Abstract

In Navier-Stokes (NS) turbulence, large-scale turbulent flows determine small-scale flows; in other words, small-scale flows are synchronized to large-scale flows. In 3D turbulence, previous numerical studies suggest that the critical length separating these two scales is determined by the Kolmogorov length. In this talk, I will introduce our theoretical framework for characterizing synchronization phenomena [1]. Specifically, it provides a computational method for the exponential rate of convergence to the synchronized state, and identifies the critical length based on the NS equations via the “transverse” Lyapunov exponent. I will also discuss the synchronization property of 2D NS turbulence and how it differs from the 3D case [2]. These insights into synchronization and critical length scales are essential for developing machine-learning closure models for turbulence, in particular their stable reproducibility [3]. Finally, I will illustrate how “generalized” synchronization is crucial for predicting chaotic dynamics [4].

[1] M. Inubushi, Y. Saiki, M. U. Kobayashi, and S. Goto, Characterizing small-scale dynamics of Navier-Stokes turbulence with transverse Lyapunov exponents: A data assimilation approach, Phys. Rev. Lett. 131, 254001 (2023). [2] M. Inubushi and C. P. Caulfield (in preparation). [3] S. Matsumoto, M. Inubushi, and S. Goto, Stable reproducibility of turbulence dynamics by machine learning, Phys. Rev. Fluids 9, 104601 (2024). [4] A. Ohkubo and M. Inubushi, Reservoir computing with generalized readout based on generalized synchronization, Sci. Rep. 14, 30918 (2024).