Numerical studies of large-amplitude internal waves shoaling and breaking at shelf slopes

Hydro carbon fields beyond the shelf break are presently being explored and developed, which has increased the scientific focus in this area. Measurements from the slopes reveal large variability in temperature and velocity, and some of the observed events are due to interactions between large-amplitude oscillations of the thermocline and the topography. The present study focuses on the strong currents that are generated near the seabed during shoaling and breaking of internal waves along shelf slopes. The parameter regime used is similar to the one for the Nordic Seas. The results show that, during shoaling of large internal waves along (gentle) slopes, the energy is transferred towards smaller scales and strong velocities (over 1 m s^− 1) can be generated. To resolve all scales involved is still not feasible, and therefore, the model results are sensitive to the grid size and the subgrid scale closure.     

Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions

A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear terms in the energy flux become increasingly important as the sill Froude Number (F _s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee wave generation and the non-linear contribution to the energy flux. Calculations show that as F _s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions.     

The beginning of geography didactics in Norway

At the end of the 19th century geography became a mandatory subject in primary and secondary schools in Norway. Geography was seen as a useful subject that contributed to the modernization of society, but also as a subject that strengthened the national ideology. A need for better education in geography arose and consequently some authors of geography textbooks wrote about teaching geography. In order to strengthen teachers’ education, geography was taught at university level, and to develop the subject it became necessary to relate it to other subjects, especially geology. The author shows that there are several similarities between the content of geography taught in Norwegian schools in the late 19th century and geography taught in schools today.     

Estimation of the internal pressure gradient in σ-coordinate ocean models: comparison of second-, fourth-, and sixth-order schemes

Sigma-coordinate ocean models are attractive because of their abilities to resolve bottom and surface boundary layers. However, these models can have large internal pressure gradient (IPG) errors. In this paper, two classes of methods for the estimation of the IPGs are assessed. The first is based on the integral approach used in the Princeton Ocean Model (POM). The second is suggested by Shchepetkin and McWilliams (2003) based on Green’s theorem; thus, area integrals of the pressure forces are transformed into line integrals. Numerical tests on the seamount problem, as well as on a northwestern Atlantic grid using both classes of methods, are presented. For each class, second-, fourth-, and sixth-order approximations are tested. Results produced with a fourth-order compact method and with cubic spline methods are also given. The results show that the methods based on the POM approach in general give smaller errors than the corresponding methods given in Shchepetkin and McWilliams (2003). The POM approach also is more robust when noise is added to the topography. In particular, the IPG errors may be substantially reduced by using the computationally simple fourth-order method from McCalpin (1994).     

Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size

A non-hydrostatic terrain-following model in cross sectional form is applied to study the processes in the lee of a sill in an idealized stratified fjord during super-critical tidal inflow. A sequence of numerical studies with horizontal grid sizes in the range from 100 to 1.5625 m are performed. All experiments are repeated using both hydrostatic and non-hydrostatic versions of the model, allowing a systematic study of possible non-hydrostatic pressure effects and also of the sensitivity of these effects to the horizontal grid size. The length scales and periods of the internal waves in the lee of the sill are gradually reduced and the amplitudes of these waves are increased as the grid size is reduced from 100 down to 12.5 m. With a further reduction in grid size, more short time and space scale motions become superimposed on the internal waves. Associated with the internal wave activity, there is a deeper separation point that is fairly robust to all parameters investigated. Another separation point nearer to the top of the sill appears in the numerical results from the high-resolution studies with the non-hydrostatic model. Associated with this shallower separation point, an overturning vortex appears in the same set of numerical solutions. This vortex grows in strength with reduced grid size in the non-hydrostatic experiments. The effects of the non-hydrostatic pressure on the velocity and temperature fields grow with reduced grid size. In the experiments with horizontal grid sizes equal to 100 or 50 m, the non-hydrostatic pressure effects are small. For smaller grid sizes, the time mean velocity and temperature fields are also clearly affected by the non-hydrostatic pressure adjustments.     

The evolution of barred spiral galaxies in the Hubble Deep Fields North and South

The frequency of barred spiral galaxies as a function of redshift contains important information on the gravitational influence of stellar discs in their dark matter haloes and may also distinguish between contemporary theories for the origin of galactic bulges. In this paper we present a new quantitative method for determining the strength of barred spiral structure, and verify its robustness to redshift-dependent effects. By combining galaxy samples from the Hubble Deep Field North with newly available data from the Hubble Deep Field South, we are able to define a statistical sample of 46 low-inclination spiral systems with I _814 W<23.2 mag. Analysing the proportion of barred spiral galaxies seen as a function of redshift, we find a significant decline in the fraction of barred spirals with redshift. The redshift distribution of 22 barred and 24 non-barred spirals with suitable inclinations is inconsistent with their being drawn from the same distribution at the 99 per cent confidence level. The physical significance of this effect remains unclear, but several possibilities include dynamically hotter (or increasingly dark-matter-dominated) high-redshift discs, or an enhanced efficiency in bar destruction at high redshifts. By investigating the formation of the 'orthogonal' axis of Hubble's classification tuning fork, our result complements studies of evolution in the early–late sequence, and pushes to later epochs the redshift at which the Hubble classification sequence is observed to be in place.     

Numerical simulation of flow and aquaculture organic waste dispersion in a curved channel

The dispersion and deposition of particulate organic matter from a fish cage located in an idealized curved channel with a 90° bend are studied for different horizontal grid resolutions. The model system consists of a three-dimensional, random-walk particle tracking model coupled to a terrain-following ocean model. The particle tracking model is a Lagrangian particle tracking simulator which uses the local flow field, simulated by the ocean model, for advection of the particles and random walk to simulate the turbulent diffusion. The sinking of particles is modeled by imposing an individual particle settling velocity. As the homogeneous water flows through the bend in the channel, the results show that a cross-channel secondary circulation is developed. The motion of this flow is similar to a helical motion where the water in the upper layers moves towards the outer bank and towards the inner bank in the lower layers. The intensity of the secondary circulation will depend on the viscosity scheme and increases as the horizontal grid resolution decreases which significantly affects the distribution of the particles on the seabed. The presence of the secondary circulation leads to that most of the particles that settle, settle close to the inner bank of the channel.