Exact budget equations for the secondorder structure function tensor, where is the difference of the th fluctuating velocity component between two points, are used to study the twopoint 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 intercomponent and multiscale 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 halftrace, the AGKE can describe intercomponent energy transfers occurring via the pressurestrain term and contain also budget equations for the offdiagonal components of. The nontrivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the nearwall cycle of a turbulent channel flow at a friction Reynolds number of is considered. The offdiagonal component, which cannot be interpreted in terms of scale energy, is discussed in detail. Wallnormal 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 spanwisevortex 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 00221120.  898:(2020), pp. 133. [10.1017/jfm.2020.399]
Structure function tensor equations in inhomogeneous turbulence
Chiarini A.;Cimarelli A.;
20200101
Abstract
Exact budget equations for the secondorder structure function tensor, where is the difference of the th fluctuating velocity component between two points, are used to study the twopoint 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 intercomponent and multiscale 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 halftrace, the AGKE can describe intercomponent energy transfers occurring via the pressurestrain term and contain also budget equations for the offdiagonal components of. The nontrivial physical interpretation of the AGKE terms is demonstrated with three examples. First, the nearwall cycle of a turbulent channel flow at a friction Reynolds number of is considered. The offdiagonal component, which cannot be interpreted in terms of scale energy, is discussed in detail. Wallnormal 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 spanwisevortex formation in the reverse boundary layer within the separation bubble is discussed for the first time.File  Dimensione  Formato  

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