Øyvind Thiem

Stability Analysis of Geostrophic Adjustment on Hexagonal Grids for Regions with Variable Depth

Hexagonal grids have been used in a number of numerical studies, and especially in relation to atmospheric models. Recent studies have suggested that ocean circulation models may also benefit from the use of hexagonal grids. These grids tend to induce less systematic errors and have better horizontal isotropy properties than traditional square grid schemes. If hexagonal grids are to be applied in ocean models, a number of features that are characteristic of ocean circulation problems need to be attended to. The topography of the ocean basin is an important feature in most ocean models. Ocean modelers can experience instabilities due to depth variations. In the present paper, analysis of the propagation matrix for the spatially discretized system is used to explain unphysical growth of the numerical solutions of the linear shallow water equations when using hexagonal grids over domains with variable depth. It is shown that a suitable weighting of the Coriolis terms may give an energy-conserving and stable numerical scheme.

Gas exploration beyond the shelf break: An oceanographic challenge

Norways second largest gas field, Ormen Lange, is located 140km west off Kristiansund at an unprecedented depth when it comes to exploration. It will be the first Norwegian project beyond the shelf break. Exploration and development of the field is thus a challenge. An important issue during the planning stage is to understand the current conditions and hydrography of the site. This is especially important regarding pipeline design, deployment and operations. A complicating factor for estimating design currents is the extreme roughness of the local topography. Submarine slides have produced escarpments and sea mounts with height variations of up to 100m. The hydrography seems to be equally complex; in situ moorings have revealed strong variations in current speed and temperature close to the seabed. A variety of numerical experiments have been and are being set up in order to recapture and if possible forecast the observed variability. The results show that the flow is influenced by the inflow of Atlantic Water, tides, atmospheric forcing and by flow of water masses inside the Norwegian Sea basin. The variability near the seabed at Ormen Lange is strongly influenced by the local topography and the stratification. Realistic model studies therefore require high resolution models for the Ormen Lange topography connected to basin scale models. The models must be non-hydrostatic and the stratification realistic to enable realistic estimates of extreme events.

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.

Effects of the bottom boundary condition in numerical investigations of dense water cascading on a slope

The flow of dense water along continental slopes is considered. There is a large literature on the topic based on observations and laboratory experiments. In addition, there are many analytical and numerical studies of dense water flows. In particular, there is a sequence of numerical investigations using the dynamics of overflow mixing and entrainment (DOME) setup. In these papers, the sensitivity of the solutions to numerical parameters such as grid size and numerical viscosity coefficients and to the choices of methods and models is investigated. In earlier DOME studies, three different bottom boundary conditions and a range of vertical grid sizes are applied. In other parts of the literature on numerical studies of oceanic gravity currents, there are statements that appear to contradict choices made on bottom boundary conditions in some of the DOME papers. In the present study, we therefore address the effects of the bottom boundary condition and vertical resolution in numerical investigations of dense water cascading on a slope. The main finding of the present paper is that it is feasible to capture the bottom Ekman layer dynamics adequately and cost efficiently by using a terrain-following model system using a quadratic drag law with a drag coefficient computed to give near-bottom velocity profiles in agreement with the logarithmic law of the wall. Many studies of dense water flows are performed with a quadratic bottom drag law and a constant drag coefficient. It is shown that when using this bottom boundary condition, Ekman drainage will not be adequately represented. In other studies of gravity flow, a no-slip bottom boundary condition is applied. With no-slip and a very fine resolution near the seabed, the solutions are essentially equal to the solutions obtained with a quadratic drag law and a drag coefficient computed to produce velocity profiles matching the logarithmic law of the wall. However, with coarser resolution near the seabed, there may be a substantial artificial blocking effect when using no-slip.