Modified Eady Waves and Frontogenesis Part II: Nonlinear Integration

Abstract

The stability analysis of the modified Eady waves (Eady,1949) in a constant shear flow with parabolic temperature profiles has been discussed in Part Ⅰ. Here, we apply the nonlinear model developed at Purdue University to study the evolution of those unstable waves obtained from Part Ⅰ.The long waves(referred to as Mode Ⅰ in Part Ⅰ)develop into fronts with the maximum perturbations of pressure and temperature being either at the top or at the bottom of the domain. They are similar to conventional Eady waves discussed by Williams (1967) and Hoskin (1978), although the amplitudes of the simulated perturbations near the top are smaller than those near the bottom, dueto a stronger stratification in the upper atmosphere in our parabolic temperature profiles. The short waves(referred to as Mode Ⅱ in PartⅠ),which need more time to develop into a front, are confined to the lower atmosphere. The modeling phase speed of the short waves is much slower than the conventional baroclinic waves, as predicted in Part Ⅰ. Both stability analyses and nonlinear integrations confirm that the surface wave/front can develop and reach finite amplitude within a few days, when the stratification in the lower atmosphere is weak. The results of this study may be related to the development of the medium scale disturbances observed over the Kuroshio Current and East China Sea during the winter.