Analysis of the Kolmogorov equation for filtered wall-turbulent flows

Cimarelli, Andrea; Angelis, E. De

doi:10.1017/s0022112011000565

Cited by 20 publications

(12 citation statements)

References 35 publications

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“…On the other hand, for filter lengths falling outside the homogeneous range, the physics captured by the LES is expected to be rather poor and the complexity of the phenomena occurring at subgrid level may bring some modelling issues. Regarding the latter point, an increase of the filter length beyond the boundary scales u * b and θ * b could generate a net flux taking origin at subgrid level to feed the larger resolved scales via a reverse cascade, as shown by Cimarelli & De Angelis (2011) in the case of a turbulent channel flow. These conditions are a challenge for LES models, which should take into account strong backscatter effects (Cimarelli & De Angelis 2014).…”

Section: Study Of the Unfiltered Data Setmentioning

confidence: 98%

“…In order to disentangle the two distinct effects that the filtering operation has on the LES result, namely the degree of resolution of the actual dynamics and the influence of the modelling, a DNS data set can be explicitly filtered to separate the resolved from the subgrid components of the different fields. This a priori approach was pursued by many authors in order to compute quantities of interest such as the equations for the filtered turbulent kinetic energy (Härtel et al 1994), the filtered energy spectrum (Domaradzki et al 1994) and the filtered scale energy (Cimarelli & De Angelis 2011).…”

Section: Study Of the Filtered Data Setmentioning

confidence: 99%

“…For this purpose, the velocity and the scalar fields obtained from a DNS are split into resolved and subgrid components using a spectral cutoff filter and analyzed by means of filtered single-point and two-point budgets. While the filtered Kolmogorov equation has been already employed by Cimarelli & De Angelis (2011), the filtered Yaglom equation is presented and discussed here for the first time.…”

Section: Introductionmentioning

confidence: 99%

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Resolved and subgrid dynamics of Rayleigh–Bénard convection

2019

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In this work we present and demonstrate the reliability of a theoretical framework for the study of thermally driven turbulence. It consists of scale-by-scale budget equations for the second-order velocity and temperature structure functions and their limiting cases, represented by the turbulent kinetic energy and temperature variance budgets. This framework represents an extension of the classical Kolmogorov and Yaglom equations to inhomogeneous and anisotropic flows, and allows for a novel assessment of the turbulent processes occurring at different scales and locations in the fluid domain. Two relevant characteristic scales, $\ell _{c}^{u}$ for the velocity field and $\ell _{c}^{\unicode[STIX]{x1D703}}$ for the temperature field, are identified. These variables separate the space of scales into a quasi-homogeneous range, characterized by turbulent kinetic energy and temperature variance cascades towards dissipation, and an inhomogeneity-dominated range, where the production and the transport in physical space are important. This theoretical framework is then extended to the context of large-eddy simulation to quantify the effect of a low-pass filtering operation on both resolved and subgrid dynamics of turbulent Rayleigh–Bénard convection. It consists of single-point and scale-by-scale budget equations for the filtered velocity and temperature fields. To evaluate the effect of the filter length $\ell _{F}$ on the resolved and subgrid dynamics, the velocity and temperature fields obtained from a direct numerical simulation are split into filtered and residual components using a spectral cutoff filter. It is found that when $\ell _{F}$ is smaller than the minimum values of the cross-over scales given by $\ell _{c,min}^{\unicode[STIX]{x1D703}\ast }=\ell _{c,min}^{\unicode[STIX]{x1D703}}Nu/H=0.8$, the resolved processes correspond to the exact ones, except for a depletion of viscous and thermal dissipations, and the only role of the subgrid scales is to drain turbulent kinetic energy and temperature variance to dissipate them. On the other hand, the resolved dynamics is much poorer in the near-wall region and the effects of the subgrid scales are more complex for filter lengths of the order of $\ell _{F}\approx 3\ell _{c,min}^{\unicode[STIX]{x1D703}}$ or larger. This study suggests that classic eddy-viscosity/diffusivity models employed in large-eddy simulation may suffer from some limitations for large filter lengths, and that alternative closures should be considered to account for the inhomogeneous processes at subgrid level. Moreover, the theoretical framework based on the filtered Kolmogorov and Yaglom equations may represent a valuable tool for future assessments of the subgrid-scale models.

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Section: Study Of the Unfiltered Data Setmentioning

confidence: 98%

Section: Study Of the Filtered Data Setmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resolved and subgrid dynamics of Rayleigh–Bénard convection

2019

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“…In that paper, a model for the energy cascade was also developed to account for the dual nature of the energy transfer consisting of forward and reverse cascades ascending from the wall. From the model a large eddy simulation (LES) closure was developed, Cimarelli & De Angelis (2011, 2012, that was shown able to account for the small scale behaviour responsible for the backward energy transfer.…”

Section: Introductionmentioning

confidence: 99%

Cascades and wall-normal fluxes in turbulent channel flows

et al. 2016

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The present work describes the multidimensional behaviour of scale-energy production, transfer and dissipation in wall-bounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scale-by-scale among different regions of the flow. Two driving mechanisms are identified. A strong scale-energy source in the buffer layer related to the near-wall cycle and an outer scale-energy source associated with an outer turbulent cycle in the overlap layer. These two sourcing mechanisms lead to a complex redistribution of scale energy where spatially evolving reverse and forward cascades coexist. From a hierarchy of spanwise scales in the near-wall region generated through a reverse cascade and local turbulent generation processes, scale energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, still ascending towards the channel centre. The attached scales of wall-bounded turbulence are then recognized to sustain a spatial reverse cascade process towards the bulk flow. On the other hand, the detached scales are involved in a direct forward cascade process that links the scale-energy excess at large attached scales with dissipation at the smaller scales of motion located further away from the wall. The unexpected behaviour of the fluxes and of the turbulent generation mechanisms may have strong repercussions on both theoretical and modelling approaches to wall turbulence. Indeed, actual turbulent flows are shown here to have a much richer physics with respect to the classical notion of turbulent cascade, where anisotropic production and inhomogeneous fluxes lead to a complex redistribution of energy where a spatial reverse cascade plays a central role.

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“…They are thus exact and do not rely on particular assumptions about the flow. Third, since in large-eddy simulations (LES), the notion of scale is inherent to the filtering operation, scale energy budgets have further been shown to be useful to better characterize the energy transfer between the resolved and subgrid scales (Gualtieri et al 2007;Cimarelli & De Angelis 2011;Cimarelli et al 2015). LES models can also be developed on the basis of such a framework (Lesieur & Metais 1996;Cui et al 2007;Lévêque et al 2007).…”

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confidence: 99%