Numerical Studies of Dispersion Due to Tidal Flow Through Moskstraumen, Northern Norway
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Ocean Dynamics (2010) 60:907–920 DOI 10.1007/s10236-010-0309-z Numerical studies of dispersion due to tidal flow through Moskstraumen, northern Norway Birgit Kjoss Lynge · Jarle Berntsen · Bjørn Gjevik Received: 24 March 2010 / Accepted: 20 May 2010 / Published online: 27 June 2010 © Springer-Verlag 2010 Abstract The effect of horizontal grid resolution on (12–24 h) is very sensitive to the grid size and that the horizontal relative dispersion of particle pairs has the spatial variability is also very large, ranging from 0 been investigated on a short time scale, i.e. one tidal to 100 km2 over a distance of 100 m. This means that M2 cycle. Of particular interest is the tidal effect on models for prediction of transport and dispersion of dispersion and transports in coastal waters where small- oil spills, fish eggs, sea lice etc. using a single diffusion scale flow features are important. A three-dimensional coefficient will be of limited value, unless the models ocean model has been applied to simulate the tidal flow actually resolves the small-scale eddies of the tidal through the Moskstraumen Maelstrom outside Lofoten current. in northern Norway, well known for its strong current and whirlpools (Gjevik et al., Nature 388(6645):837– Keywords Relative dispersion · Grid resolution · Tidal 838, 1997; Moe et al., Cont Shelf Res 22(3):485–504, current · Whirlpool · Particle tracking · Lyapunov 2002). Simulations with spatial resolution down to 50 m have been carried out. Lagrangian tracers were pas- sively advected with the flow, and Lyapunov expo- 1 Introduction nents and power law exponents have been calculated to analyse the separation statistics. It is found that the Accurate model prediction of relative dispersion of relative dispersion of particles on a short time scale particle pairs in complex current fields can be of con- siderable value for several practical purposes, i.e. oil spill, dispersion of sea lice and pollutants. An im- Responsible Editor: John Grue portant question is what horizontal grid resolution is required to predict dispersion accurately on different B. K. Lynge (B) Norwegian Hydrographic Service, Stavanger, Norway time scales, from short time scales, i.e. one tidal cycle e-mail: [email protected] to long time scales like months and years. The effect of Eulerian spatial resolution on drifting particle pairs has J. Berntsen recently been studied extensively by Poje et al. (2010) Department of Mathematics, University of Bergen, P.O. Box 7803, 5020 Bergen, Norway with an examination of several ocean models, a two- e-mail: [email protected] dimensional turbulence model, ROMS and HYCOM, on grid scales from 0.5 to 8 km and on time scales B. Gjevik from tidal periods to several months. Understanding Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway the properties of dispersion is also important in studies e-mail: [email protected] of drifters and tracers, see, e.g. LaCasce (2008)and Haza et al. (2007). Present Address: In many areas in coastal waters, flow and dispersion B. K. Lynge Department of Mathematics, University of Oslo, is driven by the barotropic tide. Tidal effects on disper- P.O. Box 1053, Blindern, 0316, Oslo, Norway sion and transports are hence of particular interest and 908 Ocean Dynamics (2010) 60:907–920 have been studied by several authors, e.g. Zimmerman Processes affecting the transport and dispersion of (1986), Geyer and Signell (1992), Signell and Butman fish eggs and larvae on long time scales (i.e. month- (1992), Ridderinkhof and Zimmerman (1992), Gjevik years) has been studied previously. The periodical tidal (1996) and Orre et al. (2006) and references therein. current in Moskstraumen combined with background Our focus in this paper will be on the horizontal currents of order 0.1–0.3 ms−1 from the Norwegian relative dispersion of particle pairs in tidal currents Coastal Current is found to introduce a tidal pump- on a short time scale when small-scale flow features ing between Vestfjorden inside Lofotodden and the are important. The site for our investigation is the shelf outside (Ommundsen 2002). Aadlandsvik (1994) Moskstraumen Maelstrom outside Lofoten on the and Vikebø et al. (2007) simulated the transport of northern coast of Norway (see Fig. 1) where the current eggs/larvae/juveniles of Arcto-Norwegian cod from the fields are known both from two-dimensional and three- Lofoten area with a coarse grid model that only resolve dimensional modelling. Moskstraumen is well known the large-scale flow features which are important for for its strong current and whirlpools, see Gjevik et al. dispersion on long time scales. The area of Vestfjorden (1997) and Moe et al. (2002). Tidal-driven currents and the Lofoten Islands is a region with complex cir- dominate wind-driven currents in the area. The sig- culation dominated by the two major currents, the nificant difference in tidal amplitude in Vestfjorden and Norwegian Coastal Current and the Norwegian At- the shelf outside Lofoten combined with a complex lantic Current. Mitchelson-Jacob and Sundby (2001) bathymetry causes strong tidal currents running with discuss how complex bathymetry in the area and in- total strength up to 3–5 ms−1. teraction with tidal currents can modify these major New technology like increased computing power currents and induce mesoscale eddies, with diameter and high-resolution bottom topography available from 20–60 km, revealed in the Vestfjord basin by satel- multibeam surveys enable us to resolve small-scale flow lite tracked drifters. Slagstad and Tande (2007)and feature with improved accuracy. The Bergen ocean Skarðhamar et al. (2007) investigated transport and model (Berntsen 2000) has been used for simulations distribution of plankton on the shelf area of Northern with 50, 100, 200, 400 and 800 m grid resolution. The Norway. objective is to investigate the sensitivity of dispersion to Strong tidal currents have a crucial effect on disper- the horizontal grid size x,y. Simulations with both sion and drift of pollutants in coastal waters. Transport homogeneous conditions and stratification have been of pollutants, for instance from oil spills and industrial carried out in order to study the sensitivity of dispersion activity, transport of sea lice or diseases from fish farms to the density field ρ(z). and transport of discharged sewage may affect the water quality and the natural marine ecosystems. Dis- persion of oil spill was studied by Proctor et al. (1994). After M.V. Braer ran aground near the southern tip of 30’ the Shetland Island in January 1993, they used a high- resolution model in an area with strong tidal current 69oN for forecast and hindcast simulations of the oil spill. 3000 Davies et al. (2000) investigated the spatial distribution 30’ of currents and waves at the time of the Braer acci- Narvik dent with a high-resolution model. They found that it o 2000 is essential to take account of wind wave turbulence 68 N 100 Lofoten when modelling transport of pollutants in the surface 200 200 layer during major wind events. The oil spill model 30’ OSCAR is described in Reed et al. (1999a, b)which Bodø 400 also provide a review of oil spill modelling. There is o 67 N VESTFJORDEN also several works on dispersion of sea lice and diseases from fish farms, e.g. Amundrud and Murray (2009)and 30’ Gillibrand and Willis (2007). o o o o E 10 E 12 E 14oE 16 E 18 2 The numerical model Fig. 1 Location of the model domain on the northern coast of Norway. Model domain is marked with a square box in the area σ of Lofoten. Contour lines shows the bottom topography in the The -coordinate ocean model (Bergen ocean model) area with depth in metres applied in the present studies is a three-dimensional Ocean Dynamics (2010) 60:907–920 909 (x, y, z) model described in Berntsen (2000)where H is the bottom depth, is applied. For advection of x and y are the horizontal Cartesian coordinates momentum and density a total variance diminishing and z the vertical coordinate. The model applies the (TVD) scheme with a superbee limiter described in Boussinesq approximation and is here applied in a Yang and Przekwas (1992) is applied in the present hydrostatic form. It is available from www.math.uib. studies. The standard second-order Princeton ocean no/BOM/. The model has recently been used for ide- model method is applied to estimate the internal pres- alized studies of internal wave generation and mixing sure gradients (Blumberg and Mellor 1987; Mellor of flow over sills (Berntsen et al. 2008, 2009). The 1996). The model is mode split with a method similar governing equations are: to the splitting described in Berntsen et al. (1981)and Kowalik and Murty (1993). The continuity equation, The time steps are performed with a predictor– ∂w corrector method both in the internal time steps and ∇ × u + = 0, (1) ∂z in the external time steps. The leapfrog method is used and the Reynolds momentum equations, as the predictor, and the fully implicit method is used as the corrector. ∂ ∂ ∂ ∂ ∂ u + × ∇ +w u − v =−1 p + u + , ∂ u u ∂ f ρ ∂ ∂ Av ∂ Fx t z 0 x z z 2.1 Model setup and boundary conditions (2) High-resolution bottom topography based on multi- ∂v ∂v 1 ∂p ∂ ∂v + × ∇v+w + =− + + , beam bathymetric data from the Norwegian Hydro- ∂ u ∂ fu ρ ∂ ∂ Av ∂ Fy t z 0 y z z graphic Service is used to generate the bottom matrices. (3) The topography is shown in Fig. 2. Horizontally, the ∂p grids applied are equidistant and the experiments are ρg =− . (4) ∂z run with horizontal grid size x = y equal to 50, 100, In the equations above, u = (u,v) is the horizontal 200, 400 and 800 m in order to investigate how the velocity field, w the vertical velocity, t the time, f dispersion is affected by the grid size.