Synchronisation in two-dimensional damped-driven Navier-Stokes turbulence: insights from data assimilation and Lyapunov analysis
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| Formato: | Preprint |
| Publicado: |
2025
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| author | Inubushi, Masanobu Caulfield, Colm-cille P. |
| author_facet | Inubushi, Masanobu Caulfield, Colm-cille P. |
| contents | In Navier--Stokes (NS) turbulence, large-scale turbulent flows inevitably determine small-scale flows. Previous studies using data assimilation with the three-dimensional NS equations indicate that employing observational data resolved down to a specific length scale, $\ell^{3D}_{\ast}$, enables the successful reconstruction of small-scale flows. Such a length scale of `essential resolution of observation' for reconstruction $\ell^{3D}_{\ast}$ is close to the dissipation scale in three-dimensional NS turbulence. % Here we study the equivalent length scale in {\it two}-dimensional NS turbulence, $\ell^{2D}_{\ast}$, and compare with the three-dimensional case. Our numerical studies using data assimilation and conditional Lyapunov exponents reveal that, for Kolmogorov flows with Ekman drag, the length scale $\ell^{2D}_{\ast}$ is actually close to the forcing scale, substantially larger than the dissipation scale. Furthermore, we discuss the origin of the significant relative difference between the length scales, $\ell^{2D}_{\ast}$ and $\ell^{3D}_{\ast}$, based on inter-scale interactions, `cascades' and orbital instabilities in turbulence dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_16920 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Synchronisation in two-dimensional damped-driven Navier-Stokes turbulence: insights from data assimilation and Lyapunov analysis Inubushi, Masanobu Caulfield, Colm-cille P. Fluid Dynamics Dynamical Systems Chaotic Dynamics 76F20 (Primary), 37N10, 37L30, 34D06, 76F02 (Secondary) In Navier--Stokes (NS) turbulence, large-scale turbulent flows inevitably determine small-scale flows. Previous studies using data assimilation with the three-dimensional NS equations indicate that employing observational data resolved down to a specific length scale, $\ell^{3D}_{\ast}$, enables the successful reconstruction of small-scale flows. Such a length scale of `essential resolution of observation' for reconstruction $\ell^{3D}_{\ast}$ is close to the dissipation scale in three-dimensional NS turbulence. % Here we study the equivalent length scale in {\it two}-dimensional NS turbulence, $\ell^{2D}_{\ast}$, and compare with the three-dimensional case. Our numerical studies using data assimilation and conditional Lyapunov exponents reveal that, for Kolmogorov flows with Ekman drag, the length scale $\ell^{2D}_{\ast}$ is actually close to the forcing scale, substantially larger than the dissipation scale. Furthermore, we discuss the origin of the significant relative difference between the length scales, $\ell^{2D}_{\ast}$ and $\ell^{3D}_{\ast}$, based on inter-scale interactions, `cascades' and orbital instabilities in turbulence dynamics. |
| title | Synchronisation in two-dimensional damped-driven Navier-Stokes turbulence: insights from data assimilation and Lyapunov analysis |
| topic | Fluid Dynamics Dynamical Systems Chaotic Dynamics 76F20 (Primary), 37N10, 37L30, 34D06, 76F02 (Secondary) |
| url | https://arxiv.org/abs/2508.16920 |