Fig 1.
Map of wind farm developments in the German exclusive economic zone of the North Sea.
Red denotes wind farms that are either operational or in construction, while blue denotes areas in the planning stage. The existing Bard and Global Tech (GT) farms are labelled, as well as the North Sea Buoy 3 (NSB3) measurement station. Contours are of mean water depth in m. Data obtained from the Bundesamt für Seeschifffahrt und Hydrographie (BSH).
Fig 2.
Basic sketch of the idealised setup considered.
A typical density profile is illustrated where stratification (i.e., change in ρ(z)) is confined to a pycnocline layer with thickness, b, at height, h, from the sea bed. Only a single foundation structure is shown in the sketch.
Table 1.
Summary of representative values for wind farm and stratification parameters.
Fig 3.
Map of estimated potential wind farm induced turbulence production in the German Bight region of the North Sea.
Contours and colours show in units of W kg−1 (a, b) and Pstr in mW m−2 (c, d). We have shown both low- and high-turbulence cases for the Bard 1 parameters with CD = 0.35 in (a, c), and Global Tech 1 parameters with CD = 1.0 in (b, d). The spatial pattern in (a, b) reflects the modelled distribution of
, and the panels differ only by a factor of 4.6 (the difference in wind farm parameters for the high- and low-turbulence cases). The location of both the Bard 1 and Global Tech 1 (GT) farms are shown, along with the North Sea Buoy 3 (NSB3) measurement station. Grey areas are not included because they are on average less than 10 m deep, or comprise tidal flats or estuaries.
Fig 4.
Solution for the time-dependent pycnocline model 2.
The results of both low- and high-turbulence simulations are identical but span different time periods, since the solutions collapse if the dimensionless time t* is used. The evolution of the dimensionless density profile 2(ρ − ρ0)/Δρ is shown in (a), along with the decrease in the stratification over time in (b). Also shown in (b) are the constant pycnocline thickness model mixing rates given by Eq (13) with b = 6 m and b = H = 40 m for comparison (slopes of red lines). In the low- and high-turbulence cases of (a), density profiles are identical, and plotted every 18 and 4 days, respectively.
Table 2.
Empirical constants used in the one-dimensional mixing model.
Fig 5.
Results of the one-dimensional mixing model 3.
(a) The evolution of the dimensionless density profile, 2(ρ − ρ0)/Δρ, as a complete mixing of the stratification occurs. The results of the low- and high-turbulence simulations show very similar results when the dimensionless time, t* is used. The time to complete mixing is found to be 469 and 107 days for the low- and high-turbulence cases. (b) The evolution of ϕ with t* where the red lines indicate the equivalent constant mixing efficiency lines at fixed pycnocline thickness (b = 6 and 9 m are shown). (c) Bulk mixing efficiencies 〈Rf〉, and the corresponding effective pycnocline thicknesses, b. Slight differences in mixing efficiency for the low- and high-turbulence cases are seen.
Table 3.
Summary of the mixing time scale estimates, τmix.
Fig 6.
Glider positions for the 2012 and 2014 campaigns.
Fig 7.
Glider measurements of North Sea stratification, summer 2014.
The upper panel shows the conservative temperature in depth and time. The pycnocline region is indicated by the light coloured lines, corresponding to the b1 definition, and the depth of the sea bed is indicated with dark grey fill. The bottom panel shows thermocline thickness using two different methods (b1, b2), and total temperature difference, ΔT. The approximate times of Storm Bertha are indicated by the dark bar at the top of the panel, and are defined by times of sustained wind speeds in excess of 10 m s−1.
Fig 8.
Histogram of the period of longest continuous stratification from the model of van Leeuwen et al. [5].
The data are presented for the location 54.5°N, 7.0°E near to the NSB3 measurement station. Mean and median values for the time of seasonal stratification are 85 and 80 days, respectively. Data supplied by S.M. van Leeuwen, Cefas (UK); contains public sector information licensed under the Open Government Licence v3.0, UK Crown Copyright.
Fig 9.
Measurements showing the build up of stratification, ϕ, over the summer months (data points) versus the rate of stratification removal by the turbine foundation structures (straight lines).
Measured stratification data are from a thermistor mooring at NSB3 in summer 2009 (black points), and glider data collected close to NSB3 from summer 2014 (green points), and from larger scale transects passing through NSB3 in summer 2012 (blue points). None of these stratifications are expected to be affected by OWFs. The lines plot the mixing power of the turbine foundations at two different thermocline thicknesses, b = 6, 9 m, based on results from models 1 and 3 using the slope Rf Pstr b/H, or equivalently the slope 〈Rf〉Pstr. Also, both the low- and high-turbulence cases are shown with the dashed and solid lines, respectively. All lines are shown starting from an arbitrary initial date of May 1. Mooring data from 2009 were obtained from BSH.
Fig 10.
Measurements showing the difference in (a) temperature, (b) salinity, and (c) density across the pycnocline over the summer months at NSB3.
These differences were calculated between measurements in the surface layer at 4 or 6 m deep (depending on the availability of data) and at depths of 35 m in the lower layer. Data were obtained from BSH.
Fig 11.
(a) Map of residual (depth-averaged) currents in the German Bight with contours indicating the magnitude, and arrows indicating direction and magnitude. The averaging period is taken over all years between 1958-2014. The dark outlined area represents the study region referred to in the text. (b) Histograms showing the distribution of times (τadv) that correspond to the minimum residence time within the study area of 70, 50, and 30% of the drifters. The mean values of each distribution are indicated by the lines at the top, and bin edges are at τadv = −5, 5, 15, 25, ….
Table 4.
Estimates of the reduction in stratification Δϕ/ϕ0.