Comparison of ADCP observations and 3D model simulations of turbulence at a tidal energy site

Field measurement of turbulence in strong tidal currents is difficult and expensive, but the tidal energy industry needs to accurately quantify turbulence for adequate resource characterisation and device design. Models that can predict such turbulence could reduce measurement costs. We present a comparison of compare a Regional Ocean Modelling System (ROMS) simulation with acoustic Doppler current profiler (ADCP) measurements from a highly-energetic tidal site: the West Anglesey Demonstration Zone off the Welsh coast. This comparison aims to validate ROMS’ prediction of turbulence parameters shows the extent to which turbulence can be quantified by ROMS, using the conventional k − ε turbulence closure model. The turbulence closure scheme used in ROMS was the conventional k − ε model. The deployment period for the ADCP was 19/09/14 to 19/11/14 Both model and observations covered the same time period, encompassing two spring-neap cycles, and the simulation covered the whole ADCP deployment. Turbulent kinetic energy (TKE) density, k, was ∗Tel: +44 1792 606612 Email address: M.Togneri@swansea.ac.uk (Michael Togneri) Preprint submitted to Renewable Energy March 20, 2017 M AN US CR IP T AC CE PT ED ACCEPTED MANUSCRIPT calculated from measurements using the variance method; turbulent dissipation, ε, was calculated using the structure function method. Measurements show that wave action, omitted from the ROMS model, dominates turbulent fluctuations in the upper half of the water column; comparing results for deeper water, however, shows very strong agreement. A best fit between ROMS and ADCP results for mean velocity yields R = 0.98; for a fit of TKE values, R is 0.84 when strongly wave-dominated times are excluded. Dissipation agrees less well: although time series of ε are well-correlated (R between 0.86 and 0.95) at similar depths, ROMS estimates a greater magnitude of dissipation than is measured, by a factor of up to 4.8.


M A N U S C R I P T
A C C E P T E D ACCEPTED MANUSCRIPT calculated from measurements using the variance method; turbulent dissipation, ε, was calculated using the structure function method. Measurements show that wave action, omitted from the ROMS model, dominates turbulent fluctuations in the upper half of the water column; comparing results for deeper water, however, shows very strong agreement. A best fit between ROMS and ADCP results for mean velocity yields R 2 = 0.98; for a fit of TKE values, R 2 is 0.84 when strongly wave-dominated times are excluded. Dissipation agrees less well: although time series of ε are well-correlated (R between 0.86 and 0.95) at similar depths, ROMS estimates a greater magnitude of dissipation than is measured, by a factor of up to 4.8.

Introduction
Tidal energy converters (TECs) generate renewable energy electricity from tidal currents, with most designs using similar physical principles to conventional wind turbines. However, the marine environment in which they are deployed and operate poses its own set of technical hurdles that must be addressed [1,2,3]. 5 Turbulence in tidal currents, which differs from atmospheric turbulence, is one of these challenges, and an important one for the development of TSTs TECs due to its impact on loading, reliability and fatigue life [4,5]. Oceanographic modelling of turbulence has generally focussed on vertical mixing for transport of sediments or nutrients [6,7] rather than the highly-energetic turbulence typical 10 of sites with strong tidal currents that are likely candidates for TEC deployment.
In this paper, we present a comparison of turbulence measurements from such a site to estimates from a basin-scale numerical model. Deploying, operating and retrieving instrumentation suitable for turbulence measurements in marine currents is an expensive and time-consuming process; by showing the extent to 15 which turbulence at these sites can be predicted by modelling, such measurement campaigns can be better targeted and their associated costs thereby reduced., M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT but the highly site-specific nature of marine turbulence means such measurements are vital to understanding turbulence in tidal currents.
If it can be shown, by comparison with measured data, that oceano- 20 graphic modelling can predict turbulence with some accuracy, then such models can be used to aid in targeting measurement campaigns at the most beneficial sites and times. Confidence in oceanographic models' ability to estimate turbulence at TEC deployment candidate sites will also mean that its predictions would be suitable for defining the inflow conditions of 25 smaller-scale models of TEC arrays or even individual devices [8,9].
The site for this study is the West Anglesey Demonstration Zone (WADZ) off the coast of Wales, which has been designated for the development of tidal power by the Crown Estate. Measurements were taken with an RDI Sentinel through the deployment period, giving a spring range of around 5m, and peak depth-averaged spring currents were 2.48 2.5ms -1 . There was a blanking distance of 1.89m between the first bin and the seabed transducer head, and subsequent bins had a vertical separation of 0.6m. A fifteen-minute burst of 40 data was collected every hour; during the burst, the measurements were taken at a rate of 2Hz. The ping frequency was 614.4kHz.
The tidal hydrodynamics were simulated using the 3D Regional Ocean Modelling System (ROMS), which uses finite-difference approximations of the Reynolds-45 Averaged Navier-Stokes equations with hydrostatic and Boussinesq assumptions [10, 11,12], and is regularly used in tidal-stream energy resource studies [13,14,15]. Turbulence is modelled in ROMS by a two-equation scheme. The M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT first equation is for the transport of turbulent kinetic energy (TKE), k; the second equation represents a generic length scale (GLS) that can be tuned to a 50 variety of standard turbulence models [16]. For this study, the well-established k − ε model was implemented.

Turbulence measurement using ADCPs
ADCPs are a widely-used tool for the measurement of marine currents. By measuring the Doppler shift in the backscattered signals from an array of acoustic beams, they are able to measure three-dimensional velocities [18,19,20]. It is possible to calculate a range of turbulence parameters using a variety of 80 methods. The variance method is a standard technique for estimating TKE density and Reynolds stresses [21,22], and dissipation can be estimated by structure function analysis [23] or spectral analysis [24]. Time-and lengthscales can be estimated from the time-lagged autocorrelation of the beam measurements [25].
The use of ADCPs for surveying turbulence at planned or current tidal stream 85 deployment sites is a well-established method, both used alone [26,27,28,29] or in combination with other techniques and instrumentation [30,31].
where the summation is over the four off-vertical beams, ξ is a parameter that characterises the anisotropy of the flow, and θ is the inclination angle of the beams. Following the work of Nezu and Nakagawa [32], we set ξ to 0.1684.

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This formulation assumes that the device accurately measures the true velocity in the fluid. In reality, instrument noise will introduce an error between the true and measured along-beam velocities. This instrument noise can be regarded as a normally distributed, zero-mean random error. For calculation of 100 mean velocities, the time-averaging process means that no bias is introduced, as the noise is zero-mean. However, in calculating the variance the instrument noise becomes more significant. If we write the fluctuation velocity measured by the i th beam, b i , as the sum of a true fluid velocity β i and Gaussian noise M A N U S C R I P T

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N , then we find that: Since the noise is a property of the instrument, it is reasonable to assume that it is uncorrelated with the flow; thus we can therefore set Cov(β i , N ) to 0. Thus, the estimated variance from the beam measurements will have a positive bias relative to the true velocity variance, and our calculated value of TKE from equation 1 will be greater than it ought to be. Our dataset includes 110 many measurements in still water, at which times the TKE will be negligibly small. Any non-zero TKE estimates at such times are therefore attributable to instrument noise, and we use the values of these estimates to quantify the TKE bias. In this way, we find that the TKE estimates have a positive bias of 9 × 10 −3 J · kg −1 ; all ADCP TKE estimates presented in this paper have been 115 corrected to account for this bias.

Dissipation
Dissipation can be estimated using structure function analysis, a method based on spatially-separated velocity measurements. It was originally developed for use in atmosphere [33], but it has been shown to be applicable in a variety of 120 marine conditions [23,34]. We start by defining the structure function D(z, r) as the time-mean value of the squared velocity difference between two points separated by a distance r: On the condition that the maximum separation, r, is on the scale of the inertial subrange, the expected dependence of D(z, r) on r is related to the 125 dissipation: Here N is an offset term that arises due to instrument noise and C ν is an empirically-determined constant; following Wiles et al. [23] and Mohrholz et al.
[ 34], we take C ν = 2.1. It is then straightforward to carry out a least-squares fit of the calculated D(z, r) values from equation 3 to the relation specified in 130 4, and from its slope get an estimate of ε. The maximum separation used for this fit is 5.1m in the along-beam direction (i.e., 8 bins); we have confirmed that this separation lies within the inertial subrange by examination of the turbulent spectra.

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The model domain, shown in figure 2, covers the area between 51°N to 56°N, and from 7°W to 2.7°W. It uses ten vertical layers (sigma coordinate system) evenly spaced throughout the water column and an orthogonal C-grid at 1 /240°fi xed longitudinal resolution (2012 × 1033 interior points, giving a grid spacing of approximately 300m). Digitised Admiralty data, at 200m horizontal 140 resolution and corrected for mean sea-level variations [35], was interpolated to the computational grid, with a minimum water depth of 10m. There was no wetting and drying as the geographic scale of inter-tidal regions was relatively small in relation to the model resolution and extent of the Irish Sea [15]. Our ROMS model has previously been successfully applied to Irish Sea tidal-stream resource analysis and is well validated [35], and so the model is described only briefly in this paper. A drag coefficient C D = 0.003 was assumed within the quadratic friction model parameterisation, which is consistent with previous ROMS studies of energetic 170 tidal sites (e.g., Neill et al. [13]). Similar results have been found when comparing turbulence closure and GLS schemes in ROMS [16]. This is the reason for the choice of turbulence closure GLS model tuned to the k − ε turbulence model, with standard parameters: p = 3, m = 1.5 and n = -1 (for further details see Warner et al. [16]).

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Model validation is detailed in Lewis et al. [35] and is only summarised here.
Results were compared with seven tide gauges from the National Tidal and Sea Level Facility (see www.ntslf.org), and the model was shown to have an 4% accuracy in simulating the amplitude of the major semi-diurnal lunar con-180 stituent, M2, (0.11m RMSE), with M2 phase accurate to within 4°; for the major semi-diurnal solar constituent (S2) tidal height was simulated with 9% accuracy (0.08m RMSE) and phase with 9°accuracy. Nine depth-averaged, and 131 depth-specific, M2 tidal current stations were used to validate simulated tidal currents, with a 10% velocity error and a 4°-7°phase error found.

Results
We first compare the measured and modelled mean flow properties. The principle semi-diurnal lunar (M2) tidal ellipse analysis of depth-mean tidal velocity data from the ADCP deployment compared to that simulated by our ROMS model gave a RMSE of 5% for C max (the semi-major ellipse velocity 190 component) and 0% C min (the semi-minor ellipse velocity component). The inclination of the current ellipse error was 3°and phase error (degrees relative to Greenwich) was 6°: we are therefore satisfied that our model has accurately captured the mean flow dynamics at the measurement site.  The ability of ROMS to capture mean flow velocities is already well attested [13], and this is borne out by the results presented in the lower panel of figure This does not extend down to the seabed due to the ADCP's blanking distance, the ADCP itself and its support frame. ROMS discretises the water column into ten sigma layers, which correspond to different depths as the sea level changes over the tidal cycle. We use the lower five sigma layers for our estimate 220 of column-mean TKE; this depth range always starts at the seabed but its maximum value ranges from 16.8m to 18.8m over the simulated period. We can see that the agreement between ROMS and ADCP measurements is quite satisfactory. The spring-neap cycle is clearly apparent in the TKE data [13]), which, as shown in figure 6, is not due solely to differences in the mean flow: we see that TKE is consistently higher on ebbs than floods even when mean velocity magnitude is the same. Concomitantly, turbulence intensity is greater on ebbs than on floods, on average by 5.4% to 5% 8% when looking at ROMS estimates or by 6.4% to 5.9% 9% when looking at ADCP measurements. sense. Note that in calculating these PDFs we have applied the 95 th percentile 280 condition on waves. We see that there is good agreement at the high-energy end of the PDFs, but less so at lower TKE values. Unsurprisingly, this means that when we divide the data points into slacks, ebbs and floods, the non-slack PDFs agree quite closely with one another but the slacks show a greater disparity. 285 We can also examine the comparative distributions of TKE between ROMS and ADCP results using q-q plots, as seen in figure 10. Visualising the results in this manner reinforces the conclusions we have drawn from studying the probability distributions themselves. For low TKE values the ADCP measurements tend to be significantly higher than ROMS estimates, which is visible as the are high, all data points on the q-q curve lies below the line of equality.

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In addition to the temporal variation and distribution of the TKE, we are interested in its vertical variation. Figure 11 compares profiles of TKE density from the ROMS model and ADCP measurements. It also shows how the vertical profile from ADCP data varies depending on how strictly high-wave conditions are excluded from consideration. Obviously this has a more significant effect in 300 the upper half of the water column: in this region, the 95 th percentile profiles exceeded the 75 th percentile profiles by 68% on the flood and 54% on the ebbs, whereas in the lower half the differences were only 9% and 4% respectively.
The quantitative agreement between ROMS and ADCP is satisfactory for this deeper section: the ADCP data exceeds the ROMS prediction by 13% on ebbs  The agreement in dissipation is less satisfactory. Figure 12 shows comparisons of dissipation time series at four locations in the lower half of the water column. As we mention above, ROMS sigma layers and ADCP bins do not

Discussion
We have found that the ROMS predictions of TKE match the measured values well over the whole tidal cycle, although at times of relatively low turbulence the ADCP measurements are higher than the estimates produced by ROMS. This is visible in the low end of the probability distributions depicted 325 in figure 9; we can also see it in the 'drooping tail' of the q-q plots in figure   10. We can conclude, then, that at these times either the measurements are erroneously high or the numerical predictions too low.
A systematic overestimation of TKE by the ADCPs would suggest that the 330 M A N U S C R I P T A C C E P T E D This suggests that the discrepancy must be due to an underestimate of TKE in the numerical model. However, recall that with the variance method it is not possible to distinguish between fluctuations due to turbulence and due to other sources, as is clearly illustrated by the dominance of wave effects seen to this as at least a partial explanation.

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The importance of wave effects is one of the most striking observations from ADCP data. Previous studies of turbulence at energetic tidal sites based on ADCP measurements [17,29] did not indicate such strong influence by waves, but these were in more sheltered bodies of water with much shorter fetch and turbulence throughout much of the water column, to the extent that some methods of analysing ADCP data cannot be applied: specifically, spectral analysis for estimation of turbulent dissipation. Spectral analysis is a well-known technique for determining the turbulent dissipation [24,27], based on Kolmogorov's theory of the inertial subrange which 20 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT asserts that, for some range of frequencies (or wavenumbers), the power spectral density (PSD) of turbulent velocity fluctuations will exhibit a -5/3 power-law dependence on frequency. In this subrange, the PSD is a function only of the 370 frequency and the turbulent dissipation rate, ε. Thus, by fitting the spectrum to the expected slope, it is possible to obtain an estimate of ε. However, as can be seen in figure 14, there is a large, broad peak in the middle of the expected inertial subrange. This peak coincides with the median wave period during the ADCP deployment: it is reasonable to conclude that this corresponds to wave 375 activity during the measurement period. Note that Doppler noise begins to dominate the spectrum as we approach the Nyquist frequency of 1 Hz, so it is not possible to perform a fit in this part of the spectrum.
It may be possible to filter out the wave effects, either in a simple bandpass If this is the case, the observations presented in this paper suggest that, for 390 TEC deployment sites that are not sheltered from waves, the effects of waves on fatigue load will be of much greater concern than the effects of turbulence in the marine currents. This is obviously dependent on the location of the TEC within the water column: seabed-mounted devices that are small relative to the total water depth will be more sensitive to the turbulence in the tidal currents, 395 but larger devices, and floating or semi-submersible designs of all sizes, will be far more affected by wave action.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT
Earlier work on validating the turbulence models of ROMS for highly-energetic tidal sites [17] found that dissipation was well-matched between predictions and 400 measurements, while turbulent kinetic energy was not captured as satisfactorily.
Differences in TKE were attributed to the limited lengthscales represented by k in the turbulence closure model; correcting the ROMS estimates based on this assumption led to a much better agreement.

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The work we present here, however, finds that ROMS estimates of TKE are very well corroborated by the measured values, and no similar correction term is required. Dissipation, on the other hand, is found to differ significantly between model and measurements. It is not clear why this is. The structure function method is being applied in an appropriate manner: based on spectral 410 analysis, the separation distances used in its calculation lie within the inertial subrange, and the fits to the expected 2 /3 slope are satisfactory. If instead the problem lies with ROMS overestimating dissipation, then we would also expect that the turbulent production should be much greater, but there is no indication that this is the case. 415

Conclusions
To conclude: We have found that ROMS estimates of turbulence, as measured by TKE, agree very well with ADCP measurements at a site with strong tidal currents across two complete spring-neap cycles. There are a few caveats to • Two months of ROMS and ADCP turbulence data at an energetic tidal site are compared.
• Wave action is strongly dominant in the upper half of the water column.
• Good agreement between predicted and measured turbulent kinetic energy at low depths.
• Dissipation predictions show poorer agreement.