Exact budget equations for the second-order structure function tensor, where is the difference of the th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure-strain term and contain also budget equations for the off-diagonal components of. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of is considered. The off-diagonal component, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at and. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.

Structure function tensor equations in inhomogeneous turbulence / Gatti, D.; Chiarini, A.; Cimarelli, A.; Quadrio, M.. - In: JOURNAL OF FLUID MECHANICS. - ISSN 0022-1120. - 898:(2020), pp. 1-33. [10.1017/jfm.2020.399]

### Structure function tensor equations in inhomogeneous turbulence

#### Abstract

Exact budget equations for the second-order structure function tensor, where is the difference of the th fluctuating velocity component between two points, are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The anisotropic generalised Kolmogorov equations (AGKE) describe the production, transport, redistribution and dissipation of every Reynolds stress component occurring simultaneously among different scales and in space, i.e. along directions of statistical inhomogeneity. The AGKE are effective to study the inter-component and multi-scale processes of turbulence. In contrast to more classic approaches, such as those based on the spectral decomposition of the velocity field, the AGKE provide a natural definition of scales in the inhomogeneous directions, and describe fluxes across such scales too. Compared to the generalised Kolmogorov equation, which is recovered as their half-trace, the AGKE can describe inter-component energy transfers occurring via the pressure-strain term and contain also budget equations for the off-diagonal components of. The non-trivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the near-wall cycle of a turbulent channel flow at a friction Reynolds number of is considered. The off-diagonal component, which cannot be interpreted in terms of scale energy, is discussed in detail. Wall-normal scales in the outer turbulence cycle are then discussed by applying the AGKE to channel flows at and. In a third example, the AGKE are computed for a separating and reattaching flow. The process of spanwise-vortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.
##### Scheda breve Scheda completa Scheda completa (DC)
2020
898
1
33
Structure function tensor equations in inhomogeneous turbulence / Gatti, D.; Chiarini, A.; Cimarelli, A.; Quadrio, M.. - In: JOURNAL OF FLUID MECHANICS. - ISSN 0022-1120. - 898:(2020), pp. 1-33. [10.1017/jfm.2020.399]
Gatti, D.; Chiarini, A.; Cimarelli, A.; Quadrio, M.
File in questo prodotto:
File
div-class-title-structure-function-tensor-equations-in-inhomogeneous-turbulence-div.pdf

Open access

Tipologia: Versione pubblicata dall'editore
Dimensione 961.17 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1207416`