### Abstract:

The dynamics of the growth of linear disturbances
to a chaotic basic state is analyzed in an asymptotic model of
weakly nonlinear, baroclinic wave-mean interaction. In this
model, an ordinary differential equation for the wave amplitude
is coupled to a partial differential equation for the zonal
flow correction. The leading Lyapunov vector is nearly parallel
to the leading Floquet vector ø1 of the lowest-order unstable
periodic orbit over most of the attractor. Departures of
the Lyapunov vector from this orientation are primarily rotations
of the vector in an approximate tangent plane to the
large-scale attractor structure. Exponential growth and decay
rates of the Lyapunov vector during individual Poincaré
section returns are an order of magnitude larger than the Lyapunov
exponent λ ≈ 0.016. Relatively large deviations of the
Lyapunov vector from parallel to ø1 are generally associated
with relatively large transient decays. The transient growth
and decay of the Lyapunov vector is well described by the
transient growth and decay of the leading Floquet vectors of
the set of unstable periodic orbits associated with the attractor.
Each of these vectors is also nearly parallel to ø1. The
dynamical splitting of the complete sets of Floquet vectors
for the higher-order cycles follows the previous results on
the lowest-order cycle, with the vectors divided into wavedynamical
and decaying zonal flow modes. Singular vectors
and singular values also generally follow this split. The
primary difference between the leading Lyapunov and singular
vectors is the contribution of decaying, inviscidly-damped
wave-dynamical structures to the singular vectors.