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Triadic resonances driven by thermal convection in a rotating sphere

Published online by Cambridge University Press:  23 December 2020

Yufeng Lin Open the ORCID record for Yufeng Lin [Opens in a new window]
Yufeng Lin*
Affiliation:
Department of Earth and Space Sciences, Southern University of Science and Technology,Shenzhen518055, PR China
*
†Email address for correspondence: linyf@sustech.edu.cn
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Abstract

We report for the first time on triadic resonances in a rotating convection system. Using direct numerical simulations, we find that convective modes in a rotating spherical fluid can excite a pair of inertial modes whose frequencies and wavenumbers match the triadic resonance conditions. Depending on the structures of the convective modes, triadic resonances can lead to the growth of either a pair of modes with lower frequencies and wavenumbers, or a pair of modes with higher frequencies and wavenumbers, providing a possible mechanism for the bi-directional energy cascade. Increased thermal forcing leads to fully developed turbulence, which also exhibits wave-like motions, and is reminiscent of the energy spectrum of inertial wave turbulence. Our results suggest that the interaction of inertial waves plays an important role in rotating convection, which is of great importance in understanding the dynamics of planetary and stellar interiors.

JFM classification

Geophysical and Geological Flows: Rotating flows Instability: Parametric instability Convection: Convection in cavities
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 909 , 25 February 2021 , R3
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Aldridge, K. & Toomre, A. 1969 Axisymmetric inertial oscillations of a fluid in a rotating spherical container. J. Fluid Mech. 37, 307–323.CrossRefGoogle Scholar
Aubert, J., Brito, D., Nataf, H.-C., Cardin, P. & Masson, J.-P. 2001 Asystematic experimental study of rapidly rotating spherical convection in water and liquid gallium. Phys. Earth Planet. Inter. 128, 51–74.CrossRefGoogle Scholar
Aurnou, J.M., Bertin, V., Grannan, A.M., Horn, S. & Vogt, T. 2018 Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns. J. Fluid Mech. 846, 846–876.CrossRefGoogle Scholar
Aurnou, J.M., Calkins, M.A., Cheng, J.S., Julien, K., King, E.M., Nieves, D., Soderlund, K.M. & Stellmach, S. 2015 Rotating convective turbulence in earth and planetary cores. Phys. Earth Planet. Inter. 246, 52–71.CrossRefGoogle Scholar
Barker, A.J. 2016 Non-linear tides in a homogeneous rotating planet or star: global simulations of the elliptical instability. Mon. Not. R. Astron. Soc. 459 (1), 939–956.CrossRefGoogle Scholar
Bretherton, F.P. 1964 Resonant interactions between waves. The case of discrete oscillations. J. Fluid Mech. 20 (3), 457–479.CrossRefGoogle Scholar
Busse, F.H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441–460.CrossRefGoogle Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.Google Scholar
Christensen, U.. 2002 Zonal flow driven by strongly supercritical convection in rotating spherical shells. J. Fluid Mech. 470, 115–133.CrossRefGoogle Scholar
Gastine, T., Wicht, J. & Aubert, J. 2016 Scaling regimes in spherical shell rotating convection. J. Fluid Mech. 808, 690–732.CrossRefGoogle Scholar
Godeferd, F.S. & Moisy, F. 2015 Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results. Appl. Mech. Rev. 67 (3), 1–13.CrossRefGoogle Scholar
Greenspan, H.P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Guervilly, C., Cardin, P. & Schaeffer, N. 2019 Turbulent convective length scale in planetary cores. Nature 570 (7761), 368–371.CrossRefGoogle ScholarPubMed
Hollerbach, R. & Kerswell, R.R. 1995 Oscillatory internal shear layers in rotating and precessing flows. J. Fluid Mech. 298, 327–339.CrossRefGoogle Scholar
Horn, S. & Schmid, P.J. 2017 Prograde, retrograde, and oscillatory modes in rotating Rayleigh–Bénard convection. J. Fluid Mech. 831, 182–211.CrossRefGoogle Scholar
Jones, C.A. 2015 Thermal and Compositional Convection in the Outer Core. In Treatise on Geophysics, vol. 8, pp. 115–159. Elsevier.CrossRefGoogle Scholar
Jones, C.A., Soward, A.M. & Mussa, A.I. 2000 The onset of thermal convection in a rapidly rotating sphere. J. Fluid Mech. 405 (2000), 157–179.CrossRefGoogle Scholar
Kaplan, E.J., Schaeffer, N., Vidal, J. & Cardin, P. 2017 Subcritical thermal convection of liquid metals in a rapidly rotating sphere. Phys. Rev. Lett. 119 (9), 094501.CrossRefGoogle Scholar
Kerswell, R.R. 2002 Elliptical instability. Annu. Rev. Fluid Mech. 34, 83–113.CrossRefGoogle Scholar
Lam, K., Kong, D. & Zhang, K. 2018 Nonlinear thermal inertial waves in rotating fluid spheres. Geophys. Astrophys. Fluid Dyn. 112 (5), 357–374.CrossRefGoogle Scholar
Le Bars, M., Cébron, D. & Le Gal, P. 2015 Flows driven by libration, precession, and tides. Annu. Rev. Fluid Mech. 47 (1), 163–193.CrossRefGoogle Scholar
Le Reun, T., Favier, B., Barker, A.J. & Le Bars, M. 2017 Inertial wave turbulence driven by elliptical instability. Phys. Rev. Lett. 119 (3), 034502.CrossRefGoogle ScholarPubMed
Lin, Y. & Jackson, A. 2020 Large-scale vortices and zonal flows in spherical rotating convection. J. Fluid Mech. (in press).Google Scholar
Lin, Y., Noir, J. & Jackson, A. 2014 Experimental study of fluid flows in a precessing cylindrical annulus. Phys. Fluids 26 (4), 046604.CrossRefGoogle Scholar
Marti, P. & Jackson, A. 2016 A fully spectral methodology for magnetohydrodynamic calculations in a whole sphere. J. Comput. Phys. 305, 403–422.CrossRefGoogle Scholar
McEwan, A.D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40 (03), 603.CrossRefGoogle Scholar
Net, M., Garcia, F. & Sánchez, J. 2008 On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions. J. Fluid Mech. 601, 317–337.CrossRefGoogle Scholar
Noir, J., Brito, D., Aldridge, K. & Cardin, P. 2001 Experimental evidence of inertial waves in a precessing spheroidal cavity. Geophys. Res. Lett. 28 (19), 3785–3788.CrossRefGoogle Scholar
Ogilvie, G.I. 2014 Tidal dissipation in stars and giant planets. Annu. Rev. Astron. Astrophys. 52, 1–46.CrossRefGoogle Scholar
Ogilvie, G.I. & Lin, D.N.C. 2004 Tidal dissipation in rotating giant planets. Astrophys. J. 610 (1), 477–509.CrossRefGoogle Scholar
Plumley, M. & Julien, K. 2019 Scaling laws in Rayleigh–Bénard convection. Earth Space Sci. 6 (9), 1580–1592.CrossRefGoogle Scholar
Rieutord, M., Georgeot, B. & Valdettaro, L. 2001 Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum. J. Fluid Mech. 435, 103–144.CrossRefGoogle Scholar
Spiegel, E.A. 1971 Convection in stars. I. Basic Boussinesq convection. Annu. Rev. Astron. Astrophys. 9, 323–352.CrossRefGoogle Scholar
Vidal, J. & Barker, A.J. 2020 Efficiency of tidal dissipation in slowly rotating fully convective stars or planets. Mon. Not. R. Astron. Soc. 497 (4), 4472–4485.CrossRefGoogle Scholar
Zahn, J.P. 1989 Tidal evolution of close binary stars. I - Revisiting the theory of the equilibrium tide. Astron. Astrophys. 220 (1–2), 112–116.Google Scholar
Zhang, K. 1994 On coupling between the Poincaré equation and the heat equation. J. Fluid Mech. 268, 211.CrossRefGoogle Scholar
Zhang, K. & Liao, X. 2017 Theory and Modeling of Rotating Fluids: Convection, Inertial Waves, and Precession. Cambridge University Press.CrossRefGoogle Scholar
Zhou, Y. 1995 A phenomenological treatment of rotating turbulence. Phys. Fluids 7 (8), 2092–2094.CrossRefGoogle Scholar

Lin supplementary movie 1

Radial velocity in the equatorial plane of three interacting modes for the first case in table 1.

Download Lin supplementary movie 1(Video)
Video 2 MB

Lin supplementary movie 2

Radial velocity in the equatorial plane of three interacting modes for the second case in table 1.

Download Lin supplementary movie 2(Video)
Video 1.9 MB

Lin supplementary movie 3

Radial velocity in the equatorial plane of three interacting modes for the third case in table 1.

Download Lin supplementary movie 3(Video)
Video 1.5 MB