We describe a shock-capturing streamline diffusion space-time discontinuous Galerkin (DG) method to discretize the shallow water equations with variable bottom topography. This method, based on the entropy variables as degrees of freedom, is shown to be energy stable as well as well-balanced with respect to the lake at rest steady state. We present numerical experiments illustrating the numeric...

We investigate both the type I and II modes of stationary instability within the boundarylayer flow over a rotating disk. Extending the work of previous studies we find that the flow can be stabilised via the introduction of shear-thinning non-Newtonian fluids. Laminar-flow profiles are determined from a generalised von Kármán similarity solution. An asymptotic study is presented in the limit o...

Experimental observations of a purely elastic flow instability occurring in the lid-driven cavity flow of two semi-dilute polymer solutions are reported and the effect of cavity aspect ratio on the dynamical structure of the unstable flow is quantitatively investigated. The spatial and temporal characteristics of the secondary flow are measured using flow visualization, laser Doppler velocimetr...

Diffusion MRI tractography is often used to estimate structural connections between brain areas and there is a fast-growing interest in quantifying these connections based on their position, shape, size and length. However, a portion of the connections reconstructed with tractography is biased by their position, shape, size and length. Thus, connections reconstructed are not equally distributed...

In this study, we provide a mathematical description of the onset of counterrotating circular vortices observed for a family of slender rotating cones (of half-angles 15° or less) in quiescent fluid. In particular, we apply appropriate scalings in order to simplify the basic-flow profiles, which are subsequently perturbed, accounting for the effects of streamline curvature. A combined large Rey...

Euler’s equation expresses the relationship between the velocity and the pressure fields in inviscid flow. Written in terms of streamline coordinates, this equation gives information about not only about the pressure-velocity relationship along a streamline (Bernoulli’s equation), but also about how these quantities are related as one moves in the direction transverse to the streamlines. The tr...

The turbulent mixing of a primary jet and its surrounding fluid in a pipe with inlet conditions that result in flow separation is studied. Detailed profiles of the axial mean and rms velocities have been measured with a laser Doppler anemometer. Measured spectra of axial velocity fluctuations show the presence of coherent structures. The performance of a two-equation turbulence model in conjunc...

A novel tensor interpolation method is introduced that allows Diffusion Tensor Imaging (DTI) streamlining to overcome low-anisotropy regions and permits branching of trajectories using information gathered from the neighbourhood of low-anisotropy voxels met during the tracking. The interpolation method is performed in Log-Euclidean space and collects directional information in a spherical neigh...

This paper is concerned with the existence of local absolute instability in the boundary-layer flow over the outer surface of a rotating cone, thereby extending earlier work by Lingwood who considered the rotating disk. Both still outer fluids and non-zero axial flow are considered, viscous and streamline-curvature effects are included, and the analysis is conducted for a wide range of cone hal...