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Schematic regime diagrams for the existence of mean zonal flows driven by mechanical forcings (planetary values estimated from Noir et al. 2009; Cébron et al. 2012; Lin et al. 2015; Vantieghem et al. 2015). Red circles: precession. Blue squares: longitudinal librations. Black triangles: latitudinal librations. Magenta stars: tides. (a) Transition between laminar and turbulent boundary layers (BL). Transition occurs when ∼ K E 1/2 (with the typical values K = 20 − 150 shown by the gray area, K = 55 by the dashed dotted line). (b) Competition between bulk and boundary driven generation of mean zonal flows. Input Rossby number Ro = O(β) for tidal forcing or Ro = O(β) for precession and libration forcings, where β is the typical boundary (equatorial or polar) ellipticity. Instabilities and bulk turbulence (hatched area) onsets when Ro ∼ K E 1/2 (dashed line with the value K = 10).

Schematic regime diagrams for the existence of mean zonal flows driven by mechanical forcings (planetary values estimated from Noir et al. 2009; Cébron et al. 2012; Lin et al. 2015; Vantieghem et al. 2015). Red circles: precession. Blue squares: longitudinal librations. Black triangles: latitudinal librations. Magenta stars: tides. (a) Transition between laminar and turbulent boundary layers (BL). Transition occurs when ∼ K E 1/2 (with the typical values K = 20 − 150 shown by the gray area, K = 55 by the dashed dotted line). (b) Competition between bulk and boundary driven generation of mean zonal flows. Input Rossby number Ro = O(β) for tidal forcing or Ro = O(β) for precession and libration forcings, where β is the typical boundary (equatorial or polar) ellipticity. Instabilities and bulk turbulence (hatched area) onsets when Ro ∼ K E 1/2 (dashed line with the value K = 10).

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The generation of mean flows is a long-standing issue in rotating fluids. Motivated by planetary objects, we consider here a rapidly rotating fluid-filled spheroid, which is subject to weak perturbations of either the boundary (e.g. tides) or the rotation vector (e.g. in direction by precession, or in magnitude by longitudinal librations). Using bo...

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... The Ekman number scalings we have observed are very different from the zonal flows generated by tidal forcing in a full sphere in the experiments (with a deformable no-slip boundary) of, for example, Morize et al. (2010), where the zonal velocity scales as 2 E −3/10 , or for those produced by libration-driven inertial waves, as studied in Cébron et al. (2021) and Lin & Noir (2021), where it instead scales as 2 E 0 or 2 E −1/10 , respectively (though these also result from self-interaction, so the zonal velocity also scales as 2 ). We underline that the best fitting laws here seem quite different from the ones emerging in Paper I in E −3/2 and E −1/2 , presumably because of (3, 3). ...
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... The Ekman number scalings we have observed are very different from the zonal flows generated by tidal forcing in a full sphere in the experiments (with a deformable no-slip boundary) of, for example, Morize et al. (2010), where the zonal velocity scales as 2 E −3/10 , or for those produced by libration-driven inertial waves, as studied in Cébron et al. (2021) and Lin & Noir (2021), where it instead scales as 2 E 0 or 2 E −1/10 , respectively (though these also result from self-interaction, so the zonal velocity also scales as 2 ). We underline that the best fitting laws here seem quite different from the ones emerging in Paper I in E −3/2 and E −1/2 , presumably because of . ...
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