Over 4000 exoplanets have been discovered in the past 25 years or so, most of which orbit cool stars. Star-planet tidal interactions are known to drive the late evolution of the shortest-period planetary systems via tidal dissipation. Such dissipation is known to vary considerably with the mass, age, rotation, and metallicity of the star. To quantify tidal dissipation as accurately as possible, two key physical mechanisms need to be further explored : stellar differential rotation and magnetism in convective regions, which have been constrained in cool stars by ground-based spectropolarimetric observations as well as space-based asteroseismic observations. In this contribution, we report our recent progress on the investigation of the impact of stellar differential rotation and magnetism on the dynamics and dissipation of tidal inertial waves, along the evolution of low-mass stars. First, we show that a large-scale magnetic field has a negligible effect on the excitation of tidal waves whereas it deeply impacts the dissipation mechanism of tidal waves in the convective envelope of all cool stars all along their evolution. Then, by developing a local shearing box model of a small patch of the convective shell, we demonstrate how tidal waves can be either fully transmitted, damped, or even amplified at the so-called critical layers (when the phase speed of the wave is equal to the local velocity of the fluid), that has potentially strong implications for angular momentum exchanges between tidal waves and zonal flows, and ultimately for the evolution of planetary systems.

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