The counter-propagating Rossby-wave perspective on baroclinic instability. Part III: Primitive-equation disturbances on the sphere

Baroclinic instability of perturbations described by the linearized primitive quations, growing on steady zonal jets on the sphere, can be understood in terms of the interaction of pairs of counter-propagating Rossby waves (CRWs). The CRWs can be viewed as the basic components of the dynamical system where the Hamiltonian is the pseudoenergy and each CRW has a zonal coordinate and pseudomomentum. The theory holds for adiabatic frictionless flow to the extent that truncated forms of pseudomomentum and pseudoenergy are globally conserved. These forms focus attention on Rossby wave activity. Normal mode (NM) dispersion relations for realistic jets are explained in terms of the two CRWs associated with each unstable NM pair. Although derived from the NMs, CRWs have the conceptual advantage that their structure is zonally untilted, and can be anticipated given only the basic state. Moreover, their zonal propagation, phase-locking and mutual interaction can all be understood by ‘PV-thinking’ applied at only two ‘home-bases’—potential vorticity (PV) anomalies at one home-base induce circulation anomalies, both locally and at the other home-base, which in turn can advect the PV gradient and modify PV anomalies there. At short wavelengths the upper CRW is focused in the mid-troposphere just above the steering level of the NM, but at longer wavelengths the upper CRW has a second wave-activity maximum at the tropopause. In the absence of meridional shear, CRW behaviour is very similar to that of Charney modes, while shear results in a meridional slant with height of the air-parcel displacement-structures of CRWs in sympathy with basic-state zonal angular-velocity surfaces. A consequence of this slant is that baroclinically growing eddies (on jets broader than the Rossby radius) must tilt downshear in the horizontal, giving rise to up-gradient momentum fluxes that tend to accelerate the barotropic component of the jet.

The counter-propagating Rossby-wave perspective on baroclinic instability. Part IV: Nonlinear life cycles

Pairs of counter-propagating Rossby waves (CRWs) can be used to describe baroclinic instability in linearized primitive-equation dynamics, employing simple propagation and interaction mechanisms at only two locations in the meridional plane—the CRW ‘home-bases’. Here, it is shown how some CRW properties are remarkably robust as a growing baroclinic wave develops nonlinearly. For example, the phase difference between upper-level and lower-level waves in potential-vorticity contours, defined initially at the home-bases of the CRWs, remains almost constant throughout baroclinic wave life cycles, despite the occurrence of frontogenesis and Rossby-wave breaking. As the lower wave saturates nonlinearly the whole baroclinic wave changes phase speed from that of the normal mode to that of the self-induced phase speed of the upper CRW. On zonal jets without surface meridional shear, this must always act to slow the baroclinic wave. The direction of wave breaking when a basic state has surface meridional shear can be anticipated because the displacement structures of CRWs tend to be coherent along surfaces of constant basic-state angular velocity, U. This results in up-gradient horizontal momentum fluxes for baroclinically growing disturbances. The momentum flux acts to shift the jet meridionally in the direction of the increasing surface U, so that the upper CRW breaks in the same direction as occurred at low levels

A new look at stratospheric sudden warmings. Part III. Polar vortex evolution and vertical structure

The evolution of the Arctic polar vortex during observed major mid-winter stratospheric sudden warmings (SSWs) is investigated for the period 1957-2002, using European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-40 Ertel’s potential vorticity (PV) and temperature fields. Time-lag composites of vertically weighted PV, calculated relative to the SSW onset time, are derived for both vortex displacement SSWs and vortex splitting SSWs, by averaging over the 15 recorded displacement and 13 splitting events. The evolving vertical structure of the polar vortex during a typical SSW of each type is clearly illustrated by plotting an isosurface of the composite PV field, and is shown to be very close to that observed during representative individual events. Results are verified by comparison with an elliptical diagnostic vortex moment technique. For both types of SSW, little variation is found between individual events in the orientation of the developing vortex relative to the underlying topography, i.e. the location of the vortex during SSWs of each type is largely fixed in relation to the Earth’s surface. During each type of SSW, the vortex is found to have a distinctive vertical structure. Vortex splitting events are typically barotropic, with the vortex split occurring near-simultaneously over a large altitude range (20-40 km). In the majority of cases, of the two daughter vortices formed, it is the ‘Siberian’ vortex that dominates over its ‘Canadian’ counterpart. In contrast, displacement events are characterized by a very clear baroclinic structure; the vortex tilts significantly westward with height, so that the top and bottom of the vortex are separated by nearly 180◦ longitude before the upper vortex is sheared away and destroyed.