An interpretation of baroclinic initial value problems: results for simple basic states with nonzero interior PV gradients

In the Eady model, where the meridional potential vorticity (PV) gradient is zero, perturbation energy growth can be partitioned cleanly into three mechanisms: (i) shear instability, (ii) resonance, and (iii) the Orr mechanism. Shear instability involves two-way interaction between Rossby edge waves on the ground and lid, resonance occurs as interior PV anomalies excite the edge waves, and the Orr mechanism involves only interior PV anomalies. These mechanisms have distinct implications for the structural and temporal linear evolution of perturbations. Here, a new framework is developed in which the same mechanisms can be distinguished for growth on basic states with nonzero interior PV gradients. It is further shown that the evolution from quite general initial conditions can be accurately described (peak error in perturbation total energy typically less than 10%) by a reduced system that involves only three Rossby wave components. Two of these are counterpropagating Rossby waves—that is, generalizations of the Rossby edge waves when the interior PV gradient is nonzero—whereas the other component depends on the structure of the initial condition and its PV is advected passively with the shear flow. In the cases considered, the three-component model outperforms approximate solutions based on truncating a modal or singular vector basis.

Parliamentary sovereignty, popular sovereignty, and Henry Parker's adjudicative standpoint

Discussions of popular sovereignty in early modern England have usually been premised upon a sharp distinction between ‘legal/constitutional’ forms of discourse (which merely interpret the law) and ‘political’ ones (which focus upon the right to make it). In such readings of the period, Henry Parker has a pivotal position as a writer who abandoned merely legalistic thinking. This chapter takes a different view. It argues that Parker’s major intellectual achievement was not so much to abandon legal/constitutional discourse as to offer a theorisation of its most distinctive features: he offered an account of a new kind of politics in which concern for ‘interests’ in property and in self-preservation replaced humanist concern with promotion of virtue. Parker drew upon ideas about representation best expressed by Sir Thomas Smith and ideas about law best expressed by Oliver St John. The theory he developed was not intended as a justification of legislative sovereignty, but of adjudicative supremacy. His picture of the two Houses as supreme adjudicators was meant to block the path to direct democracy. But the adjudicative standpoint they came to occupy presupposed that freeborn adults had ‘interests’ in life, liberty, and possessions. This had democratising implications.