Shaun Belward

Fully non-linear two-layer flow over arbitrary topography

Steady, two-dimensional, two-layer flow over an arbitrary topography is considered. The fluid in each layer is assumed to be inviscid and incompressible and flows irrotationally. The interfacial surface is found using a boundary integral formulation, and the resulting integrodifferential equations are solved iteratively using Newtons method. A linear theory is presented for a given topography and the non-linear theory is compared against this to show how the non-linearity affects the problem.

Scientists and mathematicians collaborating to build quantitative skills in undergraduate science

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum.

Interfacial waves and hydraulic falls: Some applications to atmospheric flows in the lee of mountains

Two dimensional flow of a layer of constant density fluid over arbitrary topography, beneath a compressible, isothermal and stationary fluid is considered. Both downstream wave and critical flow solutions are obtained using a boundary integral formulation which is solved numerically by Newtons method. The resulting solutions are compared against waves produced behind similar obstacles in which the compressible upper layer is absent (single layer flow) and against the predictions of a linearised theory. The limiting waves predicted by the full non-linear equations are contrasted with those predicted by the forced Korteweg-de Vries theory. In particular, it is shown that at some parameter values a multiplicity of solutions exists in the full nonlinear theory.

Atmospheric interfacial waves

Waves at the interface of a two-layer fluid are considered. The fluid in the lower layer is incompressible with constant density and is flowing irrotationally. In the upper layer, the fluid is stationary but compressible, and corresponds to an isothermal atmosphere with a density profile that decreases exponentially with height. The interface between the two fluids is assumed sharp. The formation of waves at the interface would come about typically as a result of the interaction of the moving lower layer of fluid with local topographical features, as with the classical problem of the generation of waves on the lee side of a mountain range. It is shown that the present model is capable of supporting the formation of interfacial waves that are similar in many respects to the classical gravity wave of Stokes, and that are ultimately limited in every case by the formation of a 120° angle at the wave crest. The highly nonlinear wave profiles are computed numerically and compared with the predictions of linearized theory. An extended perturbation analysis is given near the point at which the interfacial waves break down as a result of the Kelvin-Helmholtz instability.

Fully nonlinear flow over successive obstacles: hydraulic fall and supercritical flows

In this paper we consider the flow of an incompressible, inviscid and homogeneous fluid over two obstacles in succession. The flow is assumed irrotational and solutions are sought in which a hydraulic fall occurs over the first obstacle with supercritical flow over the second. The method used to solve the problem is capable of calculating flows over topography of any shape.

Curriculum Development for Quantitative Skills in Degree Programs: A Cross-Institutional Study Situated in the Life Sciences.

ABSTRACT Higher education policies are increasingly focused on graduate learning outcomes, which infer an emphasis on, and deep understanding of, curriculum development across degree programs. As disciplinary influences are known to shape teaching and learning activities, research situated in disciplinary contexts is useful to further an understanding of curriculum development. In the life sciences, several graduate learning outcomes are underpinned by quantitative skills or an ability to apply mathematical and statistical thinking and reasoning. Drawing on data from a national teaching project in Australia that explored quantitative skills in the implemented curricula of 13 life sciences degree programs, this article presents four program-level curricular models that emerged from the analysis. The findings are interpreted through the lens of discipline-specific research and general curriculum design theories to further our understanding of curriculum development for graduate learning outcomes. Implications for future research and to guide curriculum development practices in higher education are discussed.

Atmospheric interfacial waves in the presence of two moving fluid layers

Atmospheric waves at the interface between two flowing layers of air are studied in this paper. The lower layer is assumed to be incompressible and to flow irrotationally, and its motion might be the result of a distant thunderstorm, for example. The upper layer is modeled as a compressible isothermal atmosphere, so that if it were stationary, its density and pressure would both decrease exponentially with height. The equations of motion in the upper layer are linearized under the assumption that the lower layer of incompressible fluid is ‘‘thin’’ (its weight is a small fraction of the total), but the possibility of large‐amplitude disturbances at the interface is nevertheless allowed. A linearized theory of wave propagation in this system is discussed, and a numerical scheme is outlined for the solution of the nonlinear equations. The results confirm the predictions of a model of Forbes and Belward [Phys. Fluids A 4, 2222 (1992)], in which the upper atmosphere was assumed stationary, and demonstrate that...

Investigating students’ perceptions of graduate learning outcomes in mathematics

ABSTRACT The purpose of this study is to explore the perceptions mathematics students have of the knowledge and skills they develop throughout their programme of study. It addresses current concerns about the employability of mathematics graduates by contributing much needed insight into how degree programmes are developing broader learning outcomes for students majoring in mathematics. Specifically, the study asked students who were close to completing a mathematics major (n = 144) to indicate the extent to which opportunities to develop mathematical knowledge along with more transferable skills (communication to experts and non-experts, writing, working in teams and thinking ethically) were included and assessed in their major. Their perceptions were compared to the importance they assign to each of these outcomes, their own assessment of improvement during the programme and their confidence in applying these outcomes. Overall, the findings reveal a pattern of high levels of students’ agreement that these outcomes are important, but evidence a startling gap when compared to students’ perceptions of the extent to which many of these – communication, writing, teamwork and ethical thinking – are actually included and assessed in the curriculum, and their confidence in using such learning.