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.
Similar content being viewed by others
References
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. 4
Craig PD (1987) Solutions for internal tide generation over coastal topography. J Mar Res 45:83–105
Cummins PF, Oey L-Y (1997) Simulation of barotropic and baroclinic tides off Northern British Columbia. J Phys Oceanogr 27:762–781
Davies AM, Kwong SCM (2000) Tidal energy fluxes and dissipation on the European continental shelf. J Geophys Res 105:21,969–21,989
Davies AM, Lawrence J (1994) Modelling the non-linear interaction of wind and tide: its effect on current profiles. Inter J Numer Methods Fluids 18:163–188
Flather RA (1976) A tidal model of the north west European continental shelf. Mem Soc R Sci Liege 10:141–164
Fortunato AB, Baptista AM, Luettich RA (1997) A three-dimensional model of tidal currents in the mouth of the Tagus estuary. Cont Shelf Res 17:1689–1714
Fortunato AB, Oliviera A, Baptista AM (1999) On the effect of tidal flats on the hydrodynamics of the Tagus estuary. Oceanol Acta 22:31–44
Hall P, Davies AM (2005a) Comparison of finite difference and element models of internal tides on the Malin-Hebrides shelf. Ocean Dyn 55:272–293
Hall P, Davies AM (2005b) The influence of an irregular grid upon internal wave propagation. Ocean Model 10:193–209
Hall P, Davies AM (2005c) Effect of coastal boundary resolution and mixing upon internal wave generation and propagation in coastal regions. Ocean Dyn 55:248–271
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 23:359–372
Ip JTC, Lynch DR, Friedrichs CT (1998) Simulation of estuarine flooding and dewatering with application to Great Bay, New Hampshire. Estuar Coast Shelf Sci 47:119–141
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 26:1519–1541
Jones JE, Davies AM (2006b) On the sensitivity of computed higher tidal harmonics to mesh size in a finite element model (submitted)
Kunze E, Toole JM (1997) Tidally driven vorticity, diurnal shear, and turbulence atop Fieberling Seamount. J Phys Oceanogr 27:2663–2693
Lamb KG (2004) Non-linear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys Res Lett 31:L09313
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
Proctor R, James ID (1996) A fine-resolution 3D model of the southern North Sea. J Mar Syst 8:285–295
Samelson RM (1998) Large scale circulation with locally enhanced vertical mixing. J Phys Oceanogr 28:712–726
Sherwin TJ, Taylor NK (1989) The application of a finite difference model of internal tide generation to the NW European Shelf. Dtsch Hydrogr Z 42:151–167
Sherwin TJ, Taylor NK (1990) Numerical investigations of linear internal tide generation in the Rockall Trough. Deep Sea Res 37:1595–1618
Smagorinsky J (1963) General circulation experiments with the primitive equations I. The basic experiment. Mon Weather Rev 91:99–164
Spall MA (2001) Large scale circulations forced by localized mixing over a sloping bottom. J Phys Oceanogr 31:2369–2384
Vlasenko V, Stashchuk N, Hutter K (2005) Baroclinic tides: theoretical modeling and observational evidence. Cambridge University Press, Cambridge
Walters RA (2005) Coastal ocean models: two useful finite element methods. Cont Shelf Res 25:775–793
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
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 269–284
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 26:417–447
Xing J, Davies AM (1996b) Processes influencing the internal tide, its higher harmonics, and tidally induced mixing on the Malin-Hebrides shelf. Prog Oceanogr 38:155–204
Xing J, Davies AM (1997) The influence of wind effects upon internal tides in shelf edge regions. J Phys Oceanogr 27:205–262
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
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 31:535–577
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible editor: Phil Dyke
Rights and permissions
About this article
Cite this article
Hall, P., Davies, A.M. A three-dimensional finite-element model of wind effects upon higher harmonics of the internal tide. Ocean Dynamics 57, 305–323 (2007). https://doi.org/10.1007/s10236-007-0117-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10236-007-0117-2