Low frequency variability induced by continents and potential vorticity sources

Observations of atmospheric low frequency variability of the Northern Hemisphere wintertime circulation show wave trains over the continental sectors and zonally elongated features over the oceanic sectors. The explicit role of topography and external potential vorticity (PV) forcing in producing these regional structures is examined in a linear, barotropic model of the extratropical troposphere. A multiple scale analysis yields an analytical expression for the evolution of the low-pass filtered flow, which consists of stationary and low frequency wave fields.

The structure of the low frequency wave field depends on the type of forcing. If the stationary wave field is forced solely by continental-like topographic forcing, low frequency wave trains emerge. In contrast, if the stationary wave field is forced solely by PV forcing consistent with land-sea heating contrasts, zonally elongated disturbances emerge. If the local, low frequency instabilities are weak or even squelched by sufficiently large friction, they can still be excited via remote, resonant forcing.

Irrespective of the type of forcing, the stability of the flow is encapsulated by a single tuning function, mp(x), which depends explicitly on the longitudinal structure of the stationary wave field and implicitly on the meridional structure of the total flow field. A necessary condition for growing, low frequency disturbances is the existence of at least one longitude where mp(x)=0. At such longitudes, which correspond to WKB turning points, the group velocity vanishes. Flows characterized by one turning point, or two turning points that are sufficiently far apart, grow via self-resonance at the turning point. Flows characterized by two turning points that are sufficiently close together grow via mode coupling, whereby modes attached to each turning point resonate and fill the region between the turning points.