Synchronisation in two-dimensional damped-driven Navier-Stokes turbulence: insights from data assimilation and Lyapunov analysis

Fuente: arXiv
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Autores principales: Inubushi, Masanobu, Caulfield, Colm-cille P.
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
id 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