## Abstract

Context: The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star.planet and planet.moon systems. This dissipation is particularly efficient for young low-mass stars and gaseous giant planets, which are rapid rotators. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is commonly modeled as an effective eddy viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of the tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices such as those observed at the poles of Jupiter and Saturn. The large-scale vortices are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis.

Aims: We investigate the complex interactions between a tidal inertial wave and a columnar convective vortex.

Methods: We used a quasi-geostrophic semi-analytical model of a convective columnar vortex, which is validated by numerical simulations. First, we carried out linear stability analysis using both numerical and asymptotic Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) methods. We then conducted linear numerical simulations of the interactions between a convective columnar vortex and an incoming tidal inertial wave.

Results: The vortex we consider is found to be centrifugally stable in the range −Ωp ≤ Ω0 ≤ 3.62Ωp and unstable outside this range, where Ω_{0 }is the local rotation rate of the vortex at its center and Ωp is the global planetary (stellar) rotation rate. From the linear stability analysis, we find that this vortex is prone to centrifugal instability with perturbations with azimuthal wavenumbers *m* = {0, 1, 2}, which potentially correspond to eccentricity, obliquity, and asynchronous tides, respectively. The modes with *m* > 2 are found to be neutral or stable. The WKBJ analysis provides analytic expressions of the dispersion relations for neutral and unstable modes when the axial (vertical) wavenumber is sufficiently large. We verify that in the unstable regime, an incoming tidal inertial wave triggers the growth of the most unstable mode of the vortex. This would lead to turbulent dissipation. For stable convective columns, the wave-vortex interaction leads to the mixing of momentum for tidal inertial waves while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size (radius) of the vortex. Incoming tidal waves can also experience complex angular momentum exchanges locally at critical layers of stable vortices.

Conclusions: The interaction between tidal inertial waves and large-scale coherent convective vortices in rapidly-rotating planets (stars) leads to turbulent dissipation in the unstable regime and complex behaviors such as mixing of momentum and radiation of new waves in the far field or wave-vortex angular momentum exchanges in the stable regime. These phenomena cannot be modeled using a simple effective eddy viscosity.

Original language | English |
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Article number | A6 |

Number of pages | 20 |

Journal | Astronomy and Astrophysics |

Volume | 673 |

Early online date | 26 Apr 2023 |

DOIs | |

Publication status | Published - May 2023 |

### Bibliographical note

Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.### Funder

The authors acknowledge support from the European Research Council through ERC grant SPIRE 647383 and from GOLF and PLATO CNES grants at the Department of Astrophysics of CEA. J. Park acknowledges support from the Royal Astronomical Society and Office of Astronomy for Development through the RAS-OAD astro4dev grant and from the Engineering and Physical Sciences Research Council (EPSRC) through the EPSRC mathematical sciences small grant (EP/W019558/1). A. Astoul acknowledges support from the Science and Technology Facilities Council (STFC) grant ST/S000275/1, as well as the Leverhulme Trust for early career grant.## Keywords

- hydrodynamics
- convection
- instabilities
- waves
- planet-star interactions
- planets and satellites: dynamical evolution and stability

## ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science