Vestfjorden in northern Norway, a major spawning ground for the northeast Arctic cod, is sheltered from the continental shelf and open ocean by the Lofoten–Vesterålen archipelago. The archipelago, however, is well known for hosting strong and vigorous tidal currents in its many straits, currents that can produce significant time-mean tracer transport from Vestfjorden to the shelf outside. We use a purely tidally driven unstructured-grid ocean model to look into non-linear tidal dynamics and the associated tracer transport through the archipelago. Of particular interest are two processes: tidal pumping through the straits and tidal rectification around islands. The most prominent tracer transport is caused by tidal pumping through the short and strongly non-linear straits Nordlandsflaget and Moskstraumen near the southern tip of the archipelago. Here, tracers from Vestfjorden are transported tens of kilometers westward out on the outer shelf. Further north, weaker yet notable tidal pumping also takes place through the longer straits Nappstraumen and Gimsøystraumen. The other main transport route out of Vestfjorden is south of the island of Røst. Here, the transport is primarily due to tracer advection by rectified anticyclonic currents around the island. There is also an anticyclonic circulation cell around the island group Mosken–Værøy, and both cells have flow speeds up to 0.2

Increased industrial activity along the Norwegian coast raises concern about potential impacts on the marine ecosystem. To properly assess risks involved, we need to understand oceanic dynamics in nearshore regions and its associated transport of nutrients and pollutants. Together with wind and freshwater runoff, strong tidal currents may dominate the flow dynamics in coastal regions on short timescales. While strong tidal currents are known to cause efficient vertical mixing of the ocean, important for bringing up nutrients in the water column

In this study, we will investigate non-linear tidal dynamics around Lofoten–Vesterålen in northern Norway (Fig.

The majority of studies on transport in the Lofoten and Vesterålen region have focused on the large-scale ocean dynamics

A large number of straits cut through the Lofoten–Vesterålen archipelago, and these straits are well known for hosting strong and vigorous tidal currents. This includes a set of narrow and relatively long straits along the northern half of the archipelago, but even more so two to three wider but shorter straits over the shallow ridge southwest of Lofotodden

The general ocean surface circulation in the Lofoten–Vesterålen region. Black arrows show the Norwegian Coastal Current (NCC) and the red arrow shows the Norwegian Atlantic Current (NwAC). The blue two-headed arrow shows the location of Moskstraumen, situated between Lofotodden to the north and the small island of Mosken to the south.

Tidal pumping in a strait is a Reynolds flux of properties caused by a temporal asymmetry in circulation patterns between the flood and ebb phases of the tide

A sketch illustrating the flow asymmetry that leads to tidal pumping. The left panel

The second process, rectification of oscillating currents around isolated islands and banks, has been observed in several regions where cross-slope tidal currents are prominent. The phenomenon can be explained as a response to a non-linear momentum transport convergence by the oscillating currents

A sketch of mean-flow generation around a bank from oscillating flow across the bank topography. A water column oscillates up and down topography, attaining negative vorticity

Indication of large dipole vortices associated with tidal currents have been observed in satellite images from Moskstraumen (see, e.g., Fig.

Satellite images from Copernicus Sentinel-2 missions, tracing out surface currents in Moskstraumen and Nordlandsflaget. Panel

In this paper, we will isolate these two potential transport mechanisms by conducting and analyzing a purely tidally forced numerical simulation of the region. Modeling non-linear tidal dynamics in such a complex region is challenging.

We use the Finite Volume Community Ocean Model

The model domain for the unstructured-grid modeling. Panel

The model domain, with coastline and bottom depths, is shown in Fig.

Along the open boundary, we force the model with prescribed sea surface height (SSH) anomalies due to northward-propagating tidal waves. We obtain the SSH forcing fields from the TPXO 7.2 assimilated tidal model

We spin the dynamics of FVCOM up for 6 months before analyzing the model fields. In order to investigate tidal transport dynamics, we couple FVCOM with a passive tracer module, the Framework for Aquatic Biogeochemical Models

The large-scale behavior of the M2 and K1 tidal waves and associated currents is shown in Fig.

The M2

The K1 wave is the dominating diurnal constituent (right panels), but its amplitude in SSH is only about

The large-scale behavior of both M2 and K1 waves in our model corresponds well with results reported earlier by

Comparison between modeled and observed tidal properties in Lofoten. Comparisons for the SSH tidal amplitude

Amplitude and phase of modeled and observed sea surface height for M2 and K1 tidal constituents. The difference is given as model minus observation. Observations are collected from the Norwegian Mapping Authority, Hydrographic Service (2021) (also displayed in Fig. 7).

Amplitude of modeled and observed tidal velocity for M2 and K1 tidal constituents. The difference is given as model minus observation (

Figure

72 h average tracer concentration, 2 months after initial tracer release. The yellow line shows the boundary of the initial tracer release area. Inside the yellow boundary, the initial tracer concentration was 1, while everywhere else the tracer concentration was zero. The contours show the bottom topography. The main straits through the archipelago which will be investigated in this study are (1) Røsthavet, (2) Nordlandsflaget, (3) Moskstraumen, (4) Nappstraumen, (5) Gimsøystraumen, (6) Raftsundet and (7) Tjeldsundet. Note that the numbering does not correspond to the numbering of the stations given in Fig.

A visual comparison with Fig.

Tidal pumping through a strait is a property exchange associated with zero net mass transport (i.e., a Reynolds flux) caused by a temporal asymmetric flow field between the ebb and the flood tide

Before making quantitative estimates, we take a look at the flow field in two of the straits. Figure

Tracer distribution with corresponding stream-function is displayed for Nappstraumen (4) during the first full tidal cycle in the simulation. The time is given in hours after slack tide after ebb. Panels

The ebb tide (7.5, 9 and 10.5 h in Fig.

The situation is somewhat different in Moskstraumen (3) between Lofotodden and the island of Mosken, as show in Fig.

Same as Fig.

According to

While the first non-dimensional parameter,

To reiterate, the formation of a tidal jet during outflow from a strait requires flow separation which is driven, in part, by the build-up of an adverse pressure gradient. The build-up of an adverse pressure gradient, in turn, requires non-linear advection of momentum

The size of the non-linear term compared to the linear time rate of change is then found by dividing Eq. (

To assess flow asymmetry, we will use the model's pressure or sea surface height field. To understand how flow asymmetry will manifest itself in the pressure field, we again return to the sketch in Fig.

We start by forming normalized pressure gradients across each strait openings:

We calculated

The estimates of

The largest non-linearities and asymmetries are found in the northern opening of Nappstraumen (4), in both openings of Moskstraumen (3) and in the eastern (ebb) opening of Nordlandsflaget (2). It is interesting to note that the non-linearity in Røsthavet (1) is comparable to that in the northern (flood) opening of Nordlandsflaget, but that the asymmetry is lower. As it turns out, Røsthavet is the widest strait in the whole region. So although tidal currents are just as large as in Nordlandsflaget and there is actually flow separation here during both phases of the tide (not shown), the vortices formed are too far apart to form a self-propagating dipole and a trailing tidal jet. The longer straits in the north (5–7) all have moderate to low non-linearities and asymmetries. The reason for this is probably that the overall flow dynamics becomes more linear as the strait length increases

Estimates of the flow asymmetry

To finally evaluate the strength of the tidal pumping, we calculate a tracer transport efficiency for each strait. The transport efficiency

Figure

The tracer transport efficiency

In forming the various estimates above, some subjective decisions will impact the results. In particular, the exact value of the asymmetry parameter

The second non-linear process to be assessed is the rectification of oscillating tidal currents around the islands off the southern tip of Lofoten. Residual tidal currents encircling banks and islands have been observed in various places around the world, like Norfolk Island and Georges Bank

In Lofoten, the distortion of the northward-propagating tidal waves produces particularly strong tidal currents across the shallow ridge south of Lofotodden (Fig.

Time-mean tracer concentration

Before doing a quantitative analysis of these currents, we will review some of the relevant theory. One useful starting point

The total response to arbitrary forcing can be found by Fourier-transforming the above integral equation in time. The expression for each individual Fourier-component becomes

The primary slow timescale variation in forcing for our problem is the spring–neap cycle. So

We now test these predictions on the time-mean flow cells observed around the islands near the tip of Lofoten. Figure

Reynolds vorticity flux and tangential flow calculated around closed depth-contours encircling Røst (black curves) and around Mosken–Værøy (orange curves), shown in panel

However, the figure also reveals that the two circulation cells respond differently to the spring–neap cycle. The cell around Røst is nearly in phase with the Reynolds flux forcing, with a phase delay of only about half a day – close to the theoretical prediction. But the flow variability around Mosken–Værøy is more erratic and, on average, lagging the forcing by 9–10 d. The amplitude of the spring–neap flow variations around Mosken–Værøy is also smaller than that around Røst even though the amplitude of the Reynolds flux forcing is larger. Taken together, these results indicate that the theory works well at describing the slowly evolving anticyclonic circulation around Røst but that additional dynamics must be considered to understand the cell around Mosken–Værøy. We will return to this issue below but will first examine the underlying process that sets up the vorticity flux through these closed depth contours.

The direction of the vorticity flux may be understood by following a water column that moves periodically up and down a topographic slope, driven by a large-scale tidal potential

If we assume

The net effect after integrating over the movement of many such water columns is a positive relative vorticity flux towards deep regions. Hence, Eq. (

The magnitude of the rectified current depends on the steepness of the topographic slope and the strength of the cross-slope tidal oscillations

The ratio between time-mean

The ratio

The strength of the rectified tidal currents around Røst (black dots) and around Mosken–Værøy (orange dots) are plotted against the ratio

The sign of the residual currents around Mosken–Værøy is in agreement with the sign of the Reynolds vorticity flux across the closed depth contours there. But, as seen above, the time variability does not correlate trivially with the spring–neap variations in the vorticity flux. So additional dynamical processes must be at play here and, as indicated by Fig.

Figure

Close-up of the flow field around Mosken–Værøy. Panel

In essence, the strong anticyclone has deformed the geostrophic contours guiding the time-mean flow, and the integral analysis of Eq. (

While the tides in Lofoten–Vesterålen are well known to be strong and vigorous, dominating the short-term ocean dynamics, particularly in straits and around topographic features

The flexible model grid, and the ability it offers to increase resolution in key regions, allowed us to confirm that tidal pumping, caused by flow separation and vortex dipole formation at the openings of the many straits in Lofoten–Vesterålen, is a near-ubiquitous process here. But geometry and flow conditions around each strait are different, and the tracer transport due to tidal pumping varies greatly. Strong non-linearity due to high flow speeds and abrupt strait openings, as well as short strait lengths, appears to be the explanation for why Moskstraumen and Nordlandsflaget have the highest tidal transport efficiencies in the region. The longer straits further north all have lower pumping efficiencies. But notable pumping also takes place in Nappstraumen and Gimsøystraumen.

Tidal pumping, particularly in relation to tidal flushing of estuaries and nearshore regions, have been widely studied elsewhere. Certainly, the formation of dipole vortices is observed many places where prominent tidal currents exit narrow straits, for example, in Aransas Pass (USA), Messina Strait (Italy) and the Great Barrier Reef (Australia)

Our simulation also revealed non-linear rectification of tidal oscillations, leading to the generation of time-mean anticyclonic circulation cells around the island groups of Mosken–Værøy and Røst off the southern tip of the archipelago. From our knowledge, tidal rectification in southern Lofoten has neither been investigated nor recognized before. But the rectification in our model results seems to be in agreement with well-established theory of vorticity fluxes driven by cross-topographic tidal oscillations in the presence of bottom friction. The model predicted rectified current speeds up to 0.2

We find that the potential for tidal rectification can be evaluated through the relation

The non-linear tidal dynamics studied here, particularly flow separation and dipole formation, occurs on small spatial scales. In studying idealized model simulations of tidal pumping,

Our simulations were also limited by their 2-D nature. A 2-D configuration was chosen to help isolate non-linear lateral tidal dynamics, but the model was thus unable to account for baroclinic effects. Such effects include the generation of hydraulic jumps and vertical mixing around strait openings

Notwithstanding model limitations, the present study supports previous claims that tides are an important contributor to the transport of drifting material, and in particular northeast Arctic cod eggs and larvae, out of Vestfjorden. Even if the main transport routes due to tides coincide with transport routes following the mean flow, i.e., through Moskstraumen and south of Røst, the net transport could potentially be significantly enhanced when non-linear tidal dynamics are present. In truth, the connectivity between the inner and outer shelf likely relies on the

We consider the Lagrangian time evolution of a water column subject
to linear bottom friction:

Equation (

Vorticity evolution of a water column forced
to oscillate over a linear bottom slope, for

Vorticity flux averaged over an integral
number of tidal period as a function of time, for the solution of
Eq. (

We now evaluate Eq. (

Model data are available at

OAN and EB sat up the numerical model. EB conducted the numerical experiments and analyzed the data. All authors contributed to discussing and interpreting the results. EB and PEI wrote the initial draft, and all authors have contributed to editing the paper.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Trygve Halsne for providing the processed satellite images of Moskstraumen and Nordlandsflaget in Fig.

This research has been supported by VISTA – a basic research program in collaboration between the Norwegian Academy of Science and Letters and Equinor (project no. 6168).

This paper was edited by Joanne Williams and reviewed by two anonymous referees.