  We investigate the geometrical structure of instabilities in the two-scales
Lorenz 96 model through the prism of Lyapunov analysis. Our detailed study of
the full spectrum of covariant Lyapunov vectors reveals the presence of a slow
bundle in tangent space, composed by a set of vectors with a significant
projection on the slow degrees of freedom; they correspond to the smallest (in
absolute value) Lyapunov exponents and thereby to the longer time scales. We
show that the dimension of the slow bundle is extensive in the number of both
slow and fast degrees of freedom, and discuss its relationship with the results
of a finite-size analysis of instabilities, supporting the conjecture that the
slow-variable behavior is effectively determined by a non-trivial subset of
degrees of freedom. More precisely, we show that the slow bundle corresponds to
the Lyapunov spectrum region where fast and slow instability rates overlap,
"mixing" their evolution into a set of vectors which simultaneously carry
information on both scales. We suggest these results may pave the way for
future applications to ensemble forecasting and data assimilations in weather
and climate models.
