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On the origins of steady streaming in precessing fluids

Published online by Cambridge University Press:  21 January 2021

Thomas Albrecht Open the ORCID record for Thomas Albrecht [Opens in a new window] ,
Hugh M. Blackburn Open the ORCID record for Hugh M. Blackburn [Opens in a new window] ,
Juan M. Lopez Open the ORCID record for Juan M. Lopez [Opens in a new window] ,
Richard Manasseh Open the ORCID record for Richard Manasseh [Opens in a new window]  and
Patrice Meunier Open the ORCID record for Patrice Meunier [Opens in a new window]
Thomas Albrecht
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC3800, Australia
Hugh M. Blackburn*
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC3800, Australia
Juan M. Lopez
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ85287, USA
Richard Manasseh
Affiliation:
Department of Mechanical and Product Design Engineering, Swinburne University of Technology, VIC3122, Australia
Patrice Meunier
Affiliation:
IRPHE, CNRS, Aix–Marseille Université, 49 Rue Joliot-Curie, 13013Marseille, France
*
†Email address for correspondence: [email protected]
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Abstract

The finite-amplitude space–time mean flows that are precessionally forced in rotating finite circular cylinders are examined. The findings show that, in addition to conventional Reynolds-stress-type source terms for streaming in oscillatory forced flows, a set of Coriolis-type source terms due the background rotation also contribute. These terms result from the interaction between the equatorial component of the total rotation vector and the overturning flow that is forced by the precession, both of which have azimuthal wavenumbers $m={\pm }1$. The interaction is particular to precessing flows and does not exist in rotating flows driven by libration ($m=0$ forcing) or tides ($m={\pm }2$ forcing). By examining typical example flows in the quasi-linear weakly forced streaming regime, we are able to consider the contributions from the Reynolds-stress terms and the equatorial-Coriolis terms separately, and find that they are of similar magnitude. In the cases examined, the azimuthal component of streaming flow driven by the equatorial-Coriolis terms is everywhere retrograde, whereas that driven by Reynolds stresses may have both retrograde and prograde regions, but the total streaming flows are everywhere retrograde. Even when the forcing frequency is larger than twice the background rotation rate, we find that there is a streaming flow driven by both the Reynolds-stress and the equatorial-Coriolis terms. For cases forced at precession frequencies in near resonance with the eigenfrequencies of the intrinsic inertial modes of the linear inviscid unforced rotating cylinder flow, we quantify theoretically how the amplitude of streaming flow scales with respect to variations in Reynolds number, cylinder tilt angle and aspect ratio, and compare these with numerical simulations.

JFM classification

Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 910 , 10 March 2021 , A51
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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