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Small-scale shear layers in isotropic turbulence of viscoelastic fluids

Published online by Cambridge University Press:  26 February 2025

Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window] ,
Hugo Abreu Open the ORCID record for Hugo Abreu [Opens in a new window] ,
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]  and
Carlos B. da Silva Open the ORCID record for Carlos B. da Silva [Opens in a new window]
Tomoaki Watanabe*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
Hugo Abreu
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Koji Nagata
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
Carlos B. da Silva
Affiliation:
LAETA, IDMEC, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
*
†Email address for correspondence: watanabe.tomoaki.8x@kyoto-u.ac.jp
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Abstract

Small-scale shear layers arising from the turbulent motion of viscoelastic fluids are investigated through direct numerical simulations of statistically steady, homogeneous isotropic turbulence in a fluid described by the FENE-P model. These shear layers are identified via a triple decomposition of the velocity gradient tensor. The viscoelastic effects are examined through the Weissenberg number ($Wi$), representing the ratio of the longest polymer relaxation time scale to the Kolmogorov time scale. The mean flow around these shear layers is analysed within a local reference frame that characterises shear orientation. In both Newtonian and viscoelastic turbulence, shear layers appear in a straining flow, featuring stretching in the shear vorticity direction and compression in the layer normal direction. Polymer stresses are markedly influenced by the shear and strain, which enhance kinetic energy dissipation due to the polymers. The shear layers in viscoelastic turbulence exhibit a high aspect ratio, undergoing significant characteristic changes once $Wi$ exceeds approximately 2. As $Wi$ increases, the extensive strain weakens, diminishing vortex stretching. This change coincides with an imbalance between extension and compression in the straining flow. In the shear layer, the interaction between vorticity and polymer stress causes the destruction and production of enstrophy at low and high $Wi$ values, respectively. Enstrophy production at high $Wi$ is induced by normal polymer stress oriented along the shear flow, associated with the diminished extensive strain. The $Wi$-dependent behaviour of these shear layers aligns with the overall flow characteristics, underscoring their pivotal roles in vorticity dynamics and kinetic energy dissipation in viscoelastic turbulence.

JFM classification

Wakes/Jets: Shear layers Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1005 , 25 February 2025 , A14
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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