Abstract
We focus on the influence of the β‐effect on the singular modes of baroclinic instability in the Phillips model. An analytical intercomparison between normal and singular modes for the Eady problem on an f‐plane has already been performed, showing that the amplification rate of the singular mode for the kinetic‐energy norm after a dimensional time of three days is about 1.2 times larger than for the normal mode. We show here that, in the presence of the β‐effect, the maximum amplification rate of the singular mode can be 1.5 times larger than for the normal‐mode case. This difference is due to the lesser stabilizing effect of β on the singular modes compared with the normal modes. This result is obtained for the case of equal layer depths which is relevant for the atmospheric situation. For the oceanic situation with unequal layer depths the amplification due to β is further increased leading to a factor of 1.8 in amplification rates between the two types of modes after a dimensional time of about 20 days. This behaviour is explained by the fact that β only intervenes in the anti‐Hermitian part of the linear dynamical operator, the main effect of which is to alter the vertical phase tilt of the perturbations. As a consequence, the structure of the bi‐orthogonal mode becomes more inclined to the vertical in the presence of β while, on the contrary, the structure of the unstable normal mode becomes less inclined.