Quantifying the linear damping in two-dimensional turbulence

Xie, Jin-Han

doi:10.1103/physrevfluids.5.094605

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…Theoretically, the power law for the normal cascade is modified to the range between k −3 and k −5 for the moderate resolution and Reynolds number Shepherd 2002, Tran andBowman 2003). The power lows of the normal cascade in former numerical studies were also steeper than k −3 (Herring and Mcwilliams 1985, Legras et al 1988, Scott 2007, Tsang and Young 2009, Clark et al 2020, Xie 2020. It is noted that simulations at higher resolution may make the result close to the KLB theory (see the work by Boffetta (2007): the mesh resolution up to 32 768 2 resulted in the power low of ≈k −3.35 ); however, such a larger scale simulation is not in the scope of the current study, i.e.…”

Section: Design Of Numerical Configurationmentioning

confidence: 96%

Continuous data assimilation of large eddy simulation by lattice Boltzmann method and local ensemble transform Kalman filter (LBM-LETKF)

Hasegawa,

Onodera,

Asahi

et al. 2023

Fluid Dyn. Res.

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We investigate the applicability of the data assimilation (DA) to large eddy simulations (LESs) based on the lattice Boltzmann method (LBM). We carry out the observing system simulation experiment of a two-dimensional (2D) forced isotropic turbulence, and examine the DA accuracy of the nudging and the local ensemble transform Kalman filter (LETKF) with spatially sparse and noisy observation data of flow fields. The advantage of the LETKF is that it does not require computing spatial interpolation and/or an inverse problem between the macroscopic variables (the density and the pressure) and the velocity distribution function of the LBM, while the nudging introduces additional models for them. The numerical experiments with 256×256 grids and 10% observation noise in the velocity showed that the root mean square error of the velocity in the LETKF with 8×8 observation points (∼0.1% of the total grids) and 64 ensemble members becomes smaller than the observation noise, while the nudging requires an order of magnitude larger number of observation points to achieve the same accuracy. Another advantage of the LETKF is that it well keeps the amplitude of the energy spectrum, while only the phase error becomes larger with more sparse observation. We also see that a lack of observation data in the LETKF produces a spurious energy injection in high wavenumber regimes, leading to numerical instability. Such numerical instability is known as the catastrophic filter divergence problem, which can be suppressed by increasing the number of ensemble members. From these results, it was shown that the LETKF enables robust and accurate DA for the 2D LBM with sparse and noisy observation data.

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Section: Design Of Numerical Configurationmentioning

confidence: 96%

Continuous data assimilation of large eddy simulation by lattice Boltzmann method and local ensemble transform Kalman filter (LBM-LETKF)

Hasegawa,

Onodera,

Asahi

et al. 2023

Fluid Dyn. Res.

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show abstract

“…The dissipation operators in (3.1) were chosen to allow the development of inertial cascades where the direct effect of forcing and dissipative terms on structure function relations are assumed to be negligible. Recently this inertial cascade assumption has been relaxed to find structure function relations that include dissipative and forcing effects in isotropic 2-D turbulence (Xie & Bühler 2018, 2019), which can be used to diagnose properties of the dissipative operators from structure functions (Xie 2020). The structure function relations can be modified to account for the effect, as discussed in § 2.2.…”

Section: Numerical Simulationsmentioning

confidence: 99%