# Tidal Models for the Nordic Seas

Department of Mathematics, University of Oslo.

For several years a group at Mechanics Division, Department of Mathematics, has been engaged in modelling tides in the Nordic Seas and the continental shelf around Norway. The group, lead by professor Bjørn Gjevik , has been supported by the Norwegian Research Council and the oil industry, primarily Statoil, through several contracts.

First a large scale model covering the Norwegian Sea, Barents Sea and the Arctic Ocean with grid resolution from 50 to 12.5 km, was developed. The results of the model simulations have been compared extensively with observations and documented in publications (ref. 2-4 and 7).

More recently high resolution models have been developed for sections of the Norwegian continental shelf and coastal waters; Haltenbanken and the coast of western Norway from Statt to Brønnøysund with 0.5 km resolution, inner Oslofjord with 0.1 km resolution and the area around Bear Island in the Barents Sea with about 1.5 km resolution.

## Depth matrices

Several depth matrices with different grid resolution have been compiled. Two illustrative examples are included here.

Norwegian Sea (12.5 km resolution)

Haltenbanken (0.5 km resolution)

## Animation of sea level variations

Based on model simulations (ref. 1--3) we have produced the following animation of sea level changes associated with the M2-tide in the Nordic Seas. On the movie, the tidal wave entering from the North Atlantic between Scotland and Iceland is clearly seen. This wave splits north of Scotland in a wave propagating southward into the North Sea, while the main part propagates northward along the coast of Norway into the Barents Sea and the Arctic Ocean. (Animation by Elen Dybesland).

## Animation of tidal currents

In the deep ocean of the Norwegian Sea tidal currents are normally small and of the order 1 cm/s. In coastal waters tidal currents of the order of 1 m/s are common, with extreme strong currents in some cases. The Maelstrom in the Lofoten Islands in northern Norway is one famous example. The first movie included below shows the M2-tidal current in the Drøbak Sound, a bottle neck of the Oslofjord, controlling the exchange of water masses between the inner and outer part of the fjord. The second example, included here, shows the the M2-tidal current in Trondheimsleia on the west coast of Norway. We have also made similar animations of the oscillating tidal current for other locations along the Norwegian coast and in the Barents Sea. (H. Moe and B. Gjevik).

## Tidal data from model

Model data with harmonic constants for sea level and current are available for the four dominant constituents M2, S2, N2 and K1 with 25 km grid resolution. Parts of this data set were published as tables and plots in "Atlas of tides on on the shelves of the Norwegian and the Barents Seas" (ref 4).

## Tidal Predictions for the Norwegian Sea

On the next page, a tidal prediction services is made available for selected stations along the Norwegian coasts and continental shelf. You may choose day and location and thereby obtain plot of the sea level variation for the day choosen.

## Publications

1. E. Nøst, (1988) "Simulering av tidevannet på Haltenbanken" Cand scient thesis, Department of Mathematics, University of Oslo (In Norwegian).

2. B. Gjevik and T. Straume, (1989) Model simulation of the M2 and the K1 tide in the Nordic Seas and the Arctic ocean". Tellus 41A, 73--96.

3. B. Gjevik (1990) Model simulations of tides and shelf waves along the shelves of the Norwegian-Greenland-Barents Seas". Modelling Marine Systems, Vol. I p. 187--219 Ed. A.M. Davies CRC Press Inc., Boca Raton, Forida.

4. B. Gjevik, E. Nøst and T. Straume, (1990) Atlas of the tides on the shelves of the Norwegian and the Barents Seas". Report FoU-ST 90012, pp. 74, Statoil, Stavanger, Norway.

5. B. Gjevik, (1991) Tidal amplitudes and currents along the Europipe track". Report, Dept. of Math., Univ. of Oslo.

6. B. Gjevik, O. Høvik and H. Moe, (1992) Simulering av tidevannet i kystområdet innenfor Haltenbanken'' Report Dept. of Math., Univ. of Oslo to Statoil. 15 Nov 1992.

7. B. Gjevik, E. Nøst and T. Straume, (1994) Model simulations of the tides in the Barents Sea'' J. Geophysical Res., Vol 99, No C2, pp 3337--3350.

8. O. Høvik, (1993) "Simulering av tidevannet i kystområder" Cand scient thesis, Department of Mathematics, University of Oslo (In Norwegian).

9. E. Nøst, (1994) Calculating tidal current profiles from vertically integrated models near the critical latitude in the Barents Sea'' J. Geophysical Res., Vol 99, No C4, pp 7885--7901.

10. E. Nøst, (1994) Tidal currents near the critical latitude in the Barents Sea'' Dr.scient thesis, Department of Mathematics, University of Oslo.

11. T. Straume, J. H. Nilsen, T. A. McClimans, and B. Gjevik (1994) Circulation around Bear Island in the Barents Sea: Numerical and Laboratory Simulations'' Annales Geophysicae, Suppl. II to Vol.12 , C277 (Abstract).

12. B. Gjevik, (1996) Models of drift and dispersion in tidal flows'' In Waves and Non-linear Processes in Hydrodynamics. Eds. J. Grue, B. Gjevik and J. E. Weber. Kluwer Academic Publishers.

13. B. Gjevik, H. Moe and A. Ommundsen (1997) Sources of the Maelstrom ''
Nature, Vol. 388, 28 Aug. 1997, pp. 837-838. \item (with D.~Hareide)

14. B. Gjevik og D. Hareide Ekstrem vannstandsendring og strøm i Oslofjorden natten mellom 3. og 4.desember 1999''. Accepted for publication in Naturen (Norwegian journal), 2000. Manuscript available: postscript (2.3 Mb), pdf-format (231 kb).

15. H. Moe, A. Ommundsen and B. Gjevik A high resolution tidal model for the area around The Lofoten Islands, northern Norway'' Preprint Series Dept. Mathematics, University of Oslo, 2000. Submitted to Continental Shelf Research.

16. H. Moe, B. Gjevik and A. Ommundsen) A high resolution tidal model for the coast of Møre and Trøndelag, western Norway'' Preprint Series Dept. Mathematics, University of Oslo, 2000.

author: Bjørn Gjevik <bjorng@math.uio.no>