubief Y
(2022)

*First coherent structure in elasto-inertial turbulence*in Physical Review FluidsTitle | Code associated with "Finite amplitude elastic waves in viscoelastic channel flow from large to zero Reynolds number" |

Description | Numerical code associated with the publication. Please see README doc for more details |

Type Of Material | Database/Collection of data |

Year Produced | 2022 |

Provided To Others? | Yes |

Impact | too early to say yet |

URL | https://www.repository.cam.ac.uk/handle/1810/341971 |