Philip Hall Proudman Oceanographic Laboratory Liverpool

1. Variability of Internal Tides in a Three-Dimensional, Baroclinic, Finite Element Model of the Shelf-Edge Philip Hall Proudman Oceanographic Laboratory Liverpool Jonsmod Silver Jubilee Edition

2. Acknowledgements: Alan Davies, Jiuxing Xing, Eric Jones, Sarah Wakelin, John Huthnance(Liverpool) ICOM team Quoddy, Adcirc, Elcirc developers Jonsmod Silver Jubilee Edition

3. Outline • Introduction • Model/grid setup • Tidal results • Influence of idealised wind stress • Conclusions • Future Directions Jonsmod Silver Jubilee Edition

4. Internal waves can be generated and propagated near the shelf-edge at relatively small length scales Models of these processes have mainly been in 2D cross-sectional form with high resolution, but more recently have started to move to 3D (eg Xing & Davies, 1998) This work uses a 3D finite element model with high spatial resolution over the shelf-edge and seamounts. After initially simulating the barotropic and baroclinic tides produced with M2 sea surface elevation forcing, the effects of uniform wind forcing has been considered. Introduction Jonsmod Silver Jubilee Edition

5. Finite element mesh of the Hebridean Shelf edge region (12W-4W, 55N-59N), with 2894 nodes Jonsmod Silver Jubilee Edition

6. Model Details • QUODDY (e.g. Lynch & Naimie, 1993) • Finite element, baroclinic (prognostic), sigma coordinate, internal pressure gradients calculated on z-levels. • Initial conditions: Zero motion, zero elevation, zero horizontal density gradient, prescribed vertical density gradient based on data from the area and consistent with Xing & Davies (1998). • Also tried this case with Elcirc (z-level, finite volume model) Jonsmod Silver Jubilee Edition

7. Model Details • Boundary conditions: M2 tidal forcing for elevation, relaxation to initial conditions for density at the open boundaries. • Wind forcing ramping up from zero to a constant value in the chosen direction. • Grid with resolution aimed at giving good results at the shelf-edge and over seamounts. Jonsmod Silver Jubilee Edition

8. Finite element mesh of the Hebridean Shelf edge region (12W-4W, 55N-59N), with 2894 nodes

9. Finite element mesh of the Hebridean Shelf edge region (12W-4W, 55N-59N), with 3981 nodes

10. Barotropic model results can be tested against tide gauge data and current meter data analyses • The results are good with rms errors about 4cm/s from 45 current meter stations • Baroclinic results are not as easy to test due to changes in stratification, wind conditions, between instrument deployments • Test against established models, theory, or get better data sets Jonsmod Silver Jubilee Edition

11. Model vs obs m2 Jonsmod Silver Jubilee Edition

12. Results from Xing & Davies (1998) Jonsmod Silver Jubilee Edition

13. Baroclinic M2 cross-slope velocity amplitude Jonsmod Silver Jubilee Edition

14. Addition of wind forcing • With wind forcing added, is the internal tide field changed? • Sub-harmonics? • Upwelling/downwelling-favourable wind? Jonsmod Silver Jubilee Edition

15. Changes in M2, M4, M6 cross-slope baroclinic velocity amplitude due to a 0.2Pa wind Jonsmod Silver Jubilee Edition

16. Temperature change at 200m due to wind forcingh i Jonsmod Silver Jubilee Edition

17. Conclusions Increased resolution at the shelf break in order to study the processes there in detail make the use of unstructured grid models in 3D desirable. A 3D, baroclinic, finite element model has been successfully used to study internal waves at the shelf-edge, and extended to consider the influence of wind forcing. The changes to the density structure brought about by upwelling or downwelling as a result of wind forcing influence the distribution of the internal tides. To validate an internal tide model, detailed and simultaneous observations are required of density, velocity, meteorological forcing (plus detailed bathymetry). Jonsmod Silver Jubilee Edition

18. Progression of modelling We have gone from modelling idealised basins using grid compression within a traditional finite difference model, to 2D barotropic tidal simulation with finite element and finite volume models, to 3D internal tide simulation at the shelf edge, with wind forcing. Now looking to more formally compare the models that have been applied as well as to include ICOM (Imperial College Ocean Model) which is a fully-unstructured, non-hydrostatic, adaptive mesh model. Jonsmod Silver Jubilee Edition

19. Progression of modelling • We would also like to use data from a deployment at the Faeroe-Shetland Channel to test the internal tidal models. Jonsmod Silver Jubilee Edition

20. Track of F. S. Poseidon cruise 328 6-25 September 2005 Jonsmod Silver Jubilee Edition

21. Area of study:Circulation through the Faroe-Shetland Channel Jonsmod Silver Jubilee Edition (Hosegood et al., 2005)

22. Moorings Jonsmod Silver Jubilee Edition

23. Area of study with CTD sections NE transect Centre transect SW transect 24-hour timeseries Jonsmod Silver Jubilee Edition Bathymetry from Smith and Sandwell (1997)

24. SW transect  Potential temperature (°C) Salinity (PSU)  Jonsmod Silver Jubilee Edition

25. Courtesy of Sarah Wakelin Jonsmod Silver Jubilee Edition

26. Self-Adaptive Unstructured-Grid Modelling • In order to allow the numerical model results to determine where the grid should be finer/coarser an attempt has been made to incorporate a separate ‘module’ to the existing QUODDY code and the grid generation software that had been developed in the preceding work. • This code takes the results from the model and generates a new (improved?) mesh and then continues the model run from interpolated data Jonsmod Silver Jubilee Edition

27. Overview of method used for adapting grid • An initial grid and boundary conditions are used to produce results from a cold-start. • The model is run for N tidal cycles (e.g. N=1) • Results are saved at pre-determined intervals (e.g. hourly) and at the end of each run in the form of the usual ‘hot-start’ file. • Results are processed to determine regions of higher and lower variability of the variables on the old grid (the chosen criteria can be changed during the series of runs) • A new mesh is produced and the old ‘hot-start’ file, boundary conditions, bathymetry, etc, are interpolated onto the new mesh • Other setup files and program files (containing array bounds) are modified before recompilation and continuing the model from the ‘hot-start’ file Jonsmod Silver Jubilee Edition

28. Mesh adapting every tidal period Jonsmod Silver Jubilee Edition

29. Flow past a cylinder with ICOM Jonsmod Silver Jubilee Edition

30. Trial and Retribution Jonsmod Silver Jubilee Edition

31. ICOM • Imperial College Ocean Model (ICOM) • Finite elements • Fully unstructured • Adaptive mesh • Non-hydrostatic • Parallelised • Data assimilation • Is to be made generally available (Gnu PL) • Rapidly developing Jonsmod Silver Jubilee Edition

32. TELEMACEQUIVALENTTOWC+FREISM Jonsmod Silver Jubilee Edition

33. Jonsmod Silver Jubilee Edition