Development of perturbations within growing baroclinic waves

We explore the linear stability of a growing, three‐dimensional baroclinic wave by calculating the perturbation that grows most rapidly over various time intervals and at various stages in the development of the parent wave and its fronts. Three norms are used to measure growth: volume‐integrated energy, enstrophy and stream function variance. The flow is assumed adiabatic and quasi‐geostrophic for simplicity, and perturbations are required to have uniform potential vorticity. These rapidly growing perturbations can produce realistic sub‐structures within the parent wave, such as upper‐level vorticity maxima that propagate relative to a synoptic‐scale parent wave or packets of synoptic‐scale waves within a planetary‐wave basic state. For a synoptic‐scale parent wave and the energy or enstrophy norms, however, the dominant characteristic of the fastest growing perturbations is that they rapidly evolve toward a final structure corresponding to a phase shift and slight change of shape of the original wave—in essence, the initial perturbation modifies the parent wave and the jet on which it propagates, which results in a modification, which grows in time, of the phase and amplitude of the parent wave. Amplifications in energy or enstrophy are also small compared to what would be estimated based on the locally large shears and baroclinicity within the parent wave. The fronts appear to be stabilized by the combined influences of synoptic‐scale horizontal deformation and the natural movement of perturbations relative to the parent wave.