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Large-scale structures in high-Reynolds-number rotating Waleffe flow

Published online by Cambridge University Press:  10 December 2019

Shafqat Farooq ,
Martin Huarte-Espinosa  and
Rodolfo Ostilla-Mónico Open the ORCID record for Rodolfo Ostilla-Mónico [Opens in a new window]
Shafqat Farooq
Affiliation:
Cullen College of Engineering, University of Houston, Houston, TX77204, USA
Martin Huarte-Espinosa
Affiliation:
University of Houston’s Hewlett Packard Enterprise Data Science Institute, University of Houston, Houston, TX77204, USA
Rodolfo Ostilla-Mónico*
Affiliation:
Cullen College of Engineering, University of Houston, Houston, TX77204, USA
*
†Email address for correspondence: [email protected]
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Abstract

We perform direct numerical simulations of rotating turbulent Waleffe flow, the flow between two parallel plates with a sinusoidal streamwise shear driving force, to study the formation of large-scale structures and the mechanisms for momentum transport. We simulate different cyclonic and anticyclonic rotations in the range of dimensionless rotation numbers (inverse Rossby numbers) $R_{\unicode[STIX]{x1D6FA}}\in [-0.16,2.21]$, and fix the Reynolds number to $Re=3.16\times 10^{3}$, large enough such that the shear transport is almost entirely due to Reynolds stresses and viscous transport is negligible. We find an optimum rotation in the anticyclonic regime at $R_{\unicode[STIX]{x1D6FA}}=0.63$, where a given streamwise momentum transport in the wall-normal direction is achieved with minimum mean energy of the streamwise flow. We link this optimal transport to the strength of large-scale structures, as was done in plane Couette flow by Brauckmann & Eckhardt (J. Fluid Mech., vol. 815, 2017, pp. 149–168). Furthermore, we explore the large-scale structures and their behaviour under spanwise rotation, and find disorganized large structures at $R_{\unicode[STIX]{x1D6FA}}=0$ but highly organized structures in the anticyclonic regime, similar to the rolls in rotating plane Couette and turbulent Taylor–Couette flow. We compare the large-scale structures of plane Couette flow and Waleffe flow, and observe that the streamwise vorticity is localized inside the cores of the rolls. We show that the rolls take energy from the mean flow at long time scales, and relate these structures to eigenvalues of the streamfunction.

JFM classification

Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 884 , 10 February 2020 , A26
Copyright
© 2019 Cambridge University Press

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