The effect of a sharp low-level temperature inversion on flow over a mountain is investigated via a series of two-dimensional idealized numerical model simulations. The main focus of the study is the effect of the inversion on the formation of lee waves, lee-wave rotors, low-level hydraulic jumps and the occurrence of wave breaking aloft. The idealized problem considered consists of an upwind velocity profile that is independent of height (above the boundary layer) and directed normal to an isolated two-dimensional ridge. The upstream stratification consists of a neutral layer immediately above the ground capped by a sharp temperature inversion. Above this, the atmosphere is stably stratified and the Brunt–Väisälä frequency is independent of height. Simulations were conducted for a range of inversion strengths (measured by the difference in potential temperature across the inversion) and inversion heights. The effect of both a free-slip and a no-slip lower boundary condition is investigated. Results show that, when the upwind Froude number (defined in the usual way for two-layer shallow-water flow) falls below a critical value, a short-wavelength resonant lee wave forms downwind of the mountain on the inversion. It is shown that both the critical Froude-number value and the wavelength of the lee wave are accurately predicted by linear theory. The lee-wave amplitude, however, can be significantly underestimated by linear theory if the wavelength is less than the hill length scale. In the case of a no-slip boundary condition, if the wave amplitude is sufficiently large, boundary-layer separation occurs underneath the wave crests and closed rotor circulations occur. In general, flow separation (and rotors) do not occur in the free-slip case. In both the free-slip and no-slip flows, as the Froude number decreases the lee wave is eventually replaced by a stationary hydraulic jump above the lee slope of the mountain. Copyright © 2004 Royal Meteorological Society.