An efficient numerical method for the generalised Kolmogorov equation

Gatti, Davide; Remigi, Alberto; Chiarini, Alessandro; Cimarelli, Andrea; Quadrio, Maurizio

doi:10.1080/14685248.2019.1664746

Cited by 8 publications

(11 citation statements)

References 32 publications

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“…It also heavily relies on the numerical optimizations introduced by Gatti et al. (2019) for a precursory GKE version, which computes correlations pseudo-spectrally whenever possible. For maximum accuracy, the derivatives in the homogeneous directions are computed in Fourier space, whereas the derivatives in the wall-normal direction are evaluated by means of a finite-difference scheme with a five-point computational stencil.…”

Section: Methodsmentioning

confidence: 99%

Ascending–descending and direct–inverse cascades of Reynolds stresses in turbulent Couette flow

et al. 2021

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The interaction between small- and large-scale structures and the coexisting bottom-up and top-down processes are studied in a turbulent plane Couette flow, where space-filling longitudinal rolls appear at relatively low values of the Reynolds number $Re$ . A direct numerical simulation database at $Re_\tau =101$ is built to replicate the highest $Re$ considered in recent experimental work by Kawata & Alfredsson (Phys. Rev. Lett., vol. 120, 2018, 244501). Our study is based on the exact budget equations for the second-order structure function tensor $\left \langle {\delta u_i \delta u_j} \right \rangle$ , i.e. the anisotropic generalized Kolmogorov equations (AGKE). The AGKE study production, redistribution, transport and dissipation of every Reynolds stress tensor component, considering simultaneously the physical space and the space of scales, and properly define the concept of scale in the inhomogeneous wall-normal direction. We show how the large-scale energy-containing motions are involved in the production and redistribution of the turbulent fluctuations. Both bottom-up and top-down interactions occur, and the same is true for direct and inverse cascading. The wall-parallel components $\left \langle {\delta u \delta u} \right \rangle$ and $\left \langle {\delta w \delta w} \right \rangle$ show that both small and large near-wall scales feed the large scales away from the wall. The wall-normal component $\left \langle {\delta v \delta v} \right \rangle$ is different, and shows a dominant top-down dynamics, being produced via pressure-strain redistribution away from the wall and transferred towards near-wall larger scales via an inverse cascade. The off-diagonal component shows a top-down interaction, with both direct and inverse cascades, albeit the latter takes place within a limited range of scales.

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Section: Methodsmentioning

confidence: 99%

Ascending–descending and direct–inverse cascades of Reynolds stresses in turbulent Couette flow

et al. 2021

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“…The AGKE terms for the BARC flow have been computed by post-processing the DNS database described above. The code used for the analysis extends a high-performance software tool written for the GKE and developed by Gatti et al (2019), available freely at https://github.com/davecats/gke. Given the size of the problem, the AGKE terms have been computed in two sub-boxes within the computational domain, both encompassing the full body width.…”

Section: The Anisotropic Generalised Kolmogorov Equationsmentioning

confidence: 99%

Structure of turbulence in the flow around a rectangular cylinder

et al. 2022

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The separating and reattaching turbulent flow past a rectangular cylinder is studied to describe how small and large scales contribute to the sustaining mechanism of the velocity fluctuations. The work is based on the anisotropic generalised Kolmogorov equations, exact budget equations for the second-order structure function tensor in the space of scales and in the physical space. Scale-space energy fluxes show that forward and reverse energy transfers occur simultaneously in the flow, with interesting modelling implications. Over the longitudinal cylinder side, the Kelvin–Helmholtz instability of the leading edge shear layer generates large spanwise rolls, which get stretched into hairpin-like vortices and eventually break down into smaller streamwise vortices. Independent sources of velocity fluctuations act at different scales. The flow dynamics is dominated by pressure–strain: the flow impingement on the cylinder surface in the reattachment zone produces spanwise velocity fluctuations very close to the wall, and at larger wall distances reorients them to feed streamwise-aligned vortices. In the near wake, large von Kármán-like vortices are shed from the trailing edge and coexist with smaller turbulent structures, each with its own independent production mechanism. At the trailing edge, the sudden disappearance of the wall changes the structure of turbulence: streamwise vortices vanish progressively, while spanwise structures close to the wall are suddenly turned into vertical fluctuations by the pressure–strain.

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“…Given this quite high number of computational resources, we considered here only one set of parameters. The library employed here to compute two-point statistics could be substantially optimized using the methodology described by Gatti et al (2019). Hence, we expect to be able, in the short term, to reduce significantly this amount of computational time to post-process larger simulation domains.…”

Section: Numerical Domain and Flow Featuresmentioning

confidence: 99%