In Navier–Stokes (NS) turbulence, large-scale turbulent flows inevitably determine small-scale flows. Previous studies using data assimilation with the three-dimensional (3-D) NS equations indicate that employing observational data resolved down to a specific length scale, ^ 3-D, enables the successful reconstruction of small-scale flows. Such a length scale of ‘essential resolution of observation’ for reconstruction ^ 3-D is close to the dissipation scale in three-dimensional NS turbulence. Here, we study the equivalent length scale in two-dimensional (2-D) NS turbulence, ^ 2-D, 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 ^ 2-D 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, ^ 2-D and ^ 3-D, based on inter-scale interactions, ‘cascades’ and orbital instabilities in turbulence dynamics.
Inubushi et al. (Thu,) studied this question.