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

Lyapunov analysis of multiscale dynamics: The slow bundle of the two-scale Lorenz 96 model