The existence of subsynoptic-scale baroclinic instability and the nonlinear evolution of shallow disturbances

The stability of a realistic model of the midlatitude tropospheric jet stream is investigated through the application of two different methodologies, namely, by solution of the associated nonseparable linear eigenvalue problem and by solution of the related nonlinear initial value problem. The nonseparable linear analysis, formulated in terms of a hydrostatic anelastic model, is employed to identify two dominant modes of instability; the first of these is the classical Charney-Eady mode with a zonal wavelength of approximately 4000 km whereas the second is a surface confined shallow mode with a wavelength near 1000 km or smaller. In order to test these predictions of linear normal-mode theory, a series of nonlinear time integrations is performed based upon use of a nonhydrostatic anelastic model in which the zonal length of the cyclic channel is employed to select the zonal scale of the disturbance. These analyses are all initialized with the same balanced zonal flow and without the explicit addition of any superimposed disturbance. Both the Charney-Eady mode and the subsynoptic-scale shallow mode are observed to emerge naturally when the channel is set to the appropriate length and to travel at the phase speed predicted by the normal-mode stability analysis. The existence of the latter mode is apparently associated with the presence of an inertial critical layer, which is supported by nongeostrophic dynamics, and by the presence of a weak cross-front horizontal gradient of potential vorticity. It is furthermore demonstrated that in a sufficiently long channel a pair of subsynoptic-scale disturbances grow simultaneously to saturation amplitude and thereafter undergo a subharmonic pairing interaction in which the wavelength doubles and the disturbance deepens dramatically. This distinctive interaction appears to constitute a new nonlinear route to the development of a deep baroclinic disturbance