Inner-outer scale interactions in turbulent Couette flow

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Mariadebora Mauriello

The interscale interaction between small-scale structures placed near the wall and large-scale structures placed at large wall distances is investigated in turbulent plane Couette flow at Retau = 100. The tool of choice are the exact budget equations for the second-order structure function tensor, i.e. the Anisotropic Generalised Kolmogorov Equations (AGKE). The AGKE are effective to study the production, transport and dissipation of every Reynolds stress tensor component, considering simultaneously the physical space and the space of scales, and properly defining scales in the inhomogeneous directions.

The AGKE reveal that the large-scale energy-containing motions characterizing the Couette flow are also involved in the production and redistribution mechanisms of the turbulent fluctuations. The diagonal components of the AGKE reveal that both bottom-up and top-down interactions occur. In detail, δuδu and δwδw show that the small scales near the wall maintain the large scales away from the wall: both these components of the turbulent kinetic energy are mainly produced near the wall and partially transferred towards larger wall distances via the inverse cascade. On the contrary, δvδv shows the top-down interaction, revealing that the δvδv is produced by the redistribution of the pressure strain away from the wall and it is transferred towards larger scales placed in the wall vicinity. The Reynolds shear stress shows the top-down interaction; δuδv is transferred from the channel core towards the wall exhibiting both the inverse cascade, even if for a limited range of scales, and the direct cascade.

Overall, this study has provided a complete and new picture of the interscale inner-outer interactions that occur in a turbulent plane Couette flow. This may benefit both theoretical and modelling approaches to wall turbulence. For example, it may be used to improve existing models used in large-eddies simulations, where the effect of the small unresolved scales on the resolved motion should be accurately reproduced. Despite the innovative insights found already at this moderate Reynolds number, the present study may benefit from an extension to higher Reynolds numbers where a complete separation of scales occurs.