The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions I. Free waves. (arXiv:2101.04656v1 [astro-ph.SR])

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions I. Free waves. (arXiv:2101.04656v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Astoul_A/0/1/0/all/0/1">A. Astoul</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Park_J/0/1/0/all/0/1">J. Park</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Mathis_S/0/1/0/all/0/1">S. Mathis</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Baruteau_C/0/1/0/all/0/1">C. Baruteau</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Gallet_F/0/1/0/all/0/1">F. Gallet</a>

Quantifying tidal interactions in close-in two-body systems is of prime
interest since they have a crucial impact on the architecture and on 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, like differential rotation which exists in the outer convective
enveloppe of solar-like stars and giant gaseous planets. In particular, tidal
waves may strongly interact with zonal flows at the so-called corotation
resonances, where the wave’s Doppler-shifted frequency cancels out. We aim to
provide a deep physical understanding of the dynamics of tidal inertial waves
at corotation resonances, in the presence of differential rotation profiles
typical of low-mass stars and giant planets. By developping an inclined
shearing box, we investigate the propagation and the transmission of free
inertial waves at corotation, 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. We find that inertial waves can be
either 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 to the fluid when damped at critical levels, or they can extract
action flux to the fluid when amplified at critical levels. Both situations
could lead to significant angular momentum exchange between the tidally
interacting bodies.

Quantifying tidal interactions in close-in two-body systems is of prime
interest since they have a crucial impact on the architecture and on 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, like differential rotation which exists in the outer convective
enveloppe of solar-like stars and giant gaseous planets. In particular, tidal
waves may strongly interact with zonal flows at the so-called corotation
resonances, where the wave’s Doppler-shifted frequency cancels out. We aim to
provide a deep physical understanding of the dynamics of tidal inertial waves
at corotation resonances, in the presence of differential rotation profiles
typical of low-mass stars and giant planets. By developping an inclined
shearing box, we investigate the propagation and the transmission of free
inertial waves at corotation, 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. We find that inertial waves can be
either 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 to the fluid when damped at critical levels, or they can extract
action flux to the fluid when amplified at critical levels. Both situations
could lead to significant angular momentum exchange between the tidally
interacting bodies.

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