Characterizing Data Assimilation in Navier-Stokes Turbulence with Transverse Lyapunov Exponents
arXiv:2307.05941 · doi:10.1103/PhysRevLett.131.254001
Abstract
Data assimilation (DA) reconstructing small-scale turbulent structures is crucial for forecasting and understanding turbulence. This study proposes a theoretical framework for DA based on ideas from chaos synchronization, in particular, the transverse Lyapunov exponents (TLEs). The analysis with TLEs characterizes a critical length scale, below which the turbulent dynamics is synchronized to the larger-scale turbulent dynamics, indicating successful DA. An underlying link between TLEs and the maximal Lyapunov exponent suggests that the critical length scale depends on the Reynolds number. Furthermore, we discuss new directions of DA algorithms based on the proposed framework.
5 pages, 3 figures
References in corpus (11)
- Characterizing dynamics with covariant Lyapunov vectors
- Hyperbolicity and the effective dimension of spatially-extended dissipative systems
- Chaos and predictability of homogeneous-isotropic turbulence
- Scaling of Lyapunov Exponents in Homogeneous Isotropic Turbulence
- Transfer learning for nonlinear dynamics and its application to fluid turbulence
- Synchronization of turbulence in channel flow
- Linear instability of turbulent channel flow
- Mathematical reformulation of the Kolmogorov-Richardson energy cascade in terms of vortex stretching
- Synchronization of Low Reynolds Number Plane Couette Turbulence
- Scale-dependent Error Growth in Navier--Stokes Simulations
- Inferring the instability of a dynamical system from the skill of data assimilation exercises
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