Turbulent skin-friction drag reduction described with AGKE and triple decomposition

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Federica Gattere

A fully developed channel flow, subjected to oscillatory spanwise wall motion, is studied with a focus on the interaction between the coherent velocity profile introduced by the control, i.e. the Stokes layer, and the near-wall cycle. Two Direct Numerical Simulations have been performed for the controlled and uncontrolled flows at constant power input (CPI), such that at statistical equilibrium both simulations have the same power input.

Our study relies upon the Anisotropic Generalised Kolmogorov Equations (AGKE), the exact budget equations for the second-order structure function tensor. The AGKE highlight the production, transport, redistribution and dissipative processes of each component of the Reynolds stresses considering simultaneously the physical space and the space of scales. In the present work, we have derived and used the AGKE written for a triple decomposition of the velocity which takes into account the presence of mean, coherent and stochastic contributions. The effect of the control on the terms of the AGKE has been described and linked to changes in the near-wall cycle dynamics.

The decreased intensity of the normal components and the shift of their largest values towards smaller scales indicate an overall weakening of the near-wall structures and a shrinking of their sections. The Stokes layer transfers its energy to the stochastic turbulent fluctuations directly interacting with the 3,3 component only. This process occurs at precise wall distances and scales — naturally highlighted by the AGKE — that further elucidate the dynamics of the near-wall structures and their interaction with the Stokes layer when the control is applied.