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.     

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.     

Gravity currents down canyons: effects of rotation

The flow of dense water in a V-shaped laboratory-scale canyon is investigated by using a non-hydrostatic numerical ocean model with focus on the effects of rotation. By using a high-resolution model, a more detailed analysis of plumes investigated in the laboratory (Deep-Sea Res I 55:1021–1034 2008) for laminar flow is facilitated. The inflow rates are also increased to investigate plume structure for higher Reynolds numbers. With rotation, the plumes will lean to the side of the canyon, and there will be cross-canyon geostrophic currents and Ekman transports. In the present study, it is found that the cross-canyon velocities are approximately 5 % of the down-canyon velocities over the main body of the plume for the rotational case. With rotation, the flow of dense water through the body of the plume and into the plume head is reduced. The plume head becomes less developed, and the speed of advance of the head is reduced. Fluid parcels near the top of the plume will to a larger extent be left behind the faster flowing dense core of the plume in a rotating system. Near the top of the plume, the cross-canyon velocities change direction. Inside the plume, the cross-flow is up the side of the canyon, and above the interface to the ambient there is a compensating cross-flow down the side of the canyon. This means that parcels of fluid around the interface become separated. Parcels of fluid around the interface with small down-canyon velocity components and relative large cross-canyon components will follow a long helix-like path down the canyon. It is found that the entrainment coefficients often are larger in the rotational experiments than in corresponding experiments without rotation. The effects of rotation and higher inflow rates on the areal patterns of entrainment velocities are demonstrated. In particular, there are bands of higher entrainment velocities along the lateral edges of the plumes in the rotational cases.