Baroclinic Eady Wave and Fronts. Part II: Geostrophic Potential Vorticity Dynamics in Semigeostrophic Space

Abstract

The geostrophic coordinate transformation is applied to the viscous semigeostrophic (SG) Eady wave. In the transformed space, called the SG space, the potential temperature anomaly can be treated as a delta-function anomaly of geostrophic potential vorticity (GPV) at the physical boundary or imaginary boundary (along the top of the boundary layer). Since the delta-function anomaly is analogous to the surface charge of a problem in electrostatics with the induced geopotential playing the role of the electric potential, the development of the Eady wave and fronts can be interpreted in terms of the interaction between the ?surface charges? at two imaginary boundaries. It is shown that this interpretation and related GPV thinking for the viscous SG Eady wave can be made nearly as concise as its inviscid paradigm during the boundary stage (until the inviscid surface front collapses in physical space). When the viscous SG Eady wave develops into the interior stage, strong interior GPV anomalies, analogous to ?body charges,? are generated by the diffusive GPV flux. These body charges form two domes in the SG space. The geostrophic flow field induced by the body charge in each dome produces diffusive GPV fluxes that converge at the upstream edge of each dome and thus keep the body charge in step against the horizontal advection. The growth of the geometric area of each dome of body charge (or the penetration of the front into the interior in physical space), however, is caused mainly by the ageostrophic circulation forced by the geostrophic flow. It is also shown that the body charge in each dome can be represented by the surface charge (potential temperature anomaly) on an imaginary boundary that covers the dome (above the boundary layer). The growth of these surface charges can be explained by a simplified GPV thinking applied only to the nearly inviscid interior region, similar to its inviscid counterpart for the interior stage (beyond the time that the inviscid surface front collapses in physical space).