We explore the nature of instabilities in a well-known meteorological toy model, the Lorenz 96, to unravel key mechanisms of interaction between scales of different resolutions and time scales. To do so, we use a mathematical machinery known as Lyapunov analysis, allowing us to capture the degrees of chaoticity associated with fundamental directions of instability. We find a non-trivial group of such directions projecting significantly on slow variables, associated with long term dynamics.