A model for a turbulent shock wave with a structure determined by ion wave instabilities is discussed. Quasi‐linear theory for spatially growing waves is used to examine the spatial buildup of the turbulent spectrum in the leading edge of the shock transition. Although the principal calculations are made for an electrostatic shock, the response of a weak magnetic field in the plasma to such a thin ion‐wave shock is also discussed. It is suggested that the earth's bow shock in the supersonic solar wind may sometimes have a structure of the type described here and a comparison with satellite data for this shock wave is made.