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strong currents are associated with the transformation process. Also the dissipation ratespredicted are at the high end of the varied oceanographic measurements shown in Figure 9([11], [12], University of Wales, Bangor private communication) and so the transformationprocess is expected to contribute significantly to enhanced mixing and sediment resuspension.Figure 10 shows the shear distribution and flow velocity distribution as anelevation wave is forming and the maximum bed stress as a function of range. According tothe Shields criterion [13] a bed shear stress of 2N/m 2 is sufficient to lift fine sand particleswith diameter ~ 0.1mm so there is the potential for fine sediment re-suspension. If this is thecase then Figure 11 shows the effect of the wave in transporting re-suspended sediment(modelled initially as a passive scalar source between 15km and 16.5km range) up into thewater column and towards the shore.2. Dispersal effects due to passage of large amplitude internal waves off the Malin Shelf(north west coast of Scotland)The Shelf Edge Study Acoustic Measurement Experiment (SESAME associated with theShelf Edge Study (SES)) took place in the summer of 1995 off the north west coast ofScotland. SESAME was sponsored by the UK Ministry of Defence (MOD) of which Dstlforms part. One aspect of this exercise involved measurements of large amplitude (~50m)internal waves travelling towards the coast from the Malin Shelf at ~0.5m/s. Figure 12 showsthe location of study and detail of soliton tracks derived from Synthetic Aperture Radar (SAR)imagery.A typical lead soliton density profile and range velocity distribution obtained from one of themeasurement stations S140 (where the water depth was 140m) were used for the PHOENICSsimulation; these initial fields are shown in Figure 13 and were employed to investigate theeffects of the passage of such waves on the dispersal of neutrally buoyant material initiallylocated at different depths. For this particular case, turbulence was not modelled as the maininterest was in the effect of advection. A similar spatial discretisation to the first case studywas used but a longer time step was possible because elevation waves were not beingsimulated. Cyclic boundary conditions were used in the x direction to simulate repeatedpassage of such waves so a relatively short range section of ~2km was sufficient.The results are shown in Figure 14 covering a time period of about one hour. The coloursrelate to concentration values initially set to unity at the three depths shown in the top left ofthe figure. The dark solid lines are isopycnals and the white solid lines are Richardson numbercontours indicating areas were turbulence is expected from flow instability. The results showsignificant transport effects both towards and away from the shore at mid-depth and near thesurface and also reductions in the levels of concentration due to distortion of the initialmaterial volume by shear in the wave. Near the bottom, there is less of an effect.DISCUSSIONIn general the results achieved are considered reasonable. However, for the first case inparticular, which tracks an internal wave over a distance of 20km very large amounts ofcomputing time are needed. Part of this is due to the requirement for very small time stepsbecause of a first order accuracy restriction on the standard PHOENICS time discretisation.This situation can be improved by use of higher order temporal schemes as suggested in [14].Both simulations use Cartesian grids which are attractive because they are orthogonal andcomputationally efficient. However, the stepped geometry representation of variable bottom4
athymetry (first case study) is not wholly satisfactory, so planned use of the PARSOLfeature in PHOENICS [15] should allow a much better representation of the bathymetry andbottom stresses.However, even with these changes computer times are still expected to be large and possibleconsideration needs to be given to use of an adaptive formulation which will automaticallyconcentrate more grid nodes in regions of higher flow gradients and so refine the grid arounda travelling wave while retaining a coarser grid in regions not influenced by the wave.SUMMARYA CFD model has been used to predict the propagation effects of large amplitude internalwaves. Two case studies have been described. The first in an area west of the Luzon Straitwith results compared with available data from the ONR sponsored ASIAEX and the secondfor a representative large amplitude internal wave on the Malin Shelf. In the first case, bothobservations and model indicate a transformation of wave shape from waves of depression towaves of elevation. There is encouraging agreement on the evolved shape of the predictedwave, its phase speed and the currents induced by the wave. Strong turbulence is predictedalong the sea bed beneath the wave and in the elevated waves appearing behind the leadingwave. These predicted values need verification and suitable measurement data sets are beingsought. However, even modelling in two dimensions, a large number of grid nodes and verysmall time steps are needed to enable tracking of the wave over the required distance. Thisaspect may have to be addressed by using an adaptive code. The second case is much lesssevere on computer time but has again emphasised the dispersal capability of large amplitudeinternal waves near coastlines.ACKNOWLEDGEMENTSThe author was funded by the UK Ministry of Defence as part of the Electronic SystemsResearch programme. The author would like to thank Dr Justin Small of the InternationalPacific Research Centre, Hawaii, USA for helpful discussions.REFERENCES1. Vreugdenhil C B and Koren B (Eds). Numerical methods for advection-diffusion problems.Vieweg 117-138 1993.2. Launder, B. E. & Spalding D. B., The numerical computation of turbulent flows.Computer Methods in Applied Mechanics and Engineering, 3, pp. 269-289, 1974.3. Rodi, W., Examples of calculation methods for flow and mixing in stratified fluids. J.Geophys. Res., 92, pp. 5305-5328, 1987.4. Dyer, K. R., Coastal and estuarine sediment dynamics. John Wiley and Sons, 342 pp., 19865. Luyten, P. J., Deleersnijder, E., Ozer, J., & Ruddick, K. G., Presentation of a family of turbulenceclosure models for stratified shallow water flows and preliminary application to the Rhineoutflow region. Continental Shelf Research, 16, 1, pp. 101-130, 1996.5
Page 1 and 2: Title: Some applications of PHOENIC
Page 3: profiles taken during the experimen
Page 7 and 8: Figure 1. (Top) Bathymetry of South
Page 9 and 10: Figure 3. 100m amplitude wave case.
Page 11 and 12: Figure 5. (Top)Variation of wave ph
Page 13 and 14: Figure 7. (Top) PHOENICS prediction
Page 15 and 16: Figure 9. Turbulent dissipation rat
Page 17 and 18: Figure 11. (Top) Predicted concentr
Page 19 and 20: Figure 13. Malin shelf internal wav

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