  We study the fate of internal gravity waves, which are excited by tidal
forcing by a short-period planet at the interface of convection and radiation
zones, approaching the centre of a solar-type star. We study at what amplitude
these wave are subject to instabilities. These instabilities lead to wave
breaking whenever the amplitude exceeds a critical value. Below this value, the
wave reflects perfectly from the centre of the star. Wave breaking results in
spinning up the central regions of the star, and the formation of a critical
layer, which acts as an absorbing barrier for ingoing waves. As these waves are
absorbed, the star is spun up from the inside out. This results in an important
amplitude dependence of the tidal quality factor Q'. If the tidal forcing
amplitude exceeds the value required for wave breaking, efficient dissipation
results over a continuous range of tidal frequencies, leading to Q' \approx
10^5 (P/1day)^(8/3), for the current Sun. This varies by less than a factor of
5 throughout the range of G and K type main sequence stars, for a given orbit.
We predict fewer giant planets with orbital periods of less than about 2 days
around such stars, if they cause breaking at the centre, due to the efficiency
of this process. This mechanism would, however, be ineffective in stars with a
convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly
explaining the survival of their close planetary companions.
