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An experimental and numerical study of librationally driven flow in planetary cores and subsurface oceans


Many planetary bodies undergo forced longitudinal librations [Williams, J.G., Boggs, D.H., Yoder, C.F., Ratcliff, J.T., Dickey, J.O., 2001. Lunar rotational dissipation in solid body and molten core. Journal of Geophysical Research-Planets 106 (E11), 27933-27968; Comstock, R.L., Bills, B.G., 2003. A solar system survey of forced librations in longitude. Journal of Geophysical Research-Planets 108 (E9); Margot, J.L., Peale, S.J., Jurgens, R.F., Slade, M.A., Holin, I.V., 2007. Large longitude libration of mercury reveals a molten core. Science 316 (5825), 710-714]. Yet few studies to date have investigated how longitudinal libration, the oscillatory motion of a planet around its rotation axis, couples with its interior planetary fluid dynamics [e.g., Aldridge, K.D., Toomre, A., 1969. Axisymmetric inertial oscillations of a fluid in a rotating spherical container. Journal of Fluid Mechanics 37, 307; Tilgner, A., 1999. Driven inertial oscillations in spherical shells. Physical Review E 59 (2), 1789-1794]. In this study, we investigate, via laboratory experiments, the viscously driven flow in a spherical librating fluid cavity. We focus on libration frequencies less than or equal to the planetary rotation frequency (frequency ratios f* ≤ 1), moderate rotation rates (Ekman numbers E = 1 0- 4 to 1 0- 5) and a relatively broad range of librational amplitudes (libration amplitudes 10 ° ≲ Δ φ{symbol} ≲ 200 °; Rossby numbers 0.03 ≲ R o ≲ 5). In addition we model flow in three different core geometries: full sphere, rinner ≃ 0.6 router and rinner ≃ 0.9 router. Direct flow visualizations in the laboratory experiment allow us to identify three distinct librationally driven flow regimes. The transitions between these regimes are governed by critical values of the outer boundary layer Reynolds number, Re. For R e ≲ 20 the flow is dominated by inertial modes. For 20 ≲ R e ≲ 120 the system becomes unstable to longitudinal rolls that form beneath the outer boundary. This laminar instability initiates near the equator and is qualitatively similar to Taylor-Görtler instabilities. For R e ≳ 120 the flow in the vicinity of the outer boundary becomes turbulent. For several librating planets with an internal fluid layer, estimates of Re and f* lie in the range of values accessible in our laboratory experiment. Our results suggest that Mercury, Io, Europa and Titan may undergo boundary layer turbulence, whereas Earth's moon, Callisto and Ganymede may become unstable to laminar longitudinal rolls.

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