  We investigate whether tidal forcing can result in sound waves steepening
into shocks at the surface of a star. To model the sound waves and shocks, we
consider adiabatic non-spherical perturbations of a Newtonian perfect fluid
star. Because tidal forcing of sounds waves is naturally treated with linear
theory, but the formation of shocks is necessarily nonlinear, we consider the
perturbations in two regimes. In most of the interior, where tidal forcing
dominates, we treat the perturbations as linear, while in a thin layer near the
surface we treat them in full nonlinearity but in the approximation of plane
symmetry, fixed gravitational field and a barotropic equation of state. Using a
hodograph transformation, this nonlinear regime is also described by a linear
equation. We show that the two regimes can be matched to give rise to a single
mode equation which is linear but models nonlinearity in the outer layers. This
can then be used to obtain an estimate for the critical mode amplitude at which
a shock forms near the surface. As an application, we consider the tidal waves
raised by the companion in an irrotational binary system in circular orbit. We
find that shocks form at the same orbital separation where Roche lobe overflow
occurs, and so shock formation is unlikely to occur.
