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Comparison of finite difference and element models of internal tides on the Malin–Hebrides shelf

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Abstract

A three-dimensional baroclinic finite element model with a coarse and fine (i.e. local refinement along the shelf edge) grid is used to examine the influence of shelf edge grid refinement upon the internal tide generation and propagation off the west coast of Scotland. Comparisons are made with observations in the region and with a published solution using a finite difference model. The calculations show that provided that the finite element grid is refined in the internal tide generation area and the adjacent region through which the internal tide propagates, then a numerically accurate solution is obtained. In the regions of strong internal tide generation with a local grid refinement, internal wave energy can accumulate at small scales and must be removed by a scale-selective filter.

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References

  • Blumberg AF, Mellor GL (1987) A description of a three-dimensional coastal ocean circulation model, pp 1–16. In: Heaps NS (ed) Three-dimensional coastal ocean models. Coastal and Estuarine Sciences, no. 4, American Geophysical Union, Washington, DC. pp 208

  • Craig PD (1987) Solutions for internal tide generation over coastal topography. J Mar Res 45:83–105

    Article  Google Scholar 

  • Davies AM, Kwong SCM (2000) Tidal energy fluxes and dissipation on the European continental shelf. J Geophys Res 105:21,969–21,989

    Google Scholar 

  • Davies AM, Xing J (2003) On the interaction between internal tides and wind induced near inertial currents at the shelf edge. J Geophys Res , 108(C3), 3099, doi:10.1029/2002JC001375

  • Hall P, Davies AM (2005) Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions (This volume)

  • Huthnance JM (1995) Circulation, exchange and water masses at the ocean margin: the role of physical processes at the shelf edge. Prog Oceanogr 35:353–431

    Article  Google Scholar 

  • Ip JTC, Lynch DR (1995) comprehensive coastal circulation simulation using finite elements: nonlinear prognostic time-stepping model QUODDY3 users manual

  • Johns B, Dube SK, Mohanty UC, Sinha PC (1981) Numerical simulation of the surge generated by the 1977 Andhra cyclone. Q J R Meteorol Soc 107:919–934

    Article  Google Scholar 

  • Lamb KG (2004) Non-linear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys Res Lett, 31, LO9313, doi:10.1029/ 2003GLO19393

  • Legg S (2004a) Internal tides generated on a corrugated continental slope part I: cross-slope barotropic forcing. J Phys Oceanogr 34:156–173

    Article  Google Scholar 

  • Legg S (2004b) Internal tides generated on a corrugated continental slope part II: Along-slope barotropic forcing. J Phys Oceanogr 34:1824–1838

    Article  Google Scholar 

  • Luettich RA, Westerink JJ (1995) Continental shelf scale convergence studies with a barotropic tidal model. In: Lynch DR (ed) Quantitative skill assessment for coastal ocean models. A.M. Davies published American Geophysical Union, pp 349–372

  • 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 16:101–130

    Article  Google Scholar 

  • Luyten PJ, Carniel S, Umgiesser G (2002) Validation of turbulence closure parameterisations for stably stratified flows using the PROVESS turbulence measurements in the North Sea. J Sea Res 47:239–267

    Article  Google Scholar 

  • Lynch DR, Naimie CE (1993) The M2 tide and its residual on the outer banks of the Gulf of Maine. J Phys Oceanogr 23:2222–2253

    Article  Google Scholar 

  • Lynch DR, Ip JTC, Naimie CE, Werner FE (1995) Convergence studies of tidally-rectified circulation on Georges Bank. In: Lynch DR, Davies AM (ed) Quantitative skill assessment for coastal ocean models, coastal and estuarine, series 48. American Geophysical Union, Washington DC, pp 154–174

  • New AL (1988) Internal tidal mixing in the Bay of Biscay, Deep Sea Research, Part A, 35:691 –709

  • Sherwin TJ (1988) Analysis of an internal tide observed on the Malin Shelf, north of Ireland. J Phys Oceanogr 18:1035–1050

    Article  Google Scholar 

  • Sherwin TJ, Taylor NK (1990) Numerical investigations of linear internal tide generation in the Rockall Trough. Deep Sea Res 37:1595–1618

    Article  Google Scholar 

  • Smagorinsky J (1963) General circulation experiments with the primitive equations I the basic experiment. Mon Weather Rev 91:99–164

    Article  Google Scholar 

  • Walters RA (1987) A model for tides and currents in the English Channel and North Sea. Adv Water Resour 10:138–148

    Article  Google Scholar 

  • Walters RA (2005) Coastal ocean models: Two useful finite element methods. Contin Shelf Res (in press)

  • Walters RA, Werner FE (1989) A comparison of two finite element models of tidal hydrodynamics using a North Sea data set. Adv Water Resour 12:184–193

    Article  Google Scholar 

  • Werner FE (1995) A field test case for tidally forced flows: a review of the tidal flow forum. In: Lynch DR, Davies AM (ed) Quantitative skill assessment for coastal ocean models. Davies published American Geophysical Union, pp 269–284

  • Xing J, Davies AM (1997a) Formulation of a threedimensional shelf edge model and its application to internal tide generation. Cont Shelf Res 18:405–440

    Article  Google Scholar 

  • Xing J, Davies AM (1997b) The influence of wind effects upon internal tides in shelf edge regions. J Phys Oceanogr 27:205–262

    Article  Google Scholar 

  • Xing J, Davies AM (1997c) Application of a range of turbulence energy models to the computation of the internal tide. Int J Numer Meth Fluids 26:1055–1084

    Article  Google Scholar 

  • Xing J, Davies AM (1998) A three-dimensional model of internal tides on the Malin-Hebrides shelf and shelf edge. J Geophys Res 103:27821–27847

    Article  Google Scholar 

  • Xing J, Davies AM (1999) The influence of topographic features and density variations upon the internal tides in shelf edge regions. Int J Numer Meth Fluids 31:535–577

    Article  Google Scholar 

  • Xing J, Davies AM (2001a) Non-linear effects of internal tides on the generation of the tidal mean flow at the Hebrides shelf edge. Geophys Res Lett 28:3939–3942

    Article  Google Scholar 

  • Xing J, Davies AM (2001b) A three-dimensional baroclinic model of the Irish Sea : formation of thermal fronts and associated circulation. J Phys Oceanogr 31:94–114

    Article  Google Scholar 

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Acknowledgements

The authors are indebted to Mrs L. Parry for text preparation and Mr. R.A. Smith for help in finalizing the figures. Access to bottom topography, open boundary forcing and comparison data were provided by Dr. J.Xing and associated discussion with him is very much appreciated, as is access to the QUODDY code via the Web site. The use of TRIANGLE (J. Shewchuk) for part of the mesh generation processes is also gratefully acknowledged.

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  1. Proudman Oceanographic Laboratory, 6 Brownlow Street, Liverpool, L3 5DA, UK

    Philip Hall & Alan M. Davies

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  1. Philip Hall
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  2. Alan M. Davies
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Responsible Editor: Phil Dyke

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Hall, P., Davies, A.M. Comparison of finite difference and element models of internal tides on the Malin–Hebrides shelf. Ocean Dynamics 55, 272–293 (2005). https://doi.org/10.1007/s10236-005-0018-1

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