Characterizing Small-Scale Dynamics of Navier-Stokes Turbulence with Transverse Lyapunov Exponents: A Data Assimilation Approach
Masanobu Inubushi, Yoshitaka Saiki, Miki U. Kobayashi, Susumu Goto
Abstract
Data assimilation (DA) of turbulence, which involves reconstructing small-scale turbulent structures based on observational data from large-scale ones, is crucial not only for practical forecasting but also for gaining a deeper understanding of turbulent dynamics. We propose a theoretical framework for DA of turbulence based on the transverse Lyapunov exponents (TLEs) in synchronization theory. Through stability analysis using TLEs, we identify a critical length scale as a key condition for DA; turbulent dynamics smaller than this scale are synchronized with larger-scale turbulent dynamics. Furthermore, considering recent findings for the maximal Lyapunov exponent and its relation with the TLEs, we clarify the Reynolds number dependence of the critical length scale.