This paper not to be cited without prior reference to the authors.

Transcription

1 e.. This paper not to be cited without prior reference to the authors. nternational Council for the exploration of the Sea C. M C : 17 Hydrography Committee "Some model studies on the dynamics of the transition area between the North Sea and the Baltic" Sylvin Müller-Navarra Deutsches Hydrographisches nstitut Bernhard-Nocht-Straße Hamburg 4 Dr. Jan Backhaus nstitut für Meereskunde Universität Hamburg Heimhuder Straße Hamburg 13 Abstract A vertically integrated (a) and a three-dimensional model (b) were applied to.study some features of the dynamics in the Kattegat, the Belt Sea, and the western Baltic. The spatial resolution of both models is three nautical miles, model b involves four compulational planes in the vertical. Barotropic tides and a storm-surge event were simulated by means of model a, whereas for selected wind-induced cases, and for the density-driven estuarine circulation model b was applied. The matching with observational data andor with flow-interpretations of other authors is discussed. Their promising results in combination with a high "simulationspeed" qualify the models for further detailed studies, especially for long term simulations.

2 - 2-2 Computations Three different numerical mod~ls [two-dimensional explicit (2 Ex), two-dimensional implicit (2 m), three-dimensional implicit (3 m)] of the transition area were used to compute a number of problems (table 1): Table 1: model open boundary condition 2 Ex 2 m 3 m for water, elevation water elevations t at the open Storm surge, boundaries were Tides ( taken from a r1 2, M 4,... ) GMT North Sea-Baltic! GMT), fig. 3, 4 model fig. 6, 7 (fig.2, Hewer 1983)! barotropic barotropic ;; = 0 wind-driven wind-driven circulation circulation i ---l ;; = 1;;( 0) ; 00= R+P-E = fresh water 0 surplus R = river inflow p = precipitation E = evaporation _.._----- f-., A) "baroclinie" circulation (July, December). B) "baroclinie" and winddriven circulation

3 - 3-3 Model characteristics The hydrodynamical equations include non-linear terms as advective terms and bottom friction. Both, the two-dimensional and the three-dimensional model grid cover the Kattegat, the Belt Sea and the Sound area and have aresolution of 3' latitude and 5' longitude (0 (5000 m)) (fig. 1). The three-dimensional model has four layers in the vertical (s - 10 m, m, m, 30 m - bottom)j hydrostatic pressure distribution and the Boussinesq-approximation are incorporated.

4 - 4-4 Results a) Computation of barotropic lunar tides (M, M,... ): ~ Boundary values of water elevations at the northern open boundary near Skagen and the eastern open boundary near Cap Arcona were computed by means of a model (Hewer, 1983), driven by the M 2 -tide. North Sea-Baltic After computing 20 periods with the Kattegat-Belt Sea-Sound model time series at each s-point had been Fourier-analysed. The plotted co-range and co-tidal lines for the M -tide are 2 shown in figures.3 and 4. They are in good agreement with figure 5 (Svansson, 1972). n the western part of the Kattegat, a very shallow area, the amplitudes are too small in comparison with figure 5. The depth mean tidal velocities in the open waters are in the range of 0-5 cms. n the Danish straits they reach 25 cms. The windstresses at the interface of North Sea-Baltic and the atmosphere (fig. 2) were calculated from weather-charts.. (Duun-Christensen, 1975); Smith, Banke, 1975). Again boundary values for the Kattegat-Belt Sea-Sound model were computed by the overall North Sea-Baltic model. comparison of computed storm surge and observed values shows good results (fig. 6) 17 cm). The (on the average the rms-error is about The calculated seawater exchange (Q) during the computed storm surge period shows how multifarious the exchange of seawater between North Sea and Baltic come to pass. Only 36 hours of the period the volume transport in the Belts and Sound are uniform. Dur'ing til.ls e~ent about n~3s seawater enter the Baltic. the

5 - 5 - c) Computation of the "estuarine", density-driven circulation: The quotation marks "baroclinic" (table 1) indicate that in the calculations the change in time of the density is neglected but that the spatial variations are taken into consideration. The fresh water surplus (in July m 3 s) of the Baltic Sea generates a difference in mean water levels of North Sea and Baltic (0 (20 cm)) which has been accounted for. The resulting residual "baroclinic" currents are shown for the first layer (fig. 8) and may be compared with an interpretation of Svansson (1972); fig. 9. The water masses leaving the Baltic flow northwards near the westcoast of Sweden and near the coast of Jutland. n the area of the southern spur of the Norwegian trench the "countercurrent" appears. The december. eddy north of Sjaelland disappears in Knudsen and other authors supposed (1899, etc.) that in the area of the Darss sill the fresh water surplus of the Baltic generates a countercurrent near the bottom. Various experiments with the three-dimensional "baroclinic" model were made to confirm this assumption. But only in the case of north-easterly winds the countercurrent appears. n the other cases the current was uniform over the whole depth.

6 - 6-5 Concluding remarks The model studies shown seem to qualify the numerical methods for further application; especially in conjunction with the Belt-Sea project data. 6 Acknowledgements The authors are indebted to Mrs. Regina Hewer (nstitut für Meereskunde, Universität Hamburg) for providing boundary- 4t values of water elevations and atmospheric pressure values, and Mr. J. T. Duun-Christensen (Meteorologisk nstitut K0benhavn), Mr. M. Gotthardsson (The Swedish Meteorological and Hydrological nstitute) and Mr. Schiffahrtsamt Lübeck) Riechert (Wasser- und for providing sea level data.

7 - 7-7 References Backhaus, J. 0., Maier-Reimer, E. (1983). On Seasonal Circulation Patterns n The North Sea. n: North Sea Dynamies, Sündermann, J. and Lenz, W. editors, Springer Verlag Berlin Heidelberg. Bock, K.-H., (1971), Monatskarten der Dichte des Wassers in der Ostsee, dargestellt für verschiedene Tiefenhorizonte. Ergänzungsheft zur Deutschen Hydrographischen Zeitschrift Reihe B (4 0 ), Nr. 13. Duun-Christensen, J. T. (1975), The Representation of the Surface Pressure Field in a Two-Dimensional Hydrodynamic Model for the North Sea, Skagerrak and the Kattegat. Deutsche Hydrographische Zeitschrift, Band 28, Heft 3. Hewer, R. (1983) private communication. Jacobsen, T. S. (1980), The Belt Project, Sea water exchange of the Baltic. Measurements and Methods. National Agency of Environmental Protection, Denmark. Müller-Navarra, S. (1983), Simulation von Bewegungsvorgängen im übergangsgebiet zwischen Nord- und Ostsee. Diplomarbeit im Fach Ozeanographie, Universität Hamburg. Svansson, A. (1972), Canal models of the sea and salinity variations in the Baltic and adjacent waters. Fishery Board of Sweden, Series Hydrographie, Report No. 26. Smith, S. D., Banke, E. G. (1975), Variation of the Sea Surface Drag Coefficient with Wind Speed. Quarterly Journal of the Royal Meteorological Society, Volume 101.

8 SCH\4EDE.. ~ ss' ~ 't ~ 13' fig. Kattegat + l;;-point Belt Sea (pressure) Sound model

9 o,.""",,,.,,,,,,,,,,,,,,, ",,,,, '~' ", ", ", ""'Ln., ", ", "".' "'-. ",.,...., 020 fig. 2 North Sea-Baltic model isobars and windstresses (Hewer, 1983)

10 57" JUETL ND 56" o ~ ~ D~ ~... ~g 55"..., MECKLEN URG 216 f'ip" 3 13" r-- c> ----c.:::.._~.,jl,~ ~ M 2, co-tidal lines (degrees) _-." L-J related to mo on trans1. t 1n. Greenwich 1 11.}.

11 \ o SCHWEOE~ JUETL ND D o li.b. SEELAND ( SCHLESHG-HOLSTEN 4.~ 11 ' ~~., - ~~g~k;en 13~RG. M i 2, co-range lines (crn). For cornparison sorne coastal tide\ gruges are given. 12"

12 } 9cm -, 10cr:D- 3 h., ' ' M2 Phase in Hours Amplitude in cm.fig. 5 M2, co-tidal and co-range lines. (Svanssan, 1972)

13 ;: eo 8 70 CO 50.0 SO N -la < FR EG-ERic.iA 1(0)= GMT eo <0 SO lg -20 -SO -< VARBER<S 1(0)= GM1 -la -20 -SO -< o ARHUS T(0)= GMT... "'~-:f<._'-~~'."." :;: 811 ~ N 5lJ 4D SO -<0 -' ~f ~.~ < lli lob U!G FR EDE1ZKS-\A\t 1(01= GM1 100 eo :;: eo <0 SO la -20 -so -< HORNß~['( 1(0)= GMT 100 Ba :;: ea ~ lJ < ;: eo 8 ' <0 SO SO -< GOETfP:O'RU 1(01= GMT SO -< VKEN 1(0)= GMT fig. 6 Comparison of computed (full storm surge and observed (~) line) values.

14

15 W t!-- :>: Cl::: '.!l o 0 a... 0 tl Z C'1 <C Cl::: -!-- Z N W :z ~ ::J a c3 0 > t- Cl::: Cl::: ww ZVl.-t1D WOZ...JCl:::::J ~~tl E)(J+ 010" N U., n.., ~ '".., N '",., ~ '" t~., ", "" fig. 7 Calculated seawater exchange (Q) during the computed~storm surge period. nflow positive.

16 SCHHEDE\j S7' S6' "' ~ ~ 5-10 ~ ~ ,7'-7' Z fil-7' 30- (0 <C ~ ( l! ,7'-'f W filjj ::::l ~ J ~ ~120-1(0 <1: 1(0-160 <f >160 lcmsl 55' SCHLESJG-HOLSTEN n' fi~. 8 f'ig. 8 Density induced ("baroclinic") circulation in the first layer (~ - 10 m) i~ July, fresh water surplus 00= m s.

17 ' H',,' 'lorwav _.-,.. ;!l7" fig. 9 A simplified map of the surface currents of the Kattegat and the Skagerrak. (Svansson, 1972)