Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2025-01-01T07:59:19.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Precessing cube: resonant excitation of modes and triadic resonance

Published online by Cambridge University Press:  21 January 2020

Ke Wu ,
Bruno D. Welfert Open the ORCID record for Bruno D. Welfert [Opens in a new window]  and
Juan M. Lopez Open the ORCID record for Juan M. Lopez [Opens in a new window]
Ke Wu
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe AZ 85287, USA
Bruno D. Welfert
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe AZ 85287, USA
Juan M. Lopez*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe AZ 85287, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Numerical simulations of the response flow in a fluid-filled rotating cube that is subjected to precessional forcing are examined over a wide range of rotation, precession and forcing frequencies. The responses are shown to correspond to resonantly excited inertial modes of the rotating cube that have the same spatio-temporal symmetry as the precessional forcing and, under certain conditions, the response flow loses stability via symmetry breaking that is intricately associated with a triadic resonance between the forced flow and two free inertial modes whose spatio-temporal symmetries do not coincide with that of the precessional forcing.

JFM classification

Instability: Parametric instability Geophysical and Geological Flows: Rotating flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 887 , 25 March 2020 , A6
Copyright
© 2020 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albrecht, T., Blackburn, H. M., Lopez, J. M., Manasseh, R. & Meunier, P. 2015 Triadic resonances in precessing rapidly rotating cylinder flows. J. Fluid Mech. 778, R1.CrossRefGoogle Scholar
Albrecht, T., Blackburn, H. M., Lopez, J. M., Manasseh, R. & Meunier, P. 2018 On triadic resonance as an instability mechanism in precessing cylinder flow. J. Fluid Mech. 841, R3.CrossRefGoogle Scholar
Aldridge, K. D. & Toomre, A. 1969 Axisymmetric inertial oscillations of a fluid in a rotating spherical container. J. Fluid Mech. 37, 307–323.CrossRefGoogle Scholar
Bewley, G. P., Lathrop, D. P., Maas, L. R. M. & Sreenivasan, K. R. 2007 Inertial waves in rotating grid turbulence. Phys. Fluids 19, 071701.CrossRefGoogle Scholar
Boisson, J., Lamriben, C., Maas, L. R. M., Cortet, P. P. & Moisy, F. 2012 Inertial waves and modes excited by the libration of a rotating cube. Phys. Fluids 24, 076602.CrossRefGoogle Scholar
Busse, F. H. 1968 Steady fluid flow in a precessing spherical shell. J. Fluid Mech. 33, 739–751.CrossRefGoogle Scholar
Busse, F. H. 2010 Mean zonal flows generated by librations of a rotating spherical cavity. J. Fluid Mech. 650, 505–512.CrossRefGoogle Scholar
Goepfert, O. & Tilgner, A. 2016 Dynamos in precessing cubes. New J. Phys. 18, 103019.CrossRefGoogle Scholar
Goepfert, O. & Tilgner, A. 2019 Mechanisms for magnetic field generation in precessing cubes. Geophys. Astrophys. Fluid Dyn. 113, 222–234.CrossRefGoogle Scholar
Greenspan, H. P. 1964 On the transient motion of a contained rotating fluid. J. Fluid Mech. 20, 673–696.CrossRefGoogle Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Holmes, P., Lumley, J. L. & Berkooz, G. 1996 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.CrossRefGoogle Scholar
Lord Kelvin 1880 Vibrations of a columnar vortex. Phil. Mag. 10, 155–168.CrossRefGoogle Scholar
Kerswell, R. R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83–113.CrossRefGoogle Scholar
Lagrange, R., Meunier, P., Nadal, F. & Eloy, C. 2011 Precessional instability of a fluid cylinder. J. Fluid Mech. 666, 104–145.CrossRefGoogle Scholar
Lamriben, C., Cortet, P.-P., Moisy, F. & Maas, L. R. M. 2011 Excitation of inertial modes in a closed grid turbulence experiment under rotation. Phys. Fluids 23, 015102.CrossRefGoogle Scholar
Le Bars, M., Cebron, D. & Le Gal, P. 2015 Flows driven by libration, precession, and tides. Annu. Rev. Fluid Mech. 47, 163–193.CrossRefGoogle Scholar
Lopez, J. M. & Marques, F. 2014 Rapidly rotating cylinder flow with an oscillating sidewall. Phys. Rev. E 89, 013013.Google ScholarPubMed
Lopez, J. M. & Marques, F. 2016 Nonlinear and detuning effects of the nutation angle in precessionally-forced rotating cylinder flow. Phys. Rev. Fluids 1, 023602.CrossRefGoogle Scholar
Lopez, J. M. & Marques, F. 2018 Rapidly rotating precessing cylinder flows: forced triadic resonances. J. Fluid Mech. 839, 239–270.CrossRefGoogle Scholar
Maas, L. R. M. 2003 On the amphidromic structure of inertial waves in a rectangular parallelepiped. Fluid Dyn. Res. 33, 373–401.CrossRefGoogle Scholar
Malkus, W. V. R. 1968 Precession of the Earth as the cause of geomagnetism. Science 160, 259–264.CrossRefGoogle ScholarPubMed
Manasseh, R. 1992 Breakdown regimes of inertia waves in a precessing cylinder. J. Fluid Mech. 243, 261–296.CrossRefGoogle Scholar
Marques, F. & Lopez, J. M. 2015 Precession of a rapidly rotating cylinder flow: traverse through resonance. J. Fluid Mech. 782, 63–98.CrossRefGoogle Scholar
McEwan, A. D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40, 603–640.CrossRefGoogle Scholar
Meunier, P., Eloy, C., Lagrange, R. & Nadal, F. 2008 A rotating fluid cylinder subject to weak precession. J. Fluid Mech. 599, 405–440.CrossRefGoogle Scholar
Rubio, A., Lopez, J. M. & Marques, F. 2009 Interacting oscillatory boundary layers and wall modes in modulated rotating convection. J. Fluid Mech. 625, 75–96.CrossRefGoogle Scholar
Tilgner, A. 2007 Zonal wind driven by inertial modes. Phys. Rev. Lett. 99, 194501.CrossRefGoogle ScholarPubMed
Wu, K., Welfert, B. D. & Lopez, J. M. 2018 Librational forcing of a rapidly rotating fluid-filled cube. J. Fluid Mech. 842, 469–494.CrossRefGoogle Scholar

Wu et al. supplementary movie 1

Animations of the forced response flows at half-frequencies as indicated, and the corresponding inertial eigenmodes. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 1(Video)
Video 2.9 MB

Wu et al. supplementary movie 2

Animations of the forced response flows at half-frequencies as indicated, and the corresponding inertial eigenmodes. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 2(Video)
Video 6.9 MB

Wu et al. supplementary movie 3

Animations of the three inertial eigenmodes involved in the triadic resonance. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 3(Video)
Video 20.8 MB

Wu et al. supplementary movie 4

Animation over 20 forcing periods of the response flow that results from the triadic resonance. Shown are the components of vorticity orthogonal to the planes indicated.

Download Wu et al. supplementary movie 4(Video)
Video 31.4 MB