The 21th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun Edited by A. S. Brun, J. Bouvier, P. Petit Nonlinear tidal interactions in the convective envelopes of low-mass stars and giant gaseous planets Aurélie Astoul,1 Adrian Barker1 1Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK 1 * Abstract In close exoplanetary systems, tidal interactions are known to shape orbital architectures, to modify star and planet spins, and to have an impact on the internal structures of the bodies through tidal heating. Most stars around which planets have been discovered are low-mass stars and thus feature a convective envelope, as is also expected in giant gaseous planets like Hot Jupiters. Tidal flows in convective envelopes consist of large-scale equilibrium tides and inertial waves (restored by the Coriolis acceleration, and recently discovered in the Sun) excited by tides. Inertial waves contribute greatly to the tidal dissipation when they are excited and subsequently damped (through e.g. turbulent viscous friction), especially early in the life of a system. These waves are known to be subject to nonlinear effects, including triggering differential rotation in the form of zonal flows. In this context, we investigate how nonlinearities affect tidal properties, thanks to 3D nonlinear hydrodynamical simulations of tidal flows, in an adiabatic and incompressible convective shell. Unlike previous studies, we use a realistic tidal body forcing to excite inertial waves. Within our new set-up, we observe the establishment of strong cylindrically-sheared zonal flows, which modify the tidal dissipation rates from prior linear theoretical predictions. We demonstrate that the effects of this differential rotation on the waves neatly explains the discrepancies between linear and nonlinear dissipation rates in many of our simulations. Nonlinear interactions between inertial waves, and those between the waves and the background sheared flow, can lead to instabilities, for sufficiently high tidal forcing amplitudes or low viscosities. These different processes disrupt the energetic exchanges between tidal waves and the background flow, and also further modify tidal dissipation rates. 2 Introduction Due to the compact nature of many exoplanetary systems discovered so far, the study of tidal interactions is essential to understand the orbital and rotational properties of the plan- ets, as well as the rotations of their host stars. There has been a growing interest in detecting orbital decay of close Hot Jupiters, presumably caused by tidal interactions (e.g. Pa- tra et al., 2020; Harre et al., 2023). Though many ∼one-day orbital period giant gaseous planets are expected to migrate towards their host stars if tides are strong, only WASP-12 b has been convincingly confirmed to decay to date (Maciejew- ski et al., 2016). Therefore, an accurate theoretical estimation of tidal dissipation is needed to interpret the orbital decay rate of the planet/accelerating spin of star. In the WASP-12 system, non-linear wave breaking of gravity waves (restored by buoyancy) in the radiative central portions of the host star is believed to be responsible for the inward spiralling of the planet (Chernov et al., 2017; Weinberg et al., 2017; Barker, 2020). In other systems where this mechanism probably can- not apply, tidal dissipation of inertial waves (restored by the Coriolis acceleration) in stellar convective envelopes could be another avenue to explain any inferred orbital decay, as in the KELT-1 Hot Jupiter/brown dwarf system (Maciejewski et al., 2022) or for the Hot Jupiter Kepler-1658 b (Vissapra- gada et al., 2022). Given the high tidal forcing amplitudes1 ϵ = (M2/M1)(R1/a)3 expected in Hot Jupiters themselves, 1A measure of the strength of the tides with M the mass, R the radius and a the orbital semi-major axis, with subscripts 1 and 2 referring to the perturbed body and the perturber, respectively (Ogil