Modeling of internal tides in fjords

A previous model for the distribution of internal tides above irregular topography is generalized to include arbitrary stratification and a radiation condition at the open boundary. Thanks to a small amount of dissipation, this model remains valid in the presence of resonant internal tides, leading to intense wave-energy beams. An application to a Norwegian fjord correctly reproduces the observed energy pattern consisting of two beams both originating at the 60-meter deep entrance sill and extending in-fjord, one upward toward the surface, the other downward toward the bottom. After correction for the varying width of the fjord, the observed and modelled energy levels are in good agreement, especially in the upper levels where energy is the greatest. Furthermore, the substantial phase lag between these two energy beams revealed by the observations is correctly reproduced by the model. Finally, a third and very narrow energy spike is noted in the model at the level of a secondary bump inward of the sill. This beam is missed by the current meter data, because the current meters were placed only at a few selected depths. But an examination of the salinity profiles reveals a mixed layer at approximately the same depth. The explanation is that high-wave energy leads to wave breaking and vigorous mixing. The model\u27s greatest advantage is to provide the internal-tide energy distribution throughout the fjord. Discrepancies between observations and model are attributed to coarse vertical resolution in the vicinity of the sill and to unaccounted cross-fjord variations

What should be taught in Intermediate Macroeconomics?

A lack of consensus remains on what should form the theoretical core of the undergraduate intermediate macroeconomic course. In determining how to deal with the Keynesian/classical divide, instructors must decide whether to follow the modern approach of building macroeconomic relationships from microfoundations, or to use the traditional approach based on aggregate models of the macroeconomy. In this article, the authors discuss the advantages and shortcomings of each approach in the context of course objectives. Because there is significant heterogeneity in textbook coverage, the authors summarize some of the approaches taken in current intermediate-level textbooks, which should serve as a useful starting point for new instructors. The authors also discuss how each approach can be extended to analyze the recent recession in the United States

Three-layer flows in the shallow water limit

We formulate and discuss the shallow water limit dynamics of the layered flow with three layers of immiscible fluids of different densities bounded above and below by horizontal walls. We obtain a resulting system of four equations, which may be nonlocal in the non‐Boussinesq case. We provide a systematic way to pass to the Boussinesq limit, and then study those equations, which are first‐order PDEs of mixed type, more carefully. We show that in a symmetric case the solutions remain on an invariant surface and using simple waves we illustrate that this is not the case for nonsymmetric cases. Reduced models consisting of systems of two equations are also proposed and compared to the full system

Nonlinear stability of two-layer shallow water flows with a free surface

The problem of two layers of immiscible fluid, bordered above by an unbounded layer of passive fluid and below by a flat bed, is formulated and discussed. The resulting equations are given by a first-order, four-dimensional system of PDEs of mixed-type. The relevant physical parameters in the problem are presented and used to write the equations in a non-dimensional form. The conservation laws for the problem, which are known to be only six, are explicitly written and discussed in both non-Boussinesq and Boussinesq cases. Both dynamics and nonlinear stability of the Cauchy problem are discussed, with focus on the case where the upper unbounded passive layer has zero density, also called the free surface case. We prove that the stability of a solution depends only on two ‘baroclinic’ parameters (the shear and the difference of layer thickness, the former being the most important one) and give a precise criterion for the system to be well-posed. It is also numerically shown that the system is nonlinearly unstable, as hyperbolic initial data evolves into the elliptic region before the formation of shocks. We also discuss the use of simple waves as a tool to bound solutions and preventing a hyperbolic initial data to become elliptic and use this idea to give a mathematical proof for the nonlinear instability

Heat transport in rotating convection without Ekman layers

Numerical simulation of rotating convection in plane layers with free slip boundaries show that the convective flows can be classified according to a quantity constructed from the Reynolds, Prandtl and Ekman numbers. Three different flow regimes appear: Laminar flow close to the onset of convection, turbulent flow in which the heat flow approaches the heat flow of non-rotating convection, and an intermediate regime in which the heat flow scales according to a power law independent of thermal diffusivity and kinematic viscosity.Comment: 4 pages, 4 figure

Comparing Programming Self-Esteem of Upper Secondary School Teachers to CS1 Students

Teacher self-esteem has been found to impact student learning in a number of non-computing fields. As computing slowly becomes a part of the upper secondary school (high school) curriculum in many countries, instruments designed to measure teachers’ programming self-esteem can help inform classroom practice and processes such as teacher professional development needs. This study examines if there are differences in programming self-esteem (using the Bergin Programming Self-Esteem Instrument) between upper secondary school teachers and CS1 students in Ireland. In addition this study provides evidence of validity when using this instrument (originally developed for CS1 students) to measure upper secondary school teacher programming self-esteem. To test for evidence of validity, we compared the results of the programming self-esteem construct given to upper secondary school teachers (n=130) to a recent study of programming selfesteem among CS1 students (n=693). We found evidence of both reliability and validity with teachers that aligns with the evidence found for the CS1 students, demonstrating utility for use with teacher cohorts. Comparing these findings, teachers reported statistically significantly lower programming self-esteem compared to CS1 students. Interestingly CS1 students identifying as male had a statistically significant higher programming self-esteem than those identifying as female. However, we found no statistically significant difference for teacher gender, unlike previous work. Our results indicate that teacher programming self-esteem should be given consideration in the design and implementation of professional development

Generation and Structure of Solitary Rossby Vortices in Rotating Fluids

The formation of zonal flows and vortices in the generalized Charney-Hasegawa-Mima equation is studied. We focus on the regime when the size of structures is comparable to or larger than the deformation (Rossby) radius. Numerical simulations show the formation of anticyclonic vortices in unstable shear flows and ring-like vortices with quiescent cores and vorticity concentrated in a ring. Physical mechanisms that lead to these phenomena and their relevance to turbulence in planetary atmospheres are discussed.Comment: 3 pages in REVTeX, 5 postscript figures separately, submitted to Phys. Rev.