Frontal equilibration by frictional processes

The effect of friction on frontogenesis driven by a stretching deformation field is studied analytically in both a quasigeostrophic and a semigeostrophic framework for a semi-infinite, adiabatic, Boussinesq fluid on an f plane. Friction is incorporated into the model in terms of a boundary layer pumping term. The solutions demonstrate that the effect of friction is frontolytic. The quasigeostrophic fronts always equilibrate at a finite horizontal scale. The semigeostrophic fronts equilibrate at a finite horizontal scale if the strength of the frontogenesis is below a threshold value. Above this threshold, the front is predicted to collapse to a discontinuity in its thermal and momentum fields.