Non-linear tides in a homogeneous rotating planet or star: Global simulations of the elliptical instability

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Barker, AJ 

I present results from the first global hydrodynamical simulations of the elliptical instability in a tidally deformed gaseous planet (or star) with a free surface. The elliptical instability is potentially important for tidal evolution of the shortest-period hot Jupiters. I model the planet as a spin-orbit aligned or anti-aligned, and non-synchronously rotating, tidally deformed, homogeneous fluid body. A companion paper presented an analysis of the global modes and instabilities of such a planet. Here I focus on the non-linear evolution of the elliptical instability. This is observed to produce bursts of turbulence that drive the planet towards synchronism with its orbit in an erratic manner. If the planetary spin is initially anti-aligned, the elliptical instability also drives spin-orbit alignment on a similar time-scale as the spin synchronization. The instability generates differential rotation inside the planet in the form of zonal flows, which play an important role in the saturation of the instability, and in producing the observed burstiness. These results are broadly consistent with the picture obtained using a local Cartesian model (where columnar vortices played the role of zonal flows). I also simulate the instability in a container that is rigid (but stress-free) rather than free, finding broad quantitative agreement. The dissipation resulting from the elliptical instability could explain why the shortest-period hot Jupiters tend to have circular orbits inside about 2-3 d, and predicts spin synchronization (and spin-orbit alignment) out to about 10-15 d. However, other mechanisms must be invoked to explain tidal circularization for longer orbital periods.

hydrodynamics, instabilities, waves, binaries: close, planetary systems stars: rotation
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Monthly Notices of the Royal Astronomical Society
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Oxford Academic
Science and Technology Facilities Council (ST/J001570/1)
Science and Technology Facilities Council (ST/J005673/1)
Science and Technology Facilities Council (ST/L000636/1)
This work was supported by the Leverhulme Trust and Isaac Newton Trust through the award of an Early Career Fellowship, but the early stages were supported by STFC through grants ST/J001570/1 and ST/L000636/1. Some of the simulations reported here used the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility ( This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National E-Infrastructure.