A further investigation on the data assimilation-based small-scale reconstruction of turbulence

Wang, Yunpeng1,2,3; Yuan, Zelong1,2,3; Wang, Jianchun1,2,3

2023

10.1063/5.0130113

PHYSICS OF FLUIDS   Impact Factor & Quartile

1070-6631

1089-7666

Existing works have shown that the small-scale errors of turbulence can be completely eliminated through data assimilation (DA), provided that all the large-scale Fourier modes below a critical wavenumber k(c) asymptotic to 0.2 eta(-1) are continuously enforced, where eta is the Kolmogorov length scale. Here, we further explore the DA-based small-scale reconstruction problem, for which the large-scale data are insufficient. Under such conditions, an unexpected artificial jump in the energy spectrum is observed. To alleviate this issue and improve the reconstruction accuracy, several approaches have been attempted, including ensemble averaged assimilation, temporally sparse data assimilation (TSDA), and filtering the penalty term in the assimilation. It is shown that ensemble averaging can tangibly reduce the reconstruction error, but the resulted energy spectrum is invariably lower than the true spectrum; TSDA can effectively remove the jump in the energy spectrum, but the reduction of the reconstruction error is limited. Filtering the penalty term can also rectify the energy spectrum, but it makes the reconstruction error larger. Based on these observations, we re-scale the ensemble averaged solution according to the rectified energy spectrum. Both the energy spectrum and the small-scale reconstruction accuracy have been improved by the re-scaled ensemble average method. Furthermore, we also test the current approach in the spatial nudging-based reconstruction of turbulence. Again, enhanced predictions are obtained for both the energy spectrum and the instantaneous turbulent field, invariably demonstrating the effectiveness and robustness of the proposed method.

SCI

English

First ; Corresponding

National Natural Science Foundation of China["91952104","92052301","12172161","91752201"] ; National Numerical Windtunnel Project[NNW2019ZT1-A04] ; Shenzhen Science and Technology Program[KQTD20180411143441009] ; Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou)[GML2019ZD0103] ; Department of Science and Technology of Guangdong Province[2020B1212030001]

Mechanics ; Physics

Mechanics ; Physics, Fluids & Plasmas

WOS:000921518000016

AIP Publishing

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Natl Ctr Appl Math Shenzhen NCAMS, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Shenzhen 518055, Peoples R China
3.Southern Univ Sci & Technol, Guangdong Hong Kong Macao Joint Lab Data Driven Fl, Shenzhen 518055, Peoples R China

Wang, Yunpeng,Yuan, Zelong,Wang, Jianchun. A further investigation on the data assimilation-based small-scale reconstruction of turbulence[J]. PHYSICS OF FLUIDS,2023,35(1).

Wang, Yunpeng,Yuan, Zelong,&Wang, Jianchun.(2023).A further investigation on the data assimilation-based small-scale reconstruction of turbulence.PHYSICS OF FLUIDS,35(1).

Wang, Yunpeng,et al."A further investigation on the data assimilation-based small-scale reconstruction of turbulence".PHYSICS OF FLUIDS 35.1(2023).