Frontal Wave Stability during Moist Deformation Frontogenesis. Part I: Linear Wave Dynamics

It has been shown that lower tropospheric potential vorticity zones formed during moist deformation frontogenesis will support growing waves if at some time the frontogenesis ceases. In this paper, the ways in which these waves are affected by the frontogenetic process are identified. Observations show that fronts in the eastern Atlantic commonly feature saturated ascent regions characterized by zero moist potential vorticity. Furthermore, in many cases the horizontal temperature gradient in the lowest one to two kilometers of the atmosphere is rather weak. These features are incorporated in an analytical archetype. The dynamical implications of saturated ascent in conditions of zero moist potential vorticity are represented in the model by assuming that adiabatic temperature changes are precisely balanced by diabatic tendencies. The observed small temperature gradient at low levels is represented in the model by taking it to be zero in the lowest two kilometers. Consequently, the forcing of the low-level moist ageostrophic vortex stretching that strengthens the low-level potential vorticity anomaly is confined to middle and upper levels. A semianalytical initial value solution for the linear development of waves on the evolving low-level potential vorticity anomaly is obtained. The waves approximately satisfy the inviscid primitive equations whenever the divergent part of the perturbation is negligible relative to the rotational part. The range of nonmodal wave developments supported by the front is summarized using RT phase diagrams. This analysis shows that the most dramatic effects of frontogenesis on frontal wave growth are due to (a) the increase in time of the potential vorticity and hence potential instability of the flow and (b) the increase in time of the alongfront wavelength relative to the width of the strip. An optimally growing streamfunction wave is described. Finally, a diagnostic technique suitable for identifying small amplitude frontal waves in observational data is described.