“How Can He Be So Cruel?” Examining Issues of Trust in School Improvement Efforts

In this case, a high school vice-principal encounters tension and anger when she rewrites a staff member’s report card comments without his knowledge. The case narrative examines the conflict that arises when, under time constraints and pressures to produce student reports, the vice-principal acts on a decision she believes is ethically correct only to find that she incurs a significant setback with staffing relationships largely due to wavering of trust. The analysis examines how transformational leadership builds self-efficacy in all staff founded on trusting relationships. Professional reflection provides a conduit through which educational leaders can assess their own practice and implement the changes needed to sustain school improvement planning

Penetrative Convection at High Rayleigh Numbers

We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is $Ra = \left[10^6, 10^8 \right]$ and the Prandtl numbers are $Pr = 1$ and $11.6$. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new non-dimensional parameter, $\Lambda$, which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of $\Lambda$ denote increased stability of the upper stable layer. We study the effects of $\Lambda$ on the flow field using well-resolved lattice Boltzmann simulations, and show that the characteristics of the flow depend sensitively upon it. For the range $\Lambda = \left[0.01, 4\right]$, we find that for a fixed $Ra$ the Nusselt number, $Nu$, increases with decreasing $\Lambda$. We also investigate the effects of $\Lambda$ on the vertical variation of convective heat flux and the Brunt-V\"{a}is\"{a}l\"{a} frequency. Our results clearly indicate that in the limit $\Lambda \rightarrow 0$ the problem reduces to that of the classical Rayleigh-B\'enard convection.Comment: 12 pages, 19 figure

Nonlinear threshold behavior during the loss of Arctic sea ice

In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or “tipping point”) beyond which the ice–albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice–albedo feedback. Here, we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that although the ice–albedo feedback promotes the existence of multiple ice-cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea-ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely