Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

Upwelling O+ ion source characteristics

Recent observations from the Dynamics Explorer 1 (DE-1) spacecraft have shown that the dayside auroral zone is an important source of very low-energy superthermal O^+ ions for the polar magnetosphere. When observed at 2000- to 5000-km altitude, the core of the O^+ distribution exhibits transverse heating to energies on the order of 10 eV, significant upward heat flux, and subsonic upward flow at significant flux levels exceeding 10^8 cm^{-2}s^{-1}. The term "upwelling ions" has been adopted to label these flows, which stand out in sharp contrast to the light ion polar wind flows observed in the same altitude range in the polar cap and subauroral magnetosphere. We have chosen a typical upwelling ion event for detailed study, correlating retarding ion mass spectrometer observations of the low-energy plasma with energetic ion observations and local electromagnetic field observations. The upwelling ion signature is colocated with the magnetospheric cleft as marked by precipitating energetic magnetosheath ions. The apparent ionospheric heating is clearly linked with the magnetic field signatures of strong field-aligned currents in the vicinity of the dayside polar cap boundary. Electric field and ion plasma measurements indicate that a very strong and localized convection channel or jet exists coincident with the other signatures of this event. These observations indicate that transverse ion heating to temperatures on the order of 10^5 K in the 2000- to 5000-km ionosphere is an important factor in producing heavy ion outflows into the polar magnetosphere. This result contrasts with recent suggestions that electron heating to temperatures of order 10^4 K is the most important parameter with regard to O^+ outflow.