Structure function tensor equations in inhomogeneous turbulence

Abstract

Exact budget equations for the second-order structure function tensor $⟨\delta u_i\delta u_j⟩$ are used to study the two-point statistics of velocity fluctuations in inhomogeneous turbulence. The Anisotropic Generalized 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 Generalized 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 $⟨\delta u_i\delta u_j⟩$. 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 $R{e}_{\tau }=200$ is considered. The off-diagonal component $⟨-\delta u\delta v⟩$, which can not 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 $R{e}_{\tau }=500$ and $1000$. 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.

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Cited by in corpus (7)

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• Energy transfer mechanisms in adverse pressure gradient turbulent boundary layers
• Structure of turbulence in the flow around a rectangular cylinder
• Ascending-descending and direct-inverse cascades of Reynolds stresses in turbulent Couette flow
• Curvature effects on the structure of near-wall turbulence
• Structure function tensor equations with triple decomposition
• Energy, enstrophy and helicity transfers in polymeric turbulence