This chapter discusses the nature of nongeostrophic dynamics of atmospheric flows in the context of three distinctly different phenomena. The nongeostrophic effect can become important even in a large-scale flow when the momentum advection and heat advection by its ageostrophic velocity component are a significant part of the total advection. This is what we find in surface frontogenesis and in the Hadley circulation. In Section 12.1, we analytically delineate the dynamics of surface frontogenesis arising from the stretching deformation of a background flow in a semi-geostrophic model. In Section 12.2, we deduce analytically the structure of the annual/seasonal mean Hadley circulation in a zonally symmetric two-layer nonlinear primitive-equation model. The nongeostrophic effect is obviously important in small-scale disturbances, particularly when there is not even hydrostatic balance. In Section 12.3, we analyze non-hydrostatic barotropic instability as a possible mechanism for non-supercell tornadogenesis with a Hamiltonian formulation for a layer of barotropic fluid.

Surface frontogenesis

Surface fronts in the extratropical atmosphere have a local quasi-rectilinear structure across which temperature and wind vary dramatically over a short distance normal to the front. Although the cross-front velocity is considerably weaker than the along-front velocity, it has a strong dynamical impact on frontogenesis because the cross-front thermal contrast is strong. There is a substantial vertical velocity associated with the cross-front velocity especially in the neighborhood of a cold front. It follows that the cross-front advection as well as the vertical advection of momentum and heat are significant. Hence, nongeostrophic dynamics is important for surface atmospheric frontogenesis.