2025/08/23 by Masanobu Inubushi, C. P. Caulfield, Inubushi, Masanobu +1 · 1 voice · 1 citation
Engineering · Computer Science · Earth and Planetary Sciences · #34D06 #37L30 #37N10 #76F02 (Secondary) #76F20 (Primary) #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2508.16920
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, ℓ3D∗, enables the successful reconstruction of small-scale flows. Such a length scale of `essential resolution of observation' for reconstruction ℓ3D∗ is close to the dissipation scale in three-dimensional NS turbulence. % Here we study the equivalent length scale in \it two-dimensional NS turbulence, ℓ2D∗, 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 ℓ2D∗ 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, ℓ2D∗ and ℓ3D∗, based on inter-scale interactions, `cascades' and orbital instabilities in turbulence dynamics.