Revisiting 2D Viscoelastic Kolmogorov Flow: A Centre-mode-driven transition
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arXiv
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| Format: | Preprint |
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2024
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| author | Lewy, Theo Kerswell, Rich |
| author_facet | Lewy, Theo Kerswell, Rich |
| contents | We revisit viscoelastic Kolmogorov flow to show that the elastic linear instability of an Oldroyd-B fluid at vanishing Reynolds numbers ($Re$) found by Boffetta et al. (J. Fluid Mech. 523, 161-170, 2005) is the same `centre-mode' instability found at much higher $Re$ by Garg et al. (Phys. Rev. Lett. 121, 024502, 2018) in a pipe and Khalid et al. (J. Fluid Mech. 915, A43, 2021) in a channel. In contrast to these wall-bounded flows, the centre-mode instability exists even when the solvent viscosity vanishes (e.g. it exists in the upper-convective Maxwell limit with $Re=0$). Floquet analysis reveals that the preferred centre-mode instability almost always has a wavelength twice that of the forcing. All elastic instabilities give rise to familiar `arrowheads' (Page et al. Phys. Rev. Lett. 125, 154501, 2020) which in sufficiently large domains and at sufficient Weissenberg number ($W$) interact chaotically in 2D to give elastic turbulence via a bursting scenario. Finally, it is found that the $k^{-4}$ scaling of the kinetic energy spectrum seen in this 2D elastic turbulence is already contained within the component arrowhead structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting 2D Viscoelastic Kolmogorov Flow: A Centre-mode-driven transition Lewy, Theo Kerswell, Rich Fluid Dynamics We revisit viscoelastic Kolmogorov flow to show that the elastic linear instability of an Oldroyd-B fluid at vanishing Reynolds numbers ($Re$) found by Boffetta et al. (J. Fluid Mech. 523, 161-170, 2005) is the same `centre-mode' instability found at much higher $Re$ by Garg et al. (Phys. Rev. Lett. 121, 024502, 2018) in a pipe and Khalid et al. (J. Fluid Mech. 915, A43, 2021) in a channel. In contrast to these wall-bounded flows, the centre-mode instability exists even when the solvent viscosity vanishes (e.g. it exists in the upper-convective Maxwell limit with $Re=0$). Floquet analysis reveals that the preferred centre-mode instability almost always has a wavelength twice that of the forcing. All elastic instabilities give rise to familiar `arrowheads' (Page et al. Phys. Rev. Lett. 125, 154501, 2020) which in sufficiently large domains and at sufficient Weissenberg number ($W$) interact chaotically in 2D to give elastic turbulence via a bursting scenario. Finally, it is found that the $k^{-4}$ scaling of the kinetic energy spectrum seen in this 2D elastic turbulence is already contained within the component arrowhead structures. |
| title | Revisiting 2D Viscoelastic Kolmogorov Flow: A Centre-mode-driven transition |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2410.07402 |