the Creative Commons Attribution 4.0 License.

the Creative Commons Attribution 4.0 License.

# Bardsey – an island in a strong tidal stream: underestimating coastal tides due to unresolved topography

### David T. Pugh

Bardsey Island is located at the western end of the Llŷn Peninsula in
northwestern Wales. Separated from the mainland by a channel that is some 3 km wide, it
is surrounded by reversing tidal streams of up to 4 m s^{−1} during spring
tides. These local hydrodynamic details and their consequences are
unresolved by satellite altimetry and are not represented in regional
tidal models. Here we look at the effects of the island on the strong tidal
stream in terms of the budgets for tidal energy dissipation and the
formation and shedding of eddies. We show, using local observations and a
satellite-altimetry-constrained product (TPXO9), that the island has a large
impact on the tidal stream and that even in this latest altimetry-constrained product the derived tidal stream is under-represented due to the
island not being resolved. The effect of the island leads to an
underestimate of the current speed in the TPXO9 data in the channel of up to
a factor of 2.5, depending on the timing in the spring–neap cycle, and the
average tidal energy resource is underestimated by a factor up to 14. The
observed tidal amplitudes are higher at the mainland than at the island, and
there is a detectable phase lag in the tide across the island; this effect
is not seen in the TPXO9 data. The underestimate of the tide in the TPXO9
data has consequences for tidal dissipation and wake effect computation and
shows that local observations are key to correctly estimating tidal energetics
around small-scale coastal topography.

Scientific understanding of global tidal dynamics is well established.
Following the advent of satellite observations, up to 15 tidal constituents
have been mapped using altimetry-constrained numerical models, and the
resulting products are verified and constrained further using in situ tidal data; see Stammer
et al. (2014) for details. There is, however, still an issue in terms of
spatial resolution of the altimetry-constrained products: even the most
recent (global) tidal models have only 1∕30^{∘} resolution (equivalent to
∼ 3.2 km in longitude at the Equator, ∼1.9 km
in the domain here, and 3.2 km in latitude everywhere). The satellite
themselves may have track separation of hundreds of kilometres (Egbert and
Erofeeva, 2002), and the coastline can introduce biases in the altimetry data
that limit the usefulness of them in the assimilation process. Consequently,
smaller topographic features and islands are unresolved and may be
“invisible” in altimetry-constrained product even if the features may be
resolved in the latest bathymetry databases, e.g. the General Bathymetric
Chart of the Oceans (GEBCO,
https://www.gebco.net/, last access: 2 November 2020; Jakobsson et al., 2020). This can mean that the
tidal energetics in the products, and in other numerical models with insufficient
resolution, can be biased because unresolved wakes downstream of the topography can act as a large energy sink
(McCabe et al., 2006; Stigebrandt,
1980; Warner and MacCready, 2014). Whilst the globally integrated energetics
of these models are consistent with astronomical estimates from lunar
recession rates (Bills and Ray, 1999; Egbert and
Ray, 2001), the local estimates can be wrong. However, new correction
algorithms improve the satellite data near coasts
(e.g. Piccioni et al., 2018), but this is yet to
be included in global tidal products.

Because many of the altimetry-constrained tidal databases are models, and not altimeter databases, they also provide tidal currents as well as elevations. This is true for TPXO9 (see Egbert and Erofeeva, 2002, and https://www.tpxo.net/, last access: 2 November 2020, for details), the altimetry-constrained product used here. Here, we use a series of tide-gauge measurements from Bardsey Island in the Irish Sea (Fig. 1) alongside TPXO9 to evaluate the effect of the island on the tidal dynamics as they track around Bardsey Island. Bardsey Island is a rocky melange of sedimentary and igneous rocks, including some granites, located 3.1 km off the Llŷn Peninsula in northern Wales, UK (Fig. 1a). It is approximately 1 km wide (though it is only 300 m wide at the narrowest point) and 1.6 km long. It reaches 167 m at its highest point. Bardsey Sound, between the Llŷn peninsula and the island, experiences strong tidal currents. The relatively small scale of the island and the sound means that the local detail is not “seen” in the altimetry-constrained products. The active local tidal dynamics that are uncaptured by the altimetry-constrained data allow us to compare the altimetry-constrained tidal characteristics in TPXO9 for the region with accurate local observations and quantify the validity limits of TPXO9 for this type of investigation. We will make a direct comparison of the tidal amplitudes and phases measured by the bottom pressure gauges around the island; see Fig. 1b for tide gauge (TG) locations and a summary of the in situ tides. We also consider whether (and when in the tidal cycle) flow separation occurs in the wake of the island.

We will use some basic fluid–flow parameters in our analysis later.
Transition to turbulence, and hence flow separation around an object, can be
parameterized in terms of a Reynolds number, $\mathit{Re}=UD/\mathit{\nu}$, where *U* is a
velocity scale, *D* is the size of the object, and *ν*∼100 is a
horizontal diffusivity (see, e.g.
Wolanski et al., 1984). It indicates when there is a transition to flow
separation behind the island: at low Reynolds numbers, *Re*<1, the flow
is quite symmetric upstream and downstream, and there is no flow separation
at the object. As the Reynolds number is increased to the range $\mathrm{10}<\mathit{Re}<\mathrm{40}$, laminar separation happens and results in two steady vortices
downstream. As Re increases further, up to *Re*<1000, these steady
vortices are replaced by a periodic von Karman vortex street, whereas if
*Re*>1000, there is a fully separated turbulent flow
(Kundu and Cohen, 2002).

Another useful non-dimensional number for this type of investigation is the
Strouhal number, $\mathit{St}=fD/U$. Here, *f* is the frequency of the shedding of vortices.
Fully developed vortices are generated when *T*>*f*, where *T* is the frequency of the
oscillating flow (Dong
et al., 2007; Magaldi et al., 2008). If, on the other hand, the tidal
frequency is larger than *f*, only one wake eddy will be shed on each tidal
cycle, if it has time to form at all.

## 2.1 In situ data collection

The tidal elevations around Bardsey were measured in three deployments, from summer 2017 through to spring 2018 (Table 1 and Fig. 1b). Site East, the main harbour for the island at Y Cafn, was occupied twice as a control, during Deployments 1 and 3. The other instrument deployments were bottom mounted a few tens of metres laterally offshore, and all instruments were deployed at depths between 3.2 and 16.5 m. The instruments used were pressure recorders from RBR with a measurement resolution better than 0.001 m, and they were set to sample every 6 min.

The resulting pressure series were analysed to extract tides, using the
Tidal Analysis Software Kit of the National Oceanographic Centre
(NOC, 2020). Analyses were made for 26 constituents, including
mean sea level, and eight related constituents, appropriate for a month or
more of data (Pugh and Woodworth, 2014). In Table 2 the
three constituents listed are the two biggest, *M*_{2} and *S*_{2}, and
(as an indicator of the presence of shallow water tides) *M*_{4}, the
first harmonic of *M*_{2}. Shallow-water tides are enhanced around the
island because of the curvature of the flow as it bypasses the island and
headland (see Sect. 6.2.3 of Pugh and Woodworth,
2014). The non-tidal residuals, the final column in Table 1, compare well
with the residuals at Holyhead, the nearest permanent tide gauge station
some 70 km north: for Holyhead these were 0.096, 0.172, and 0.067 m for
the same periods (note that bottom pressure measurements at Bardsey include
a partial natural sea level compensation for the inverted barometer effect).
Deployment 2 residuals at both Bardsey and at Holyhead were noticeably
higher than for the other two deployments because Deployment 2 included one
of the most severe storms and waves in local memory: Hurricane Ophelia,
which had maximum local wind speeds on 16 October 2017. A good indication of
the internal quality of the in situ observations and analyses is given by the
consistency in the tidal ages and *S*_{2}∕*M*_{2} amplitude ratios. The
tidal age is the time after maximum astronomical tidal forcing and the local
maximum spring tides, or approximately the phase difference between the
phases of *S*_{2} and *M*_{2} in hours, whereas the amplitude ratios are
related to the spring–neap amplitude cycle. These are given in the final
columns of Table 2. The effects of the storm were not noticeable in the
tidal signals, as they were at very different natural frequencies. The
subsurface pressure measurements at Bardsey include atmospheric pressure
variations and any tidal variation therein. However, at these latitudes the
atmospheric pressure *S*_{2} variations are very small. At the Equator the
atmospheric *S*_{2} has an amplitude of about 1.25 mbar, which decreases
away from the Equator as cos ^{3}(latitude), and thus at 53^{∘} N the amplitude is
reduced to 0.26 mbar, a sea level equivalent of 2.5 mm.

Amplitudes and phases of tidal constituents based on short periods of
observations need adjusting to reflect the long-term values of amplitudes
and phases. The values in Table 2 have been adjusted for both nodal effects
and for an observed non-astronomical seasonal modulation of *M*_{2}.
Standard harmonic analyses include an automatic adjustment to amplitudes and
phases of lunar components to allow for the full 3.7 %, 18.6-year
modulation due to the regression of lunar nodes. However, the full 3.7 %
nodal modulation is generally heavily reduced in shallow water and shelf
seas, and thus local counter adjustments are needed. The nodal *M*_{2} amplitude
modulation at Holyhead, the nearest standard port, is reduced to 1.8 %
(Woodworth et al., 1991). We have used this value in correcting
the standard 3.7 % adjustment. The *M*_{4} nodal modulations are twice
that for *M*_{2}. The seasonal *M*_{2} modulations are generally observed to
have regional coherence, so we have used the seasonal modulations from 9
years of Newlyn data (in the period 2000–2011). *M*_{4} is not seasonally
adjusted, and *S*_{2} is not a lunar term, so it is not nodally modulated.
These very precise adjustments are possible and useful, but overall, as
stated in the caption to Table 2, for regional comparisons we assume,
slightly conservatively, confidence ranges of 1 % for amplitudes and 1.0^{∘} for phases.

## 2.2 TPXO9 data

The altimetry-constrained product used in this paper is that of the TPXO9
ATLAS, which is derived from assimilation of both satellite altimeter and
tide gauge data into a forward model solution (Egbert and Erofeeva, 2002). The resolution is
1∕30^{∘} in both latitude and longitude (3.7 and 2.2 km at Bardsey). We
used the elevation and transport information and their respective phases
for the *M*_{2}, *S*_{2}, and *M*_{4} constituents. In the following
calculations, we approximate the largest tidal current speeds or amplitudes
as the sum of the amplitudes of the above three tidal constituents. Of
course this is only a crude estimate of the full highest and lowest
astronomical tides. Note that we are not allowing for *M*_{2} to *M*_{4} phase locking, and the relatively small diurnal tides are
ignored. We refer to this as the GA (greatest astronomical) in the
following.

## 2.3 LANDSAT data

Landsat-8 data images were used to identify possible eddies in the currents and further illustrate unresolved effects due to the island. Note that we are not aiming for a full wake description in this paper. Data were downloaded from the Earth Explorer website (https://earthexplorer.usgs.gov/, last access: 2 November 2020). True colour enhanced RGB images were created with SNAP 7.0 (Sentinel Application Platform; https://step.esa.int/main/toolboxes/snap/, last access: 2 November 2020) using the panchromatic band for red (500–680 nm, 15 m resolution), band 3 for green (530–590 nm, 30 m resolution), and Band 2 for blue (450–510 nm, 30 m resolution). The blue and green bands were interpolated using a bicubic projection to the 15 m panchromatic resolution, and brightness was enhanced to allow easier visualization of the wakes. The images used were taken between 11:00 and 12:00 UTC, when the satellite passed over the area, and the two images were the only cloud-free ones during the measurement periods that were on different stages of the tide.

## 3.1 In situ observations

The results of the tidal harmonic analyses are shown in Table 2. The in situ RBR
data results are given to 0.001 m and 1.0^{∘}. Amplitudes are given to
three decimal places as appropriate for the uncertainties in the RBR data,
whereas the timing of constituent phases is probably better than
0.5^{∘} (1 min in time for *M*_{2}). Given the small local tidal
differences, it is necessary to consider possible variability among the RBR
tidal constituents across the three deployments, due to both seasonal and
nodal shifts. Also, there is a statistical uncertainty against
background noise, as discussed in Pugh and Woodworth (2014), their Sect. 4.6.
This statistical uncertainty depends on the estimate of non-tidal noise
across the semidiurnal tidal band, though this can be optimistic as noise
may be more sharply focussed at the *M*_{2} frequency. In fact, the
seasonal uncertainty is most significant here. Based on uncertainties in
making the seasonal and nodal adjustments we conclude that for regional
comparisons we can assume confidence ranges of 1 % for amplitudes and 1.0^{∘} for phases. We also note that for station East in 2017,
${M}_{\mathrm{2}}+{S}_{\mathrm{2}}+{M}_{\mathrm{4}}$ (i.e. our GA) accounts for 93.6 % of the
tidal variance, with N_{2} in fourth place providing 3.7 % of the
remainder.

A spring–neap cycle of parts of the data from the East and West gauges in
Deployment 1 is plotted in Fig. 2 and show a tidal range surpassing 4 m at
spring tide. Note that the diurnal constituents are not discussed further
due to their small (<0.1 m) amplitudes. The TG data show *M*_{2}
amplitudes of 1.210 m (North), 1.347 m (East), and 1.139 m (West; see Table
2). These give pressure gradients around the island. The East and West sites
are separated by 300 m, and the across-island difference in amplitude give,
on spring tides, a level difference of up to 0.5 m between those two gauges
There is also a 6.5^{∘} (13 min) phase difference for *M*_{2} across
the island between East and West, with East leading, which is consistent with the
tide approaching the island from the south and east and then swinging north
and east around the Llŷn Peninsula headland. Figure 2b–c show the
across island level difference plotted against the measured level at East
for two representative days of spring and neap tides, with smaller
differences during neap tides. The plots show that the East levels are some
0.5 m higher at West at high water for spring
tides. On neaps the excess is only about 0.3 m. The differences in the ebb
tide are slightly reduced, probably because the direction of flow is partly
along the island, steered by the Llŷn Peninsula.

We do not have access to any current measurements from the region, but the
tidal stream is known to reach up to 4 m s^{−1} in the sound
(Colin Evans, personal communication, 25 May 2017, and Admiralty, 2017). There is
also a simple interpretation of the differences in level across the island
from East to West, which indirectly gives approximate values for the wider
field of current speeds, which we term (but only in a local sense) the
“far-field” currents. If we ignore any other effects, the pressure head across the island is given solely by the loss of kinetic energy due to the island blocking the flow (e.g. Stigebrandt, 1980). The same approach applies
for wind forces on an impermeable fence or wall, and the sea level
difference, Δ*h*, between East and West is then given by the Bernoulli equation as

Here, *v* is the far-field tidal current speed and *g* the gravitational
acceleration. Then we may indirectly compute the far-field tidal
currents from the difference in levels across from East to West as the tide
approaches the island (see Fig. 1 for the direction of the oncoming tide).
Figure 3a and b (red curves) show the currents are computed for Day 147
(spring tides) and Day 154 (neap tides) with the speed shown in metres per
second. The black curves are the measured sea levels at East. The computed
far-field currents have a maximum over 3 m s^{−1} at springs and
around 2 m s^{−1} at neaps, similar to local estimates (Colin Evans, personal
communication, 25 May 2017). The noise in the level differences, which appears as noise in the
currents (i.e. the red curves), may be an indication of turbulence and
eddies discussed further below.

Along the island the differences between Southwest and North are only a few
millimetres for *M*_{2}, within the confidence limits on the analyses. This
curvature of the streamlines as the flow is squeezed through Bardsey Sound
and swings up around the peninsula leads to the enhanced generation of
non-linear higher tidal harmonics due to curvature on the reversing tidal
stream curves (Pugh and Woodworth, 2014). This contributes
to the large *M*_{4} amplitudes around the island and headland (Table 2).

## 3.2 Comparison with TPXO9 data

We turn now to a comparison of the tidal analysis data for *M*_{2} from the
two sources (see Table 2 for details). When the TPXO9 *M*_{2} data, which
have no Bardsey Island representation, are interpolated linearly to the TG
positions, the result is only a 0.02 m and 0.7^{∘} amplitude and phase
difference for the Deployment 1 locations. Compared to the 0.19 m amplitude
difference and 6.5^{∘} phase difference in the TG data, it is clear that
there is a substantial deficiency in the TPXO9 model in representing the
role of the island due to its limited resolution. These results are
supported by the Deployment 2 measurements (Table 2). Deployment 3 saw an
extended and different approach to the data collection. We revisited East
but also deployed two gauges on the Llŷn peninsula on the approach to
the island (South Mainland), and north of it (North Mainland). At South
Mainland, TPXO9 again underestimates the tidal amplitude by more than
10 %. At North Mainland, some 5 km north of Bardsey, and just north of the
sound, however, the TG and TPXO9 amplitudes are within 1 cm of each other.
This again shows the effect Bardsey and local topography have on the tidal
amplitudes in the region.

As a representation of the shallow-water tidal harmonics, the TPXO9 M_{4}
amplitude agrees well with the TG data at North (0.12 and 0.11 m,
respectively) but overestimates the amplitude at North Mainland (0.07 m in
the TG data and 0.12 m from TPXO; see Table 2). Because higher harmonics are
generated locally by the tidal flow itself, this again shows the effect of
the island on the tidal stream; the M4 amplitude is halved along Bardsey
Sound in the TG data, whereas TPXO9 overestimates it and shows only minor
variability. The overestimate in TPXO9 can lead to the tidal energetics
being biased high in the region if they are based on the that data alone.

This is illustrated in the TPXO9 spring and neap flood currents in
Fig. 4a–b, and the magnitude of the current in the
sound in Fig. 4c. These currents are weaker than the far-field estimate
using Eq. (1). For spring tides, TPXO9 shows a current of up to 1.5 m s^{−1} in the sound and 2.5 m s^{−1} in the far field, whereas the TG
data and Eq. (1) comes out at 3.7 m s^{−1} from Eq. (1) for the spring
tide far field (cf. Figs. 3 and 4). For neaps the corresponding values are
0.6 m s^{−1} in the sound and 1.5 m s^{−1} in the far field from TPXO9 and
3.0 m s^{−1} from the TG data and Eq. (1). The local sea-going experts
(Colin Evans, personal communication, 25 May 2017) and the Admiralty chart for the sound (Admiralty, 2017) state a current speed of up 4 m s^{−1}, and thus
TPXO9 underestimates the currents in the strait by a factor
∼2.5, whereas the observations, even under the assumptions
behind Eq. (1), get within 10 %. One can argue that the sea-level
difference along the strait will lead to an acceleration into the strait as
well (see, e.g. Stigebrandt, 1980), that could be added to
the far-field current. However, frictional effects will come into play and a
large part of the along-strait sea level difference will be needed to
overcome friction and form drag (Stigebrandt, 1980). In fact, of
the 0.32 m GA sea level difference between South Mainland and North Mainland (see
Table 1), only 0.006 m is needed to accelerate the spring flow from 3.66 to
4 m s^{−1} in Eq. (1). That means that almost the entire sea level
difference along the strait is due to energy losses.

## 3.3 Dissipation

The dissipation in a tidal stream can also be computed from *ε* = *ρ**C*_{d}|*u*|^{3}, where *C*_{d} ∼ 0.0025 is a drag
coefficient (Taylor, 1920) and *ρ*=1020 kg m^{−3} is a
reference density. The peak dissipation using the computed GA current data
from Eq. (1) and shown in Fig. 3 gives 777 MW for springs and 426 MW for
neaps, assuming the sound is 3.1 km wide and 2.2 km long. This is
0.2 %–0.4 % of the 180 GW of *M*_{2} dissipation on the European shelf (see Egbert and Ray, 2000) and is a reasonable
estimate for such an energetic region. Note that this method is independent
of the phases between the locations and does not depend on the phases
between the amplitudes and currents. If we instead use the TPXO9 current
speed in the strait, the GA spring dissipation comes out as 53 MW (using *u*=1.5 m s^{−1}), and the *M*_{2} dissipation (using a current speed of
1.2 m s^{−1}) comes out as 28 MW. This is an underestimate of a factor 14 for the GA
spring tide compared to the computation from the TG data, which again
highlights the importance of resolving small-scale topography in local tidal
energy estimates and the use of direct observations in coastal areas to
constrain any modelling effort. This dissipation here is only a small
fraction of the European Shelf and coastline, but it is a very energetic
area. Although the Bardsey tides are unusually energetic, underestimated
local coastal energy dissipation may be substantial in the TPXO9 (and
similar) data and numerical models.

## 3.4 Caveat emptor!

We have shown above that the tidal elevations are underestimated in the
TPXO9 data and that the current magnitude is most likely underestimated as
well, and thus our computations of the energetics and non-dimensional numbers are
conservative. The two extremes in tidal current magnitude in Bardsey Sound
can be taken to be the neap tide speed from TPXO9 and the GA speed computed
using TG data and TPXO9 combined. We thus have 0.9 m s^{−1} (neaps from
TPXO9, not discussed above) as the lower range and 4 m s^{−1} (computed
GA) as the upper estimate.

Even using the much-underestimated current speeds from the TPXO data, the
indications are that there would be no stratification locally. The
Simpson–Hunter parameter is $\mathit{\chi}=h/{u}^{\mathrm{3}}\approx \mathrm{70}$ for Bardsey
Sound (Simpson and Hunter, 1974). This means that the
area is vertically mixed due to the tides alone. The eddies shed from the
island will add more energy to this, further breaking down any potential
stratification from freshwater additions (the Simpson–Hunter parameter is
based on heat fluxes only) and act to redistribute sediment. The associated
Reynolds number for the island, $\mathit{Re}=UD/\mathit{\nu}$, then comes out at approximately
10 for the neap flow or approximately 40 for the astronomic tidal current
(using *D*=1000 m as the width and *ν*=100 m^{2} s^{−1} as the
eddy viscosity). This implies laminar separation into two steady vortices
downstream of the island at peak flows, and the vortices can be expected to
appear on both ebb and flood flows (Edwards et al., 2004;
Wolanski et al., 1984). There may not be any vortex shedding during neap
flows, however, because *Re*∼10.

The Strouhal number $\mathit{St}=fL/U$ is typically about 0.2 for the *Re* numbers found
here (Wolanski et al., 1984), giving $f=\mathit{St}U/L=\mathrm{0.2}U/\mathrm{1500}=>\mathrm{1}\times {\mathrm{10}}^{-\mathrm{4}}<f<\mathrm{5}\times {\mathrm{10}}^{-\mathrm{4}}$ and
an associated vortex-shedding period of 3–17 h (*L*=1500 m is the length
of the island). This means that fully developed eddies can be generated at
the higher flow rates because our tidal period (12.4 h) is longer than
the vortex-shedding period by a few hours. However, at neap flows there is no
time to develop a fully separated vortex within the time frame of a tidal
cycle.

This conclusion is supported by satellite images from Landsat 8 (Fig. 5), which show a very different picture between neaps (Fig. 5a) and springs (Fig. 5b). At spring tides, there are two clear wakes behind the tips of the island (marked with magenta arrows), whereas at neaps (Fig. 5a) there is only a more diffuse image in Bardsey Sound and no signal of a wake behind the south tip of the island.

This brief account was triggered by an interest in detailed mapping of tides in a reversing tidal stream. The results highlight the effect small coastal islands can have on tides in energetic settings, and they highlight the limitations of altimetry-constrained models near coastlines where the bathymetry used in the model is unresolved. Even though TPXO9, which is used here, is constrained by a series of tide gauges in the Irish Sea, including north and south of Bardsey, the island is some 60 km from the nearest long-term tide gauge (at Holyhead, to the north of Bardsey). Consequently, the tidal amplitudes in the database are not representative of the observed amplitudes near the island, and the currents are underestimated by a factor close to 2.5 for the GA tide. This underestimate also means that wake effects may be underestimated if one relies solely on altimetry-constrained models (or coarse resolution numerical models) unable to resolve islands, with consequences for navigation, renewable energy installations, and sediment dynamics.

Future satellite missions may be able to resolve small islands like Bardsey, and improved methods will allow for better detection of the coastlines. In order to obtain tidal currents, however, one still has to assimilate the altimetry data into a numerical model, and it will probably be some time before we can simulate global ocean tides at a resolution good enough to resolve an island like Bardsey.

The results do have wider implications for, among others, the renewable industry, because we show that local observations are necessary in regions of complex geometry to ensure the energy resource is determined accurately. Using only TPXO9 data, the dissipation – an indicator of the renewable resource – underestimates the astronomic potential by a factor up to 14 of the real resource. There is also the possibility that wake effects behind the island would be neglected without proper surveys, leading to an erroneous energy estimate. The results also highlight that concurrent sea level and current measurements are needed to fully explore the dynamics and quantify, e.g. further pressure effects of the island on the tidal stream. Consequently, we argue that in any near-coastal investigation of detailed tidal dynamics, the coastal topography must be explicitly resolved, and any modelling effort should be constrained to fit local observations of the tidal dynamics.

The data is available from the Open Science Framework (https://osf.io/kvgur/?view_only=ff2d8bd12a61493aa1dfa9011ecdde81, last access: 4 June 2020, Green, 2020).

JAMG wrote the manuscript and did the computations. DTP did the measurements, processed the TG data, and assisted with the writing.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Developments in the science and history of tides (OS/ACP/HGSS/NPG/SE inter-journal SI)”. It is not associated with a conference.

Instrument deployments and recovery were planned and executed with the assistance of the Bardsey ferry operator, Colin Evans, and by Ernest Evans, a local lobster fisherman and expert on Bardsey tidal conditions. The Deployment 1 observations were partly funded by the Crown Estate. The Landsat data were processed by Madjid Hadjal and David McKee at University of Strathclyde, and constructive comments provided by Phil Woodworth and two anonymous reviewers improved the manuscript.

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

Admiralty: Cardigan Bay Northern Part, Chart no. 1971, UK Hydrographic Office, Taunton , 2017.

Bills, B. G. and Ray, R. D.: Lunar orbital evolution: A synthesis of recent results, Geophys. Res. Lett., 26, 3045–3048, https://doi.org/10.1029/1999GL008348, 1999.

Dong, C., McWilliams, J. C., and Shchepetkin, A. F.: Island Wakes in Deep Water, J. Phys. Oceanogr., 37, 962–981, https://doi.org/10.1175/jpo3047.1, 2007.

Edwards, K. A., MacCready, P., Moum, J. N., Pawlak, G., Klymak, J. M., and Perlin, A.: Form Drag and Mixing Due to Tidal Flow past a Sharp Point, J. Phys. Oceanogr., 34, 1297–1312, https://doi.org/10.1175/1520-0485(2004)034<1297:fdamdt>2.0.co;2, 2004.

Egbert, G. D. and Erofeeva, S. Y.: Efficient inverse Modeling of barotropic ocean tides, J. Atmos. Ocean. Tech., 19, 183–204, 2002.

Egbert, G. D. and Ray, R. D.: Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data, Nature, 405, 775–778, https://doi.org/10.1038/35015531, 2000.

Egbert, G. D. and Ray, R. D.: Estimates of *M*_{2} tidal energy dissipation from
Topex/Poseidon altimeter data, J. Geophys. Res., 106, 22475–22502, 2001.

Green, J. A. M.: Bardsey – an island in a strong tidal stream, available at: https://osf.io/kvgur/?view_only=ff2d8bd12a61493aa1dfa9011ecdde81, last access: 4 June 2020.

Jakobsson, M., Mayer, L. A., Bringensparr, C., Castro, C. F., Mohammad, R., Johnson, P., Ketter, T., Accettella, D., Amblas, D., An, L., Arndt, J. E., Canals, M., Casamor, J. L., Chauché, N., Coakley, B., Danielson, S., Demarte, M., Dickson, M. L., Dorschel, B., Dowdeswell, J. A., Dreutter, S., Fremand, A. C., Gallant, D., Hall, J. K., Hehemann, L., Hodnesdal, H., Hong, J., Ivaldi, R., Kane, E., Klaucke, I., Krawczyk, D. W., Kristoffersen, Y., Kuipers, B. R., Millan, R., Masetti, G., Morlighem, M., Noormets, R., Prescott, M. M., Rebesco, M., Rignot, E., Semiletov, I., Tate, A. J., Travaglini, P., Velicogna, I., Weatherall, P., Weinrebe, W., Willis, J. K., Wood, M., Zarayskaya, Y., Zhang, T., Zimmermann, M., and Zinglersen, K. B.: The International Bathymetric Chart of the Arctic Ocean Version 4.0, Sci. Data, 7, 176, https://doi.org/10.1038/s41597-020-0520-9, 2020.

Kundu, P. K. and Cohen, I. M.: Fluid Mechanics, 2nd Edn., Academic Press, San Diego, 2002.

Magaldi, M. G., Özgökmen, T. M., Griffa, A., Chassignet, E. P., Iskandarani, M., and Peters, H.: Turbulent flow regimes behind a coastal cape in a stratified and rotating environment, Ocean Model., 25, 65–82, https://doi.org/10.1016/J.OCEMOD.2008.06.006, 2008.

McCabe, R. M., MacCready, P., and Pawlak, G.: Form drag due to flow separation at a headland, J. Phys. Oceanogr., 36, 2136–2152, https://doi.org/10.1175/JPO2966.1, 2006.

NOC: Tidal Analysis Software Kit, available at: https://www.psmsl.org/train_and_info/software/task2k.php (last access: 2 November 2020), 2020.

Piccioni, G., Dettmering, D., Passaro, M., Schwatke, C., Bosch, W., and Seitz, F.: Coastal Improvements for Tide Models: The Impact of ALES Retracker, Remote Sens., 10, 700, https://doi.org/10.3390/rs10050700, 2018.

Pugh, D. and Woodworth, P.: Sea-Level Science, Cambridge University Press, Cambridge, 2014.

Simpson, J. H. and Hunter, J. R.: Fronts in the Irish Sea, Nature, 250, 404–406, https://doi.org/10.1038/250404a0, 1974.

Stammer, D., Ray, R. D., Andersen, O. B., Arbic, B. K., Bosch, W., Carrère, L., Cheng, Y., Chinn, D. S., Dushaw, B. D., Egbert, G. D., Erofeeva, S. Y., Fok, H. S., Green, J. A. M., Griffiths, S., King, M. A., Lapin, V., Lemoine, F. G., Luthcke, S. B., Lyard, F., Morison, J., Müller, M., Padman, L., Richman, J. G., Shriver, J. F., Shum, C. K., Taguchi, E., and Yi, Y.: Accuracy assessment of global barotropic ocean tide models, Rev. Geophys., 52, 243–282, https://doi.org/10.1002/2014RG000450, 2014.

Stigebrandt, A.: Some aspects of tidal interaction with fjord constrictions, Estuar. Coast. Mar. Sci., 11, 151–166, 1980.

Taylor, G. I.: Tidal friction in the Irish Sea, Proc. R. Soc. Lon. Ser.-A, 96, 1–33, 1920.

Warner, S. J. and MacCready, P.: The dynamics of pressure and form drag on a sloping headland: Internal waves versus eddies, J. Geophys. Res., 119, 1554–1571, https://doi.org/10.1002/2013JC009757, 2014.

Wolanski, E., Imberger, J., and Heron, M. L.: Island wakes in shallow coastal waters, J. Geophys. Res., 89, 10553, https://doi.org/10.1029/jc089ic06p10553, 1984.

Woodworth, P. L., Shaw, S. M., and Blackman, D. L.: Secular trends in mean tidal range around the British Isles and along the adjacent European coastline, Geophys. J. Int., 105, 593–609, 1991.