The baroclinic growth of perturbations on zonally symmetric jets can be described exactly by the interaction of two counter-propagating Rossby waves (CRWs), if each perturbation can be constructed from a growing normal mode and its decaying complex conjugate. Here, the structure and interaction of these CRWs is studied for growth on a realistic jet with a tropopause (the LC1 jet of Thorncroft, Hoskins and McIntyre, 1993). First we obtain the fastest growing normal mode for the primitive equations for a range of zonal wavenumbers, m. The CRWs are then constructed following the recipe given in Part I.
It is found that one CRW is always located on the ground where the strong temperature gradients act as large negative PV gradients. The upper CRW's "home level" varies with m but the structures of both CRWs are very simple in all cases. In particular, they are untilted in the x-z and x-y planes. Although Ertel PV perturbations, P', are large only near the tropopause, this is found to be a misleading observation. For m > 7 the tropopause plays virtually no role; the home level of the upper CRW is almost coincident with its maximum in quasi-geostrophic PV which lies at about 700mb, just above the steering level. Both CRW structures are very similar to those from the Charney model. This structure is also seen in inverse Ertel PV, (1/P)', which proves to be a more useful diagnostic than P'. As zonal wavelength increases, the depth-scale of the upper and lower CRWs increases and there is secondary maximum in upper CRW amplitude at the tropopause. For m<5 this tropopause perturbation begins to dominate the associated flow and the picture of baroclinic instability then resembles the Eady model. The strength of interaction between the CRWs and their self-propagation speeds are found as a function of m, as well as the amplitude ratio and phase attained as the CRWs move into a phase-locked position (the growing normal mode). Some examples of finite time baroclinic growth, described by CRWs, are given including development from initial conditions where upper or lower level perturbations are dominant.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics