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Date
2021Type
- Journal Article
Abstract
Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study, we numerically investigate flows in longitudinally librating spherical shells. We focus on the Ekman number dependencies of several shear layers when the libration frequency is less than twice of the rotation frequency and the libration amplitude is small. Time-dependent flows mainly consist of inertial waves excited at the critical latitudes due to the Ekman pumping singularities, forming conical shear layers. In particular, previous theoretical studies have proposed different scalings for the conical shear layers spawned from the critical latitudes at the inner boundary. Our numerical results favour the velocity amplitude scaling (Formula presented.) predicted by Le Dizès & Le Bars (J. Fluid Mech. 2017, 826, 653) over the scaling (Formula presented.) initially proposed by Kerswell (J. Fluid Mech. 1995, 298, 311), though the Ekman numbers in our calculations are not sufficiently small to pin down this scaling. Non-linear interactions in the boundary layers drive a mean zonal flow with several geostrophic shears. Our numerical results show that geostrophic shears associated with the critical latitudes at the inner and outer boundaries exhibit the same scalings, i.e. an amplitude of (Formula presented.) over a width of (Formula presented.). Apart from the geostrophic shear associated with the critical latitude, our numerical results show that the reflection of inertial waves can induce a geostrophic shear with an amplitude of (Formula presented.) over a width of (Formula presented.). As the amplitude of the geostrophic shears increases as reducing the Ekman number, the geostrophic shears in the mean flows may be significant in planetary cores and subsurface oceans given small Ekman numbers of these systems. Show more
Publication status
publishedExternal links
Journal / series
Geophysical and Astrophysical Fluid DynamicsVolume
Pages / Article No.
Publisher
Taylor & FrancisSubject
Libration; Inertial waves; Mean flows; Shear layersOrganisational unit
03734 - Jackson, Andrew / Jackson, Andrew
Funding
165641 - Understanding planetary magnetic fields from theoretical, numerical and analogue models (SNF)
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