Two-dimensional balanced model of internal frontogenesis in geostrophic and isentropic coordinates

Abstract

Here we seek to both improve and simplify the method by which upper frontoge­nesis may be studied. Using a two-dimensional form of the geostrophic momentum approximation in geostrophic/isentropic coordinates, our dynamic model reduces to a predictive equation for the potential pseudo-density (inverse Rossby-Ertel po­tential vorticity), with associated diagnostic equation for the Bernoulli function from which the wind and mass fields can be calculated. Ageostrophic motions are implicit, and vertical motions retained for the adiabatic case employed, by this choice of coordinates. Initialization of the domain incorporates a realistic vertical distribution of the mass field along with upper/lower boundaries which are either isobaric/isentropic or constant potential vorticity surfaces. Vertical wind shears such as are commonly associated with baroclinic waves are idealized and act as the forcing mechanism for frontogenesis. Major model results include the formation of upper fronts with associated wind and thermal fields which, when viewed together, are well correlated with obser­vations of these parameters in terms of magnitude and gradient as well as their proximity to one another. Well-defined folding of the dynamic tropopause occurs in geostrophic space; thus, unlike previous balanced models, the transformation back to physical space is not required in order to produce the desired results. However, we show that performing the coordinate transformation enhances the realism of the results. Our findings document the applicability of the geostrophic momentum approxi­mation to non-curved flows containing high relative vorticity, and the simplicity of the dynamics when applied to these particular coordinates. Further, we find that generalizing the forcing mechanism can also produce noteworthy aspects of internal frontogenesis; this was accomplished by extracting an essential feature of baroclinic waves-vertical wind shearing-and incorporating it first into the classical defor­mation field and later applying it to the zonal flow directly. The results suggest more can be learned about frontogenesis by application of balanced two-dimensional theory even when relatively extreme simplifications, such as adiabatic, frictionless flow, are made.