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.

On a class of non-self-adjoint periodic eigenproblems with boundary and interior singularities

We prove that all the eigenvalues of a certain highly non-self-adjoint Sturm–Liouville differential operator are real. The results presented are motivated by and extend those recently found by various authors (Benilov et al. (2003) [3], Davies (2007) [7] and Weir (2008) [18]) on the stability of a model describing small oscillations of a thin layer of fluid inside a rotating cylinder.

Interior Life

Interior Life was curated by Tim Renshaw, Mary Maclean and Bernice Donszelmann who together form ‘Outside Architecture’. The aim of this project was to argue that interior space should not be negatively defined as a retreat from the public realm. Instead, following the thought of the philosopher Peter Slotterdijk, interior space was proposed as a human need. The five artists selected by ‘Outside Architecture’ each visualized this need differently. A contention here was that interiors give rise to a multiplicity of experiences that potentially change the way we dwell in contemporary man-made space. This contention was primarily figured in relation to the materiality of contemporary interiors. Each gave attention to the effects of contemporary materials and surfaces and each considered that these forms produce new modes of sensing and immersion in a place. The exhibition included two talks by the members of ‘Outside Architecture. The project was supported by an Arts Council of England grant of £6,323 www.ucreative.ac.uk/galleries