Temporally sparse data assimilation for the small-scale reconstruction of turbulence

Previous works have shown that the small-scale information of incompressible homogeneous isotropic turbulence is fully recoverable as long sufficient large-scale structures are continuously enforced through temporally continuous data assimilation (TCDA). In current work, we show time step can be relaxed to values about 1–2 orders larger than for TCDA, using a sparse (TSDA) strategy, while accuracy still maintained or even slightly better in presence non-negligible errors. One-step (ODA) examined unravel mechanism TSDA. It relaxation effect errors above wavenumber k responsible error decay ODA. Meanwhile, contained large scales propagate into small and make high-wavenumber ([Formula: see text]) noise slower with TCDA This further confirmed by incorporating different levels reference flow field. The advantage TSDA found grow magnitude incorporated Thus, it potentially more beneficial adopt if contain Finally, an outstanding issue raised previous regarding possibility recovering dynamics sub-Kolmogorov direct numerical simulation at Kolmogorov scale resolution also discussed.