  Tidal interactions in close star-planet or binary star systems may excite
inertial waves (their restoring force is the Coriolis force) in the convective
region of the stars. The dissipation of these waves plays a prominent role in
the long-term orbital and rotational evolution of the bodies involved. If the
primary star rotates as a solid body, inertial waves have a Doppler-shifted
frequency restricted to the range $[-2\Omega, 2\Omega]$ ($\Omega$ being the
angular velocity of the star), and they can propagate in the entire convective
region. However, turbulent convection can sustain differential rotation with an
equatorial acceleration (as in the Sun) or deceleration that modifies the
frequency range and propagation domain of inertial waves and allows corotation
resonances for non-axisymmetric oscillations. In this work, we perform
numerical simulations of tidally excited inertial waves in a differentially
rotating convective envelope with a conical (or latitudinal) rotation profile.
The tidal forcing that we adopt contains spherical harmonics that correspond to
the case of a circular and coplanar orbit. We study the viscous dissipation of
the waves as a function of tidal frequency for various stellar masses and
differential rotation parameters, as well as its dependence on the turbulent
viscosity coefficient. We compare our results with previous studies assuming
solid-body rotation and point out the potential key role of corotation
resonances in the dynamical evolution of close-in star-planet or binary
systems.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics