  In this paper we extend earlier results regarding the effects of the lower
layer of the ocean (below the thermocline) on the baroclinic instability within
the upper layer (above the thermocline). We confront quasigeostrophic
baroclinic instability properties of a 2.5-layer model with those of a 3-layer
model with a very thick deep layer, which has been shown to predict spectral
instability for basic state parameters for which the 2.5-layer model predicts
nonlinear stability. We compute and compare maximum normal-mode perturbation
growth rates, as well as rigorous upper bounds on the nonlinear growth of
perturbations to unstable basic states, paying particular attention to the
region of basic state parameters where the stability properties of the 2.5- and
3-layer model differ substantially. We found that normal-mode perturbation
growth rates in the 3-layer model tend to maximize in this region. We also
found that the size of state space available for eddy-amplitude growth tends to
minimize in this same region. Moreover, we found that for a large spread of
parameter values in this region the latter size reduces to only a small
fraction of the total enstrophy of the system, thereby allowing us to make
assessments of the significance of the instabilities.
