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Ocean Dynamics

, Volume 60, Issue 4, pp 907–920 | Cite as

Numerical studies of dispersion due to tidal flow through Moskstraumen, northern Norway

  • Birgit Kjoss Lynge
  • Jarle Berntsen
  • Bjørn Gjevik
Article

Abstract

The effect of horizontal grid resolution on the horizontal relative dispersion of particle pairs has been investigated on a short time scale, i.e. one tidal M 2 cycle. Of particular interest is the tidal effect on dispersion and transports in coastal waters where small-scale flow features are important. A three-dimensional ocean model has been applied to simulate the tidal flow through the Moskstraumen Maelstrom outside Lofoten in northern Norway, well known for its strong current and whirlpools (Gjevik et al., Nature 388(6645):837–838, 1997; Moe et al., Cont Shelf Res 22(3):485–504, 2002). Simulations with spatial resolution down to 50 m have been carried out. Lagrangian tracers were passively advected with the flow, and Lyapunov exponents and power law exponents have been calculated to analyse the separation statistics. It is found that the relative dispersion of particles on a short time scale (12–24 h) is very sensitive to the grid size and that the spatial variability is also very large, ranging from 0 to 100 km2 over a distance of 100 m. This means that models for prediction of transport and dispersion of oil spills, fish eggs, sea lice etc. using a single diffusion coefficient will be of limited value, unless the models actually resolves the small-scale eddies of the tidal current.

Keywords

Relative dispersion Grid resolution Tidal current Whirlpool Particle tracking Lyapunov 

Notes

Acknowledgements

This work was partly supported by the Research Council of Norway. The Norwegian Hydrographic Service, Stavanger, has provided us with a high-resolution depth matrix.

References

  1. Aadlandsvik B (1994) Modelling the transport of cod larvae from the Lofoten area. ICES Mar Sci Symp 198:379–392Google Scholar
  2. Afanasyev YD, Peltier WR (2001a) On breaking internal waves over the sill in knight inlet. Proc R Soc Lond 457:2799–2825CrossRefGoogle Scholar
  3. Afanasyev YD, Peltier WR (2001b) Reply to comment on the paper on breaking internal waves over the sill in knight inlet. Proc R Soc Lond 457:2831–2834CrossRefGoogle Scholar
  4. Aldridge JN, Davies AM (1993) A high-resolution three-dimensional hydrodynamic tidal model of the Eastern Irish Sea. ICES Mar Sci Symp 23(2):207–224Google Scholar
  5. Amundrud TL, Murray AG (2009) Modelling sea lice dispersion under varying environmental forcing in a Scottish sea loch. J Fish Dis 32(1):27–44CrossRefGoogle Scholar
  6. Berntsen J (2000) Users guide for a modesplit σ-coordinate numerical ocean model. Technical report, Technical Report 135, Dept of Applied Mathematics, University of Bergen, Johs. Bruns gt.12, N-5008. Bergen, Norway, p 48Google Scholar
  7. Berntsen J, Xing JX, Davies AM (2008) Numerical studies of internal waves at a sill: sensitivity to horizontal grid size and subgrid scale closure. Cont Shelf Res 28(10–11):1376–1393CrossRefGoogle Scholar
  8. Berntsen J, Xing JX, Davies AM (2009) Numerical studies of flow over a sill: sensitivity of the non-hydrostatic effects to the grid size. Ocean Dyn 59(6):1043–1059CrossRefGoogle Scholar
  9. Berntsen H, Kowalik Z, S\(\ae\)lid S, Sørli K (1981) Efficient numerical-simulation of ocean hydrodynamics by a splitting procedure. Model Identif Control 2(4):181–199Google Scholar
  10. Blumberg AF, Mellor GL (1987) A description of a three-dimensional coastal ocean circulation model. In: Heaps NS (ed) Coastal and estuarine sciences, vol 4. Three-dimensional coastal ocean models. Xi+208p. American Geophysical Union, Washington, D.C. Illus, pp 1–16Google Scholar
  11. Burchard H, Rennau H (2008) Comparative quantification of physically and numerically induced mixing in ocean models. Ocean Model 20(3):293–311CrossRefGoogle Scholar
  12. Cummins PF, Vagle S, Armi L, Farmer D (2003) Stratified flow over topography: upstream influence and generation of nonlinear waves. Proc R Soc Lond 459:1467–1487CrossRefGoogle Scholar
  13. Davies AM, Jones JE (1996) Sensitivity of tidal bed stress distributions, near-bed currents, overtides, and tidal residuals to frictional effects in the Eastern Irish Sea. J Phys Oceanogr 26(12):2553–2575CrossRefGoogle Scholar
  14. Davies AM, Xing J (2007) On the influence of stratification and tidal forcing upon mixing in sill regions. Ocean Dyn 57:431–451CrossRefGoogle Scholar
  15. Davies AM, Kwong SCM, Flather RA (2000) On determining the role of wind wave turbulence and grid resolution upon computed storm driven currents. Cont Shelf Re 20(14):1825–1888CrossRefGoogle Scholar
  16. Engedahl H, Aadlandsvik B, Martinsen EA (1998) Production of monthly mean climatological archives for the Nordic Seas. J Mar Syst 14(1–2):1–26CrossRefGoogle Scholar
  17. Farmer DM, Freeland HJ (1983) The physical oceanography of fjords. Prog Oceanogr 12:147–220CrossRefGoogle Scholar
  18. Farmer DM, Armi L (1999) Stratified flow over topography: the role of small-scale entrainment and mixing in flow establishment. Proc R Soc Lond 455:3221–3258CrossRefGoogle Scholar
  19. Farmer DM, Armi L (2001) Stratified flow over topography: models versus observations. Proc R Soc Lond 457:2827–2830CrossRefGoogle Scholar
  20. Geyer WR, Signell RP (1992) A reassessment of the role of tidal dispersion in estuaries and bays. Estuaries 15(2):97–108CrossRefGoogle Scholar
  21. Gillibrand PA Willis KJ (2007) Dispersal of sea louse larvae from salmon farms: modelling the influence of environmental conditions and larval behaviour. Aquat Biol 1(1):63–75Google Scholar
  22. Gjevik B (1996) Models of drift and dispersion in tidal flows. In: Grue J et al (eds) Waves and nonlinear processes in hydrodynamics, 34. Kluwer Academic, Dordrecht, pp 343–354Google Scholar
  23. Gjevik B, Moe H, Ommundsen A (1997) Sources of the maelstrom. Nature 388(6645):837–838CrossRefGoogle Scholar
  24. Haidvogel D, Beckmann A (1999) Numerical ocean circulation modeling. Series on environmental science and management, vol 2. Imperial College Press, London, p 318Google Scholar
  25. Haney RL (1991) On the pressure-gradient force over steep topography in sigma coordinate ocean models. J Phys Oceanor 21(4):610–619CrossRefGoogle Scholar
  26. Haza AC, Griffa A, Martin P, Molcard A, Ozgokmen TM, Poje AC, Barbanti R, Book JW, Poulain PM, Rixen M, Zanasca P (2007) Model-based directed drifter launches in the Adriatic Sea: results from the dart experiment. Geophys Res Lett 34(10)Google Scholar
  27. Inall M, Cottier F, Griffiths C, Rippeth T (2004) Sill dynamics and energy transformation in a jet fjord. Ocean Dyn 54:307–314CrossRefGoogle Scholar
  28. Inall M, Rippeth T, Griffiths C, Wiles P (2005) Evolution and distribution of TKE production and dissipation within stratified flow over topography. Geophys Res Lett 32:L08607. doi: 10.1029/2004GL022289 CrossRefGoogle Scholar
  29. Jones JE, Davies AM (2008) On the modification of tides in shallow water regions by wind effects. J Geophys Res Ocean 113(C5):C05014. doi: 10.1029/2007JC004310 CrossRefGoogle Scholar
  30. Klymak JM, Gregg MC (2001) Three-dimensional nature of flow near a sill. J Geophys Res 106:22295–22311CrossRefGoogle Scholar
  31. Klymak JM, Gregg MC (2003) The role of upstream waves and a downstream density pool in the growth of lee waves: stratified flow over the knight inlet sill. J Phys Oceanogr 33:1446–1461CrossRefGoogle Scholar
  32. Klymak JM, Gregg MC (2004) Tidally generated turbulence over the knight inlet sill. J Phys Oceanogr 34:1135–1151CrossRefGoogle Scholar
  33. Kowalik Z, Murty TS (1993) Numerical modeling of ocean dynamics. Advanced series on ocean engineering, vol 5. World Scientific, SingaporeGoogle Scholar
  34. LaCasce JH (2008) Statistics from Lagrangian observations. Prog Oceanogr 77(1):1–29CrossRefGoogle Scholar
  35. Lamb KG (2004) On boundary-layer separation and internal wave generation at the knight inlet sill. Proc R Soc Lond 460:2305–2337CrossRefGoogle Scholar
  36. Martinsen EA, Engedahl H (1987) Implementation and testing of a lateral boundary scheme as an open boundary-condition in a barotropic ocean model. Coast Eng 11(5–6):603–627CrossRefGoogle Scholar
  37. Mellor G (1996) User guide for three-dimensional, primitive equation, numerical ocean model. Technical report, Technical report, Princeton University.Google Scholar
  38. Mellor GL, Yamada T (1982) Development of a turbulence closure-model for geophysical fluid problems. Rev Geophys 20:851–875CrossRefGoogle Scholar
  39. Mellor GL, Oey LY, Ezer T (1998) Sigma coordinate pressure gradient errors and the seamount problem. J Atmos Ocean Technol 15(5):1122–1131CrossRefGoogle Scholar
  40. Mitchelson-Jacob G, Sundby S (2001) Eddies of Vestfjorden, Norway. Cont Shelf Res 21(16–17):1901–1918CrossRefGoogle Scholar
  41. Moe H, Ommundsen A, Gjevik B (2002) A high resolution tidal model for the area around the Lofoten Islands, northern Norway. Cont Shelf Res 22(3):485–504CrossRefGoogle Scholar
  42. Ommundsen A (2002) Models of cross shelf transport introduced by the Lofoten Maelstrom. Cont Shelf Res 22(1):93–113CrossRefGoogle Scholar
  43. Orre S, Gjevik B, Lacasce JH (2006) Characterizing chaotic dispersion in a coastal tidal model. Cont Shelf Res 26(12–13):1360–1374CrossRefGoogle Scholar
  44. Poje AC, Haza AC, Özgökmen TM, Magaldi MG, and Garraffo ZD (2010) Resolution dependent relative dispersion statistics in a hierarchy of ocean models. Ocean Model 31(1–2):36–50CrossRefGoogle Scholar
  45. Proctor R, Elliot AJ, Flather RA (1994) Forecast and hindcast simulations of the Braer oil-spill. Mar Pollut Bull 28(4):219–229CrossRefGoogle Scholar
  46. Reed M, Ekrol N, Rye H, Turner L (1999a) Oil spill contingency and response (Oscar) analysis in support of environmental impact assessment offshore Namibia. Spill Sci Technol Bull 5(1):29–38CrossRefGoogle Scholar
  47. Reed M, Johansen O, Brandvik PJ, Daling P, Lewis A, Fiocco R, Mackay D, Prentki R (1999b) Oil spill modeling towards the close of the 20th century: overview of the state of the art. Spill Sci Technol Bull 5(1):3–16CrossRefGoogle Scholar
  48. Rennau H, Burchard H (2009) Quantitative analysis of numerically induced mixing in a coastal model application. Ocean Dyn 59(5):671–687CrossRefGoogle Scholar
  49. Ridderinkhof H, Zimmerman JTF (1992) Chaotic stirring in a tidal system. Science 258(5085):1107–1111CrossRefGoogle Scholar
  50. Signell RP, Geyer WR (1991) Transient eddy formation around headlands. J Geophys Oceans 96(C2):2561–2575CrossRefGoogle Scholar
  51. Signell RP, Butman B (1992) Modeling tidal exchange and dispersion in Boston Harbor. J Geophys Oceans 97(C10):15591–15606CrossRefGoogle Scholar
  52. Skar\(\eth\)hamar J, Slagstad D, Edvardsen A (2007) Plankton distributions related to hydrography and circulation dynamics on a narrow continental shelf off northern Norway. Estuar Coast Shelf Sci 75(3):381–392CrossRefGoogle Scholar
  53. Slagstad D, Tande KS, (2007) Structure and resilience of overwintering habitats of Calanus finmarchicus in the Eastern Norwegian Sea. Deep-Sea Res Part II Top Stud Oceanogr 54(23–26):2702–2715CrossRefGoogle Scholar
  54. Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91(3):99–164CrossRefGoogle Scholar
  55. Stashchuk N, Inall M, Vlasenko V (2007) Analysis of supercritical stratified tidal flow in a Scottish fjord. J Phys Oceanogr 37:1793–1810CrossRefGoogle Scholar
  56. Thorpe SA (2005) The turbulent ocean. Cambridge University Press, CambridgeGoogle Scholar
  57. Vikebø F, Jorgensen C, Kristiansen T, Fiksen O (2007) Drift, growth, and survival of larval Northeast Arctic cod with simple rules of behaviour. Mar Ecol Prog Ser 347:207–219CrossRefGoogle Scholar
  58. Vlasenko VI, Stashchuk N, Hutter K (2005) Baroclinic tides: theoretical modeling and observational evidence. Cambridge monographs on mechanics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  59. Wahl T (1995) The Maelström seen from space. Nord Space Act 2–3:22–23Google Scholar
  60. Xing J, Davies A (2006a) Processes influencing tidal mixing in the region of sills. Geophys Res Lett 33(4):L04603. doi: 10.1029/2005GL025226 CrossRefGoogle Scholar
  61. Xing JX, Davies AM (2006b) Influence of stratification and topography upon internal wave spectra in the region of sills. Geophys Res Lett 33(23):L23606. doi: 10.1029/2006GL028092 CrossRefGoogle Scholar
  62. Xing JX, Davies AM, (2007) On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions. Cont Shelf Res 27:2162–2185CrossRefGoogle Scholar
  63. Yang HQ, Przekwas AJ (1992) A comparative-study of advanced shock-capturing schemes applied to Burgers-equation. J Comput Phys 102(1):139–159CrossRefGoogle Scholar
  64. Zimmerman JTF (1986) The tidal whirlpool—a review of horizontal dispersion by tidal and residual currents. Neth J Sea Res 20(2–3):133–154CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Birgit Kjoss Lynge
    • 1
  • Jarle Berntsen
    • 2
  • Bjørn Gjevik
    • 3
  1. 1.Norwegian Hydrographic ServiceStavangerNorway
  2. 2.Department of MathematicsUniversity of BergenBergenNorway
  3. 3.Department of MathematicsUniversity of OsloOsloNorway

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