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 Newton's 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.

As the type of student entering university changes, we are obliged as educators to adapt our teaching styles to suit the new demographic. With many students unable to physically attend lectures and with the internet being accessible to the vast majority of students, the need for flexibility has become paramount. In a direct response to this need, mathematics lecturers at James Cook University created screencasts for a number of their subjects, both as lecture replacement and as supplement. These screencasts involve screen and audio capture of handwritten, typed or powerpoint lectures created using a tablet computer. This article discusses student opinion on the effectiveness of the screencasts used in teaching mathematics at James Cook University. Examining the students responses to this relatively new technology raises questions on the viability of the traditional face to face lecture and the role academics will play in a technology driven tertiary sector.

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 Newton's 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.

A mathematical model is proposed to describe atmospheric solitary waves at the interface between a ‘shallow’ layer of fluid near the ground and a stationary upper layer of compressible air. The lower layer is in motion relative to the ground, perhaps as a result of a distant thunderstorm or a sea breeze, and possesses constant vorticity. The upper fluid is compressible and isothermal, so that its density and pressure both decrease exponentially with height. The profile and speed of the solitary wave are determined, for a wave of given amplitude, using a boundary-integral method. Results are discussed in relation to the ‘morning glory’, which is a remarkable meteorological phenomenon evident in the far north of Australia.

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.