Nonlinear tides in a homogeneous rotating planet or star: global simulations of the elliptical instability

Abstract

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 nonlinear 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 timescale as the spin synchronisation. 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 days, and predicts spin-synchronisation (and spin-orbit alignment) out to about 10-15 days. However, other mechanisms must be invoked to explain tidal circularisation for longer orbital periods.

19 pages, 19 figures, 1 table, accepted for publication in MNRAS (2016 March 22)

References in corpus (12)

• Tidal dissipation in stars and giant planets
• On the tidal evolution of Hot Jupiters on inclined orbits
• Spinning down newborn neutron stars: nonlinear development of the r-mode instability
• Theory and simulations of rotating convection
• Shear-driven parametric instability in a precessing sphere
• Are Tidal Effects Responsible for Exoplanetary Spin-Orbit Alignment?
• Tidally driven dynamos in a rotating sphere
• A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid
• Nonlinear tides in a homogeneous rotating planet or star: global modes and elliptical instability
• Latitudinal libration driven flows in triaxial ellipsoids
• Tidal interactions of a Maclaurin spheroid. I: Properties of free oscillation modes
• Tilt-over mode in a precessing triaxial ellipsoid

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