The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions

Abstract

Context. Quantifying tidal interactions in close-in two-body systems is of prime interest since they have a crucial impact on the architecture and the rotational history of the bodies. Various studies have shown that the dissipation of tides in either body is very sensitive to its structure and to its dynamics. Furthermore, solar-like stars and giant gaseous planets in our Solar System experience differential rotation in their outer convective envelopes. In this respect, numerical simulations of tidal interactions in these objects have shown that the propagation and dissipation properties of tidally excited inertial waves can be strongly modified in the presence of differential rotation. Aims. In particular, tidal inertial waves may strongly interact with zonal flows at the so-called co-rotation resonances, where the wave’s Doppler-shifted frequency is cancelled out. The energy dissipation at such resonances could deeply modify the orbital and spin evolutions of tidally interacting systems. In this context, we aim to provide a deep physical understanding of the dynamics of tidal waves at co-rotation resonances in the presence of differential rotation profiles that are typical of low-mass stars and giant planets. Methods. In this work, we have developed an analytical local model of an inclined shearing box that describes a small patch of the differentially rotating convective zone of a star or a planet. We investigate the propagation and the transmission of free inertial waves at co-rotation, and more generally at critical levels, which are singularities in the governing wave differential equation. Through the construction of an invariant called the wave action flux, we identify different regimes of wave transmission at critical levels, which are confirmed with a one-dimensional three-layer numerical model. Results. We find that inertial waves can be fully transmitted, strongly damped, or even amplified after crossing a critical level. The occurrence of these regimes depends on the assumed profile of differential rotation, on the nature as well as the latitude of the critical level, and on wave parameters such as the inertial frequency and the longitudinal and vertical wavenumbers. Waves can thus either deposit their action flux in the fluid when damped at critical levels, or they can extract action flux from the fluid when amplified at critical levels. Both situations can lead to significant angular momentum exchange between the tidally interacting bodies.

Detecting deep axisymmetric toroidal magnetic fields in stars. The traditional approximation of rotation for differentially rotating deep spherical shells with a general azimuthal magnetic field

“…The first two singularities are potentially the hydrodynamic and hydromagnetic critical layers, where the waves can be damped (Booker & Bretherton 1967;Rudraiah & Venkatachalappa 1972). The first singularity ω = 0 corresponds to a corotation resonance, which is present in the hydrodynamic case (Booker & Bretherton 1967;Watts et al 2003;Alvan et al 2013;Astoul et al 2021). The second singularity, which appears only in the magnetic case, adds two supplementary critical layers, ω = ±mω A , thus called hereafter magnetic critical layers.…”

Magnetic and tidal migration of close-in planets. Influence of secular evolution on their population

“…For instance, to get a complete picture of tidal dissipation in stars, the dynamical tide in the stellar radiative zone needs to be taken into account (e.g., Zahn 1975;Goldreich & Nicholson 1989;Goodman & Dickson 1998;Terquem et al 1998), which is likely to compete with the dissipation of inertial waves in convective layers (Ivanov et al 2013) and to affect secular evolution of star-planet systems (Barker & Ogilvie 2010;Barker 2011;Guillot et al 2014;Barker 2020). Moreover, in differentially rotating stellar convective zones, tidal inertial waves may interact with mean flows at critical layers; they can therefore either deposit or extract angular momentum from or to the surrounding fluid, which leads to exchanges of angular momentum between the star and the planet (Astoul et al 2021). Finally, tides can be affected by stellar and planetary magnetic fields (Wei 2016;Lin & Ogilvie 2018;Astoul et al 2019).…”

Dynamical tide in stellar radiative zones. General formalism and evolution for low-mass stars

“…Differential rotation on tides should also be taken into account because it affects propagation of gravito-inertial waves, leading to a large variety of resonant cavities and chaotic zones (Mathis 2009;Prat et al 2018). It also allows the deposition of angular momentum in critical layers and therefore interactions between waves and mean flows (Goldreich & Nicholson 1989;Alvan et al 2013;Astoul et al 2021). A strong differential rotation may set up during the PMS due to stellar contraction (Charbonnel et al 2013;Hypolite & Rieutord 2014;Gouhier et al 2021), when the tidal dissipation through gravity waves is highest.…”