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Structure function tensor equations with triple decomposition

Published online by Cambridge University Press:  30 March 2023

Federica Gattere Open the ORCID record for Federica Gattere [Opens in a new window] ,
Alessandro Chiarini Open the ORCID record for Alessandro Chiarini [Opens in a new window] ,
Emanuele Gallorini Open the ORCID record for Emanuele Gallorini [Opens in a new window]  and
Maurizio Quadrio Open the ORCID record for Maurizio Quadrio [Opens in a new window]
Federica Gattere
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Alessandro Chiarini
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Emanuele Gallorini
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Maurizio Quadrio*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: maurizio.quadrio@polimi.it
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Abstract

Exact budget equations are derived for the coherent and stochastic contributions to the second-order structure function tensor. They extend the anisotropic generalised Kolmogorov equations (AGKE) by considering the coherent and stochastic parts of the Reynolds stress tensor, and are useful for the statistical description of turbulent flows with periodic or quasi-periodic features, like, for example, the alternate shedding after a bluff body. While the original AGKE describe production, transport, inter-component redistribution and dissipation of the Reynolds stresses in the combined space of scales and positions, the new equations, called $\varphi$AGKE, contain the phase $\varphi$ as an additional independent variable, and describe the interplay among the mean, coherent and stochastic fields at the various phases. The newly derived $\varphi$AGKE are then applied to a case where an exactly periodic external forcing drives the flow: a turbulent plane channel flow modified by harmonic spanwise oscillations of the wall to reduce drag. The phase-by-phase action of the oscillating transversal Stokes layer generated by the forcing on the near-wall turbulent structures is observed, and a detailed description of the scale-space interaction among mean, coherent and stochastic fields is provided thanks to the $\varphi$AGKE.

JFM classification

Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 960 , 10 April 2023 , A7
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

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