  We simulate the propagation and dissipation of tidally induced nonlinear
gravity waves in the cores of solar-type stars. We perform hydrodynamical
simulations of a previously developed Boussinesq model using a spectral-element
code to study the stellar core as a wave cavity that is periodically forced at
the outer boundary with a given azimuthal wavenumber and an adjustable
frequency. For low-amplitude forcing, the system exhibits resonances with
standing g-modes at particular frequencies, corresponding to a situation in
which the tidal torque is highly frequency-dependent. For high-amplitude
forcing, the excited waves break promptly near the centre and spin up the core
so that subsequent waves are absorbed in an expanding critical layer, as found
in previous work, leading to a tidal torque with a smooth frequency-dependence.
For intermediate-amplitude forcing, we find that linear damping of the waves
gradually spins up the core such that the resonance condition can be altered
drastically. The system can evolve towards or away from g-mode resonances,
depending on the difference between the forcing frequency and the closest
eigenfrequency. Eventually, a critical layer forms and absorbs the incoming
waves, leading to a situation similar to the high-amplitude case in which the
waves break promptly. We study the dependence of this process on the forcing
amplitude and frequency, as well as on the diffusion coefficients. We emphasize
that the small Prandtl number in the centre of solar-like stars facilitates the
development of a differentially rotating core owing to the nonlinear feedback
of waves. Our simulations and analysis reveal that this important mechanism may
drastically change the phase of gravity waves and thus the classical picture of
resonance locking in solar-type stars needs to be revised.
