Semigeostrophic Eady wave frontogenesis in the presence of Newtonian cooling

The semigeostrophic, two-dimensional, uniform potential vorticity Eady wave model developed by Hoskins and Bretherton has been modified by embedding Newtonian (radiative) cooling. The observation that with this modification the potential vorticity varies in a known manner following fluid particles has provided the retention of the analytical representation of the solution. A principal result of this study is that the effects of radiation may critically change the dynamics of semigeostrophic frontogenesis promoted by Eady wave instability even though the damping timescale significantly exceeds the flow timescale. In particular, the formation of a frontal discontinuity from short-wave initial disturbances, with the wavenumbers beyond the short-wave cutoff of the adiabatic theory, becomes possible.