We analysed relative dispersion of surface drifters released as pairs (six instances) or triplets (two instances) during three field experiments conducted in the German Bight in close proximity to wind farms. There is some tentative evidence that nearly exponential growth of relative dispersion (non-local dispersion) preferably occurs for drifter pairs that are most exposed to the influence of a wind farm. Kinetic energy spectra and velocity structure functions are analysed with regard to the assumption that turbulent energy could be injected by tides, possibly also via an interaction between tidal currents and wind turbine towers. Applicability of inertial range turbulence theory, however, can be doubted given distinct peaks of overtides observed in velocity power spectra. More comprehensive studies would be needed to better separate submesoscale effects of wind farms, tides and possibly baroclinic instabilities on observed drifter behaviour in a complex coastal environment.
Observing the spreading of drifters deployed pairwise is a powerful tool for analysing submesoscale flow structures. Submesoscale features are of interest for different reasons. From a theoretical point of view, studying mesoscale turbulent features helps understand the mechanisms of how energy in a 2-D quasi-geostrophic regime cascading towards larger scales
Drifters considered in this study.
Drifters released as pairs or triplets during three different field experiments in the German Bight. Initial and final locations were defined according to the list of locations communicated via the satellite communication network. Length: sum of the lengths of linear segments connecting observed drifter locations. Dist: linear distance between the first and the last drifter location observed.
In this study we analyse drift trajectories in the German Bight (North Sea) that cover just short periods (maximum 3.9 d, see Table
A recent summary of relative dispersion in the ocean was given by
The study area German Bight. Drifter experiments were conducted in close vicinity to the two wind farms indicated in the plot. Research station FINO3 provides hydrodynamic currents on a 10 min basis.
Based on data from experiments in the Mediterranean Sea,
The issue of either local or non-local dispersion at submesoscale seems to not yet have been solved.
The data studied here represent quite a complex situation in which effects of tides modified by travelling under shallow sea conditions, baroclinic instabilities on the scale of the Rossby deformation radius and anthropogenic effects of OWFs may possibly combine. Section
Surface drifter data were collected during three research cruises with RV
Initial distances between drifter pairs.
Distances “Dist” refer to the time of the first synchronous GP-based localisation (recordings every 20 min). See Sect.
Although Albatros MD03 drifters have been widely used during the last years
Drifter positions were obtained from the Global Positioning System (GPS) and transmitted to the lab via the satellite communication system Iridium. A lab test was set up to evaluate accuracies of GPS devices. Four drifters were deployed in a small water tank at fixed positions so that changes in their distances relative to each other (recorded for each of six pairs yielded from the four drifters) could directly be attributed to errors of GPS-based localisation. Based on 48 h of observations, the
In all field experiments sampling rates were about once every 20 min. For being able to calculate time-dependent separations between drifters, all drifter locations were linearly interpolated to regular 20 min time intervals. Drifter velocities were derived from these interpolated regular data.
On 21 May 2015, three drifters ( The three drifters are a subset of nine drifters released in May 2015 during a longer cruise (HE445) of RV On 29 June 2017, one drifter triplet ( Drifters were tracked for 1.9, 2.9 and 3.9 d, respectively. Another pair of drifters ( On 14/15 September 2017, five drifter pairs were deployed with spatial spacing of 5 nautical miles along a north–south transect to the west of OWF Global Tech I (Fig.
Eulerian surface currents observed at 2 m depth were available from research station FINO3 (
Power spectra of both Eulerian and Lagrangian drifter velocities have been calculated using the maximum entropy method (MEM) based on algorithms presented in
Besides all mentioned advantages, a drawback of the MEM method is that the statistical significance of the spectral peaks is difficult to assess. Nevertheless, to estimate the statistical significance of spectral peaks, a permutation test
Let
Relative dispersion is to be distinguished from absolute dispersion, a parameter from single-particle statistics that describes a particle cloud's spread around its centre of mass in combination with its drift from its release point. Differences between absolute and relative dispersion are relevant at medium timescales when two-particle velocity cross correlation depends on the character of Eulerian flows
In his seminal paper,
Both time evolution of relative dispersion
After a sufficiently long time, particle motions will become decorrelated and the power law behaviour of squared drifter separation will settle into normal diffusion
Following K41 scaling
For drifter simulations we employed the 2-D Lagrangian transport module PELETS
BSHcmod is run on a two-way nested grid covering both the North Sea and the Baltic Sea. In the German Bight its horizontal resolution is 900 m. Although the vertical coordinate in BSHcmod is dynamical
Grid resolution limits the scale of flow features that can be resolved. Drifter separations of less than 1 km are clearly beyond the resolution of BSHcmod. The general approach to overcome such a problem is to include sub-grid-scale turbulent processes via a scale-dependent random diffusion term. With such an approach being implemented, even particles released at the same initial location will start separating. Assuming that movements in the two dimensions are decoupled, in PELETS updates of a particle's position vector
Following
To improve performance at early times after drifter deployment, Eq. (
The objective of this study is to examine whether drifter separations observed during three different experiments reflect the presence of wind-farm-related turbulence. It is reasonable to assume that wind farm effects would increase with decreasing distance between drifter and wind farm. However, due to the large wind farm area this distance is not well defined. Table
Distances between drifters and wind farm
For drifters from set A, distances are evaluated relative to wind farm DanTysk; for drifters from sets B and C they refer to wind farm Global Tech I. For drifters
It must also be noted that all experiments were conducted in different years and therefore under completely independent weather conditions. Unfortunately, experiments can therefore not be interpreted as a set of realisations within a fixed experimental set-up. Section
Time evolutions of pairwise squared distances between members of drifter triplet
Trajectories of drifters
Figure
For all three pairs yielded from the drifter triplet, semi-log plots in Fig.
This experiment comprised two drifter releases at slightly different locations. One triplet (
Time evolutions of squared drifter separations are presented in Fig.
Figure
In experiment C, five drifter pairs were deployed at different locations along a south–north transect west of OWF Global Tech I (Fig.
Squared separations reveal large differences between the five drifter pairs (Fig.
Panels show for each drifter pair the time dependent squared distance between them. For drifter pair
Figure
Time evolutions of squared distances between drifters not released together (members of different drifter pairs). Colours used for segmentation of the observational period agree with those used in Figs.
Figure
Power spectrum of Eulerian velocities observed at research platform FINO3 (see Fig.
The spectrum shows a broadened peak around the frequency of the lunar semidiurnal tide
According to
Fig.
Power spectra of Lagrangian velocities observed for four selected drifters. Auxiliary black lines indicate reference spectral slopes. Vertical magenta lines indicate frequencies of tidal constituents.
While single-point velocity fluctuations are often close to a Gaussian distribution
According to Fig.
Probability distribution functions of
The limited number of drifters travelling pairwise motivates a consideration of Lagrangian velocity increments
Distributions of
Like in the Eulerian framework, distributions of Lagrangian longitudinal separation velocities look smooth and nearly normal with, however, slightly enhanced probabilities of large positive or negative values. Distributions obtained from different sets of drifters are again very similar. By contrast, distributions of transverse velocity components (Fig.
Returning to the Eulerian framework, Fig.
The most striking feature that occurs for both
For data from experiment C, values of the longitudinal structure function
Second-order velocity structure functions depending on drifter separation
We did not consider the Lagrangian counterparts of the Eulerian structure functions shown in Fig.
Taking drifter
Time evolution of squared separation between observed and simulated trajectories of drifter
Replacing the random walk by a random flight stochastic model (Eq.
Coastal currents can be complex and corresponding drifter experiments more site specific than open-ocean experiments evaluated by
In our analyses, noisy scatter of relative dispersion occurred at times when drifter separation was still below approximately 100 m. At this spatial scale, averaging over larger ensembles seems indispensable to achieve a stable statistical characterisation, and errors in drifter localisation may be relevant for the analysis. In the longer term, however, all drifter pairs we studied could clearly be classified into those with separation growing monotonically and others that did not show such regular behaviour. The latter group of drifters was found to combine those with the largest distances to the wind farm.
For 8 out of 12 individual drifter pairs, assuming that relative dispersion grows exponentially was found to be in reasonable agreement with observations. Except for one instance (
Squared distances from all pairs of experiment B are combined using a logarithmic time axis. Time series replicate the data already shown in Fig.
Pooling roughly 75 drifter pairs deployed with 5–10 m spacing in the Santa Barbara Channel,
Many studies find the Rossby radius of deformation to separate exponential growth of pair separation from a Richardson growth regime. Data from the Gulf of Mexico Surface Current Lagrangian Program (SCULP), for instance, provided a large set of 140 drifter pairs (the majority of them being chance pairs) with initial separation below 1 km
Also for drifters released near the Brazil Current,
Taken altogether, results on relative dispersion at submesoscale are still inconclusive. Uncertainties are high and results from different studies may be conflicting. According to
Rich data from the GLAD experiment conducted in the Gulf of Mexico from July to October 2012 provides 300 CODE drifters positions and two-point Lagrangian velocities with high resolution in both space (
By contrast, conducting a comprehensive analysis of surface drifter data from the NOAA Global Drifter Program (GDP),
Oscillatory tidal currents are dominant components of drifter transport in the German Bight (see Fig.
For OWF forcing being non-local (relative dispersion growing exponentially), turbulent energy should be injected at a spatial scale larger than drifter separation. In fact drifter separations stayed below the distance of individual wind turbines (approximately 800 m) for most of the time drifters were tracked. Also the OWF as a whole might generate relevant hydrodynamic features at a larger scale. An interesting event at the end of the journey of drifters
Finally, it is interesting to see also that the discrepancy between the observed trajectory
Some aspects of the Lagrangian velocity spectra in Fig.
In the Gulf of Mexico study the two spectral ranges were sharply separated at the frequency of a diurnal oscillation.
For high frequencies beyond the range of tidal signals a Eulerian power spectrum of even less than
The low-frequency part of the Eulerian spectrum in Fig.
According to Fig.
A second explanation
For isotropic turbulence the following relationship should relate the longitudinal and transverse second-order structure functions to each other
Figure
Simulation errors exceed simulated random spread of drifters. Simulations that employ an either zeroth-order (Eq.
By analysing 11 trajectory pairs released in the German Bight, trajectories could clearly be grouped into eight pairs that showed a long-term monotonic increase in drifter separation (for distances exceeding estimated uncertainty of GPS-based drifter localisation) and three pairs' distances of which changed in an irregular non-monotonic way (one pair travelled too short for a clear assessment). In all cases with monotonic behaviour, exponential growth of squared pair distance seemed a reasonable assumption, supported also by the fact that for seven pairs the fitted
Shelf sea conditions with irregular coastal geometry and bathymetry manifest themselves in characteristic hydrodynamic structures at specific spatial scales. Non-monotonic drifter separation could possibly be indicative of drifters getting trapped by coherent structures. Indeed, already at distances
A dedicated and more comprehensive field study would be needed to really pin down possible effects of OWFs on turbulent mixing in the German Bight. Longer drift times could reveal transitions between different regimes like non-local or local dispersion. Reference drifter pairs travelling windward of the wind farm would enable a better distinction between wind-farm-related and other turbulent effects in the complex coastal environment. The present study combined data from three independent experiments that were conducted under different weather conditions. With a sufficiently large number of drifters being deployed, conditioning on atmospheric forcing could further support the analysis.
The raw data sets A (HE445), B (HE490) and C (HE496) are freely available from
JF, JH and RC collected the field data, RC was in charge of data management including quality control and documentation. MQ performed the spectral analyses. UC provided numerical drift simulations and prepared the paper with contributions from the four co-authors.
The authors declare that they have no conflict of interest.
The three RV
The article processing charges for this open-access publication were covered by a Research Centre of the Helmholtz Association.
This paper was edited by John M. Huthnance and reviewed by two anonymous referees.