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Ocean Dynamics

, Volume 57, Issue 4–5, pp 305–323 | Cite as

A three-dimensional finite-element model of wind effects upon higher harmonics of the internal tide

  • Philip Hall
  • Alan M. Davies
Article

Abstract

A non-linear three-dimensional unstructured grid model of the M2 tide in the shelf edge area off the west coast of Scotland is used to examine the spatial distribution of the M2 internal tide and its higher harmonics in the region. In addition, the spatial variability of the tidally induced turbulent kinetic energy and associated mixing in the area are considered. Initial calculations involve only tidal forcing, although subsequent calculations are performed with up-welling and down-welling favourable winds to examine how these influence the tidal distribution (particularly the higher harmonics) and mixing in the region. Both short- and long-duration winds are used in these calculations. Tidal calculations show that there is significant small-scale spatial variability particularly in the higher harmonics of the internal tide in the region. In addition, turbulence energy and mixing exhibit appreciable spatial variability in regions of rapidly changing topography, with increased mixing occurring above seamounts. Wind effects significantly change the distribution of the M2 internal tide and its higher harmonics, with appreciable differences found between up- and down-welling winds and long- and short-duration winds because of differences in mixing and the presence of wind-induced flows. The implications for model validation, particularly in terms of energy transfer to higher harmonics, and mixing are briefly discussed.

Keywords

Finite-element model Wind effects Internal tide 

Notes

Acknowledgements

The authors are indebted to Mrs. L. Parry for typing the paper and Mr. R.A. Smith for help in figure production. Access to bottom topography and open boundary forcing were provided by Dr. J. Xing and are gratefully acknowledged. Access to the QUODDY code via the website is much appreciated.

References

  1. Blumberg AF, Mellor GL (1987) A description of a three-dimensional coastal ocean circulation model. In: Heaps NS (ed) Three-dimensional coastal ocean models. American Geophysical Union, Washington, DC, pp 1–16 Coastal and Estuarine Sciences, No. 4Google Scholar
  2. Craig PD (1987) Solutions for internal tide generation over coastal topography. J Mar Res 45:83–105CrossRefGoogle Scholar
  3. Cummins PF, Oey L-Y (1997) Simulation of barotropic and baroclinic tides off Northern British Columbia. J Phys Oceanogr 27:762–781CrossRefGoogle Scholar
  4. Davies AM, Kwong SCM (2000) Tidal energy fluxes and dissipation on the European continental shelf. J Geophys Res 105:21,969–21,989Google Scholar
  5. Davies AM, Lawrence J (1994) Modelling the non-linear interaction of wind and tide: its effect on current profiles. Inter J Numer Methods Fluids 18:163–188CrossRefGoogle Scholar
  6. Flather RA (1976) A tidal model of the north west European continental shelf. Mem Soc R Sci Liege 10:141–164Google Scholar
  7. Fortunato AB, Baptista AM, Luettich RA (1997) A three-dimensional model of tidal currents in the mouth of the Tagus estuary. Cont Shelf Res 17:1689–1714CrossRefGoogle Scholar
  8. Fortunato AB, Oliviera A, Baptista AM (1999) On the effect of tidal flats on the hydrodynamics of the Tagus estuary. Oceanol Acta 22:31–44CrossRefGoogle Scholar
  9. Hall P, Davies AM (2005a) Comparison of finite difference and element models of internal tides on the Malin-Hebrides shelf. Ocean Dyn 55:272–293CrossRefGoogle Scholar
  10. Hall P, Davies AM (2005b) The influence of an irregular grid upon internal wave propagation. Ocean Model 10:193–209CrossRefGoogle Scholar
  11. Hall P, Davies AM (2005c) Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions. Ocean Dyn 55:248–271CrossRefGoogle Scholar
  12. Heniche M, Secretin Y, Boudreau P, Leclerc M (2000) A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries. Adv Water Resour 23:359–372CrossRefGoogle Scholar
  13. Ip JTC, Lynch DR, Friedrichs CT (1998) Simulation of estuarine flooding and dewatering with application to Great Bay, New Hampshire. Estuar Coast Shelf Sci 47:119–141CrossRefGoogle Scholar
  14. Jones JE, Davies AM (2006a) Application of a finite element model (TELEMAC) to computing the wind induced response of the Irish Sea. Cont Shelf Res 26:1519–1541CrossRefGoogle Scholar
  15. Jones JE, Davies AM (2006b) On the sensitivity of computed higher tidal harmonics to mesh size in a finite element model (submitted)Google Scholar
  16. Kunze E, Toole JM (1997) Tidally driven vorticity, diurnal shear, and turbulence atop Fieberling Seamount. J Phys Oceanogr 27:2663–2693CrossRefGoogle Scholar
  17. Lamb KG (2004) Non-linear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys Res Lett 31:L09313CrossRefGoogle Scholar
  18. Luyten PJ, Deleersnijder E, Ozer J, Ruddick KG (1996) Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the Rhine outflow region. Cont Shelf Res 16:101–130CrossRefGoogle Scholar
  19. Proctor R, James ID (1996) A fine-resolution 3D model of the southern North Sea. J Mar Syst 8:285–295CrossRefGoogle Scholar
  20. Samelson RM (1998) Large scale circulation with locally enhanced vertical mixing. J Phys Oceanogr 28:712–726CrossRefGoogle Scholar
  21. Sherwin TJ, Taylor NK (1989) The application of a finite difference model of internal tide generation to the NW European Shelf. Dtsch Hydrogr Z 42:151–167CrossRefGoogle Scholar
  22. Sherwin TJ, Taylor NK (1990) Numerical investigations of linear internal tide generation in the Rockall Trough. Deep Sea Res 37:1595–1618CrossRefGoogle Scholar
  23. Smagorinsky J (1963) General circulation experiments with the primitive equations I. The basic experiment. Mon Weather Rev 91:99–164CrossRefGoogle Scholar
  24. Spall MA (2001) Large scale circulations forced by localized mixing over a sloping bottom. J Phys Oceanogr 31:2369–2384CrossRefGoogle Scholar
  25. Vlasenko V, Stashchuk N, Hutter K (2005) Baroclinic tides: theoretical modeling and observational evidence. Cambridge University Press, CambridgeGoogle Scholar
  26. Walters RA (2005) Coastal ocean models: two useful finite element methods. Cont Shelf Res 25:775–793CrossRefGoogle Scholar
  27. Walters RA, Werner FE (1989) A comparison of two finite element models of tidal hydrodynamics using a North Sea data set. Adv Water Resour 12:184–193CrossRefGoogle Scholar
  28. Werner FE (1995) A field test case for tidally forced flows: a review of the tidal flow forum. In: Lynch DR, Davies AM (eds) Quantitative skill assessment for coastal ocean models. American Geophysical Union, Washington, DC, pp 269–284Google Scholar
  29. Xing J, Davies AM (1996a) Application of turbulence energy models to the computation of tidal currents and mixing intensities in shelf edge regions. J Phys Oceanogr 26:417–447CrossRefGoogle Scholar
  30. Xing J, Davies AM (1996b) Processes influencing the internal tide, its higher harmonics, and tidally induced mixing on the Malin-Hebrides shelf. Prog Oceanogr 38:155–204CrossRefGoogle Scholar
  31. Xing J, Davies AM (1997) The influence of wind effects upon internal tides in shelf edge regions. J Phys Oceanogr 27:205–262CrossRefGoogle Scholar
  32. Xing J, Davies AM (1998) A three-dimensional model of internal tides on the Malin-Hebrides shelf and shelf edge. J Geophys Res 103:27821–27847CrossRefGoogle Scholar
  33. Xing J, Davies AM (1999) The influence of topographic features and density variations upon the internal tides in shelf edge regions. Int J Numer Methods Fluids 31:535–577CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Proudman Oceanographic LaboratoryLiverpoolUK

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