Fully Lagrangian Numerical Solutions of Unbalanced Frontogenesis and Frontal COllapse

Abstract

Numerical simulation has failed to answer some fundamental questions about atmospheric frontogenesis because of the artificial minimum resolved scale in grid point and spectral models alike. To alleviate this handicap and shed light on some recent ideas about the possibility of a finite limiting scale for inviscid fronts, a fully Lagrangian primitive-equation numerical model is developed for nonturbulent, slab-symmetric flow on an f-plane. With physical position treated as an explicit function of particle label and time, the model grid deforms to follow natural changes in disturbance length scales. Exact conservation of volume and potential vorticity, as well as of basic tracer variables, is demonstrated, and details of the truncation error for energy conservation are obtained for the case of second-order central differencing in label space. The Lagrangian model is used to simulate frontogenesis by horizontal wind deformation in a dry, Boussinesq atmosphere, with no prior assumption of hydrostatic or geostrophic balance. A comparison is made between solutions for different values of uniform potential vorticity. Frontal collapse (the formation of discontinuities) is considered to occur when two grid points carrying contrasting fluid properties come into contact with each other on a solid boundary. For realistic choices of the parameters governing the rate of frontogenesis, imbalances alone are found to be insufficient to prevent frontal collapse. For small values of the normalized potential vorticity, the ageostrophic secondary circulation is weaker than in the corresponding balanced solutions, and frontal collapse is accordingly delayed. A further manifestation of imbalance is a splitting of the frontal updraft into two ascent maxima separated by a distance comparable to the width of the baroclinic region. Neutral wave activity develops if the potential vorticity is significantly nonzero, but plays only a passive role during the formation of discontinuities. The geostrophic momentum approximation is invoked in arguing that the splitting effect is not fundamentally wave-like.