AbstractThe structure of an asymptotic analytic solution for linear baroclinic waves on a frontal basic state is analysed and compared with finite‐difference solutions. The accuracy of the geostrophic fields is good for fronts with widths less than about 400 km. There is direct cancellation between along‐front advection of the disturbance by the strong frontal jet, and disturbance cross‐front advection of the sharp basic‐state gradients. This cancellation of small‐scale effects leaves the larger scales to control the evolution of the disturbance. It follows that the structure is very similar to that of the classic, meridionally uniform, Eady model. Secondary features, such as the ageostrophic circulation, are more sensitive to the frontal width and hence less accurately reproduced in the asymptotic solution. The analysis illustrates significant differences between the ageostrophic circulation associated with deformation frontogenesis and that which occurs in the linear stage of the instability, forced by along‐front curvature. In the latter case, the horizontal ageostrophic wind associated with the rising motion is characterized by along‐front convergence and cross‐front divergence (i.e. ageostrophic frontolysis).