Frontogenesis and frontal motion due to confluent deformation with a translating dilatation axis

A two-dimensional model of primitive-equation frontogenesis is formulated i n which the forcing is due to a basic-state field of confluent deformation with a dilatation axis that translates in the cross-front direction. Althou gh the translation speed and direction of motion of the basic-state dilatat ion axis have no effect on frontal structure when the total deformation is spatially uniform, they can influence considerably the motion of the front. At the surface, this motion may be separated into two components: (i) inte rnal motion, directed towards the warm air, which is associated with the se condary ageostrophic circulation of the front itself; and (ii) external mot ion, either towards cold or warm air, which is associated with the initial location and translation speed of the basic-state dilatation axis. The latt er component ultimately dominates, and thus the motion of a mature front ma y be thought of as being controlled by the large-scale flow. However, the f ormer may dominate early on in the frontal evolution, resulting in signific antly different frontal trajectories depending on the initial location of t he basic-state dilatation axis and on whether this axis is moving towards t he cold or the warm air. The relative locations of various conventional fro ntal measures are examined in the special case of a uniformly translating d ilatation axis. Of these measures the axes of maximum baroclinicity and vor ticity become collocated at the surface as the front intensifies. However, the basic-state dilatation axis and the confluence axis, the latter being d efined as the location of zero total wind in the cross-front direction, may be displaced considerably from this merger point, with this displacement d epending on the initial location and subsequent motion of the basic-state d ilatation axis. Potential extensions of the model are discussed with regard to improved understanding of the difference in structure and motion betwee n cold and warm fronts.