Evaluation of turbulence-related high-frequency tidal current velocity fluctuation

Evaluation of turbulence-related high-frequency tidal current velocity fluctuation P. Garcia Novo, Y. Kyozuka, M.J. Ginzo-Villamayor Version: Accepted Manuscript HOW TO CITE García Novo, P., Kyozuka, Y., Ginzo-Villamayor, M.J. (2019). Evaluation of turbulencerelated high-frequency tidal current velocity fluctuation Renewable Energy. 139. pp. 313-325. FUNDING The authors would like to thank the Ministry of Environment of Japan for permission to publish of the data used in this study, which were obtained through the project for Promotion of Realization of Tidal Current Power Generation supported by the ministry in 2014 and 2015. © 2019 Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc- nd/4.0/ Abstract1 Within the development needed for economy viability of tidal stream energy,2 adaptability of laboratory converters to sea flow conditions is a milestone. The3 objective of this work is to investigate the high frequency fluctuations in currennt4 velocity magnitude and direction related to the turbulent nature of the flow and5 present a new method for their prediction. With this purpose, high frequency data6 measured by two ADV (32 Hz) and two ADCP (8 Hz) at four different points in the7 sea area surrounding Goto Islands (Japan) are analyzed. The data were divided in8 short-time samples (3-minutes data for ADV and 5-minutes data for ADCP) and9 treated separately. Velocity magnitude fits a normal distribution, with prediction10 levels higher than 95% for a margin of error of 0.25 m/s when comparing different11 percentiles between 0.1 and 99.9. Flow direction is analyzed in terms of opening12 angle between two representative percentiles equidistant from the median(99.9-0.1,13 95-5,. . . ), giving as a result a leptokurtic distribution, more outlier-prone than nor-14 mal. Empirically, for opening angles 99.9-0.1, 97.7-2.3 and 95-5, slopes of 6.79 (615 in normal distribution), 4.17 (4) and 3.38 (3.29) were found, with results similar to16 a theoretical normal distribution for narrower angles. The new prediction method17 for high frequency fluctuations is based in this direct correlation between velocity18 magnitude and direction fluctuations with turbulence intensity and transverse tur-19 bulence intensity, respectively. These two parameters can be estimated indirectly20 by numerical models, giving rise to a tool for the prediction of turbulence-related21 high frequency fluctuation.22 Keywords— Tidal energy, Turbulence, ADCP, ADV23 1 Evaluation of turbulence-related high-frequency tidal24 current velocity fluctuation25 Patxi Garcia Novo, Yusaku Kyozuka, Maria Jose Ginzo Villamayor26 January 21, 201927 1 Introduction28 Tidal stream energy has been presented as one of the most promising renewable energy29 options among other reasons due to the high prediction level of available resource. Tides30 can be defined as the sum of constituent components as a result of the interaction31 between Earth, Sun and Moon gravitational attractions, expressed mathematically as32 [1]:33 ζ= n X i=0 aicos(ωit+ϕi) (1) being t the time; aithe angular frequency dependent on the relative movement between34 Earth, Sun and Moon; and ωiand ϕithe amplitude and phase, respectively, for each35 tide constituent, which varies according to the geographical position. This definition has36 been a base for widely proven tide level prediction methods [2, 3].37 Harmonic forcing simulating tide conditions has been also used for numerical modelling-38 based tidal stream energy assessment works [4, 5, 6], with good agreement both in terms39 of water level [4] and tidal velocity [5, 6] when comparing 3-minutes averaged [6] mea-40 sured data with prediction results.41 Nevertheless, when thinking on energy extraction, not only tides but also currents42 must be taken into account. In this regard, despite the capability of harmonic analysis43 based approaches to predict averaged tidal current velocities [5, 6], there are certain44 current properties (three-dimensional nature, effect of local geomorphology and non-45 sinusoidal characteristics such as sub-tidal variations, supra-tidal variations or turbu-46 lence) differentiable from tides which limit these methods for current evaluation. This47 issue was already pointed a few decades ago by Godin [7], who concluded that currents48 cannot be predicted with the same level of precision as the tide. These variations from49 the harmonic analysis-based estimation have meaningful consequences in the turbine50 loads [8], making of this a key point for tidal stream energy technologies. A case that51 clearly exemplifies this statement is the failure of an OpenHydro turbine in the Bay of52 Fundy in November 2009, due to tidal flows that were two and a half times stronger53 than expected [9].54 2 With the aim of getting a better understanding of tidal currents, Polagye et al [10]55 analyzed high frequency velocity data measured in Puget Sound, observing two kinds56 of variations. First, non-sinusoidal fluctuations over time scales around 1 hour, which,57 although cannot be estimated by harmonic analysis, exhibit a certain degree of peri-58 odicity, allowing its description by site-specific empirical functions which must include59 ebb and flood variations or diurnal inequality. Second, turbulence related fluctuation60 over time scales under one minute. This fluctuation was found more important than the61 first one in terms of magnitude (over 0.5 m/s for peak currents) and it was considered62 unpredictable.63 Regarding this second fluctuation type, although its effect on energy potential esti-64 mation is lower, its study is necessary for turbine design considerations, such us blade65 loads, support structures, seabed connections [11] or devices stabilization on the bot-66 tom by the generation of down force from the tidal flow [12]. For these reasons, several67 authors have carried out turbulence studies at potential tidal stream energy exploita-68 tion sites based on velocity measurement. In these studies, besides the calculation of69 representative turbulent related parameters such as turbulence intensity, turbulent ki-70 netic energy or integral time and length scales, whose characterization is also crucial for71 turbine design due to its effect on blade loads, power and thrust coefficients or wake72 characteristics [13, 14, 15, 16], high frequency velocity fluctuation was also analyzed. In73 this respect, velocity fluctuations within a range higher than 1 m/s during a 1-minute74 period for which averaged value was approximately 2 m/s were found in the streamwise75 signal of an ADV measurements in the Sound of Islay [17]. Also, in Kobe Strait [18],76 instantaneous streamwise velocities between 0.5 m/s and 2.5 m/s were observed with an77 ADCP for a 5-minute averaged value of 1.5 m/s.78 Recently, the efforts of tidal energy researchers have been focused on the prediction of79 turbulence conditions at a given location. On this point, results from turbulence models80 simulating current conditions at tidal stream energy sites able to estimate turbulent81 kinetic energy have been recently published [19]. In terms of velocity fluctuation, Harding82 et al [11] presented a long-term prediction method for extreme velocities (higher and83 lower than the averaged) based on 32 Hz and 2 Hz velocity data measured by an ADV and84 an ADCP, respectively, simultaneously and at the same point in Puget Sound. With one85 month data, a 50-year velocity perturbation from a 64s mean velocity could be predicted.86 However, the results show considerable discrepancies between the measurements of both87 devices and “several years of data is required to perform the analysis to an acceptable88 level of confidence”.89 In this context, this study attempts to seek a new method to predict turbulence90 related velocity perturbations both in terms of magnitude and direction, thus reducing91 the need for in-situ measurement, following the Godin [7] suggestion that “the study92 of currents is essentially a research problem and should not be considered a matter for93 routine data processing at the clerical or technical level”. The present proposal is based94 on the analysis of data measured by two 32 Hz ADVs (Acoustic Doppler Velocimeter)95 and two 8 Hz ADCPs (Acoustic Doppler Current Profiler) at four different points in96 Goto Islands, Japan.97 3 2 Materials and Methods98 2.1 Location99 Located in Nagasaki Prefecture, southwestern Japan, between the Strait of Korea and100 the Pacific Ocean, Goto Islands is an archipelago formed by 140 islands (see Fig.1). Five101 of these islands form four main channels (from west to east, Tanoura Strait, Naru Strait,102 Takigawara Strait, and Wakamatsu Strait). The big amount of water passing through103 these channels generates strong currents, making of this area a good location for tidal104 stream energy exploitation. Therefore, two of these channels (Tanoura Strait and Naru105 Strait) have been designated as a tidal energy test site by the Japanese government [20].106 At this area, the tide type is typically mixed mainly semidiurnal, being M2 the main107 tidal constituent. Figure 1: Tanoura Strait, Naru Strait and Kobe Strait in Goto Islands, Nagasaki Prefecture, Japan 108 The areas selected for measuring devices installation are Naru Strait, Tanoura Strait109 and Kobe Strait, a small semi-enclosed channel formed by an inner island in Wakamatsu110 Strait (for a more detailed description of these channels refer to [18, 21]). The importance111 of the first two channels lies in their high tidal stream energy potential, as mentioned112 in the previous paragraph. Kobe Strait, due to its lower depth and current velocity,113 could be a considerable option for testing low-velocity converter devices or in an earlier114 development stage. A brief description of the four measuring locations for this study is115 4 presented below.116 2.2 Data measurement117 One Nortek Vector ADV was operating during 8 days from November 17th at 0:00h to118 November 24th at 17:10h in 2014 in (32◦46’45.2”N, 128◦50’3.1”E; hereafter P1), Tanoura119 Strait, between Fukue Island and Hisaka Island. The dimensions of this channel are 6120 km length and 2 km width, approximately. Water flows in a SE-NW direction during121 flood tide and vice versa during ebb tide, with minor variations due to very local geomor-122 phologic characteristics. In the southern mouth, water move is affected by Tatarajima123 Island, dividing the flow into two bifurcations. The sea bottom is mainly rocky. Focus-124 ing on the measuring point, it is located at nearly 200 m from Hisaka Island western125 coastline, where the averaged depth during the data collection period was 26.1 m. The126 ADV installed at 3 meter from the sea bottom at this point was set to measure during127 the first 3 minutes of every 10-minute period, followed by 7 minutes in stand-by. This128 device collects high resolution velocity, temperature and pressure data. The internal129 sampling rate is 250 Hz, while the sampling output rate was set as 32 Hz, thus collecting130 5760 data for every 3-minute measuring period. The sampling volume dimensions are131 15 mm diameter and 5 mm height. Its velocity measurement accuracy is 0.5% of the132 measured value ±1 mm/s.133 Simultaneously, in Naru Strait (32◦49’41.1”N, 128◦58’56.4”E; hereafter P2) a second134 Nortek Vector ADV, with the same characteristics above presented, was operating under135 analogous setup conditions. Naru channel length and width are approximately 7 km136 and 2 km, respectively, with the exceptions of the narrowing due to Kagaribisaki cape137 and Suetsujima Island. As with Tanoura Strait, bottom is mainly rocky and the main138 axis orientation is NW-SE. The averaged depth during the 8-days period at the ADV139 measuring point, nearly 300 m east of Warabikojima Island, was 24.6 m. At this same140 channel, at approximately 200 m east from the ADV measuring point (32◦49’38.8”N,141 128◦54’3.7”E; hereafter P3), one Nortek Signature 1000 AD2CP was operational from142 April 14th until May 24th, 2016. Nevertheless, it must be said that quality of data143 collected during the last 15 days is not good enough to guarantee reliable results, so144 they were removed for further analysis. This device beam frequency and width are 1145 MHz and 2.9◦, respectively. The measuring sampling volume for each beam and layer is146 defined by a polyhedron of 142 mm height and 212 mm length, its minimum accuracy is147 a 0.3% of the measured value and the velocity resolution is 0.1 cm/s. This AD2CP was148 set to cyclically measure with an 8Hz sampling output rate during 5 minutes followed149 by 15 minutes in standby. The number of vertical layers is 22, 1 m width each one, with150 a blanking distance of 1 m. Since the time averaged depth during the measuring period151 was 35.0 m, approximately two-thirds of the water column were covered.152 The same AD2CP had been operational from February 27th to March 14th, 2014,153 at (32◦52’40.81”N, 129◦01’46.79”E; hereafter P4) in Kobe Strait. At this point, where154 the time averaged depth during this 15-day period was 18.0 m, 36 vertical layers (0.5 m155 thickness) were measured with the same timing and frequency measuring setup (8 Hz,156 5-minute on, 15-minute off) as previously presented for P3. The blanking distance was157 5 set as 0.1 m. Due to the water column width limitations, data measured for the seven158 last vertical layers counting from the bottom (29 to 36) are unreal and not considered for159 the water flow analysis. Likewise, due to bottom interaction, an accurate measurement160 cannot be guaranteed in the deepest layer, so it is discarded.161 2.3 Data treatment162 2.3.1 Signal pretreatment163 Previous to the velocity fluctuation and turbulence analysis, a data quality pretreatment164 is necessary. In the four cases, this pretreatment consisted of two steps: denoising and165 despiking. Noise was eliminated following the manufacturer recommendations, replacing166 points for which correlation is under 70% for the ADV signals [22] and under 50% for167 the AD2CP signals [23] by the linearly interpolated values. The already denoised signal168 was treated with a Kernel Density based algorithm developed by Islam and Zhu [24] and169 tested in this kind of data despiking. After noise elimination, 5-minute (ADCP) and 3-170 minute (ADV) averaged values for the three signals, one for each component of velocity,171 were calculated. Based on these averaged values and using a least square method which172 guarantees that the mean value of all the 5-minute or 3-minute averaged transverse173 velocities during the measuring period is null, a rotation angle is calculated to convert174 the original data to a streamwise (parallel to N-S axis), transverse (perpendicular to175 N-S axis) and vertical coordinate system. Rotation angles were calculated separately176 for flood and ebb tide and for each measuring point and vertical layer (in the case of177 ADCP). This data rotation allows a clearer analysis of the flow characteristics.178 2.3.2 Velocity magnitude fluctuation179 In order to analyze only turbulence-related variations and minimize the influence of180 other fluctuation generator factors, every data block corresponding to a 3-minute mea-181 suring period for ADV data and 5-minute measuring period for ADCP data was treated182 separately. The velocity magnitude fluctuations are parameterized by percentiles. For183 each data block, percentiles for each multiple of five from 5 to 95, as well as those per-184 centiles corresponding with sigma integer multiplying factors for a theoretical normal185 distribution (0.1, 2.3, 15.9, 84.1, 97.7, 99.9), are extracted.186 2.3.3 Current direction fluctuation187 The analysis in the current direction fluctuation is analogous to the presented for velocity188 magnitude. Considering 0◦for East and 90◦for North, a numerical value is given for the189 direction observed for each 8 Hz (ADCP) or 32 Hz (ADV) measurement. With these190 values, the same percentiles presented in 2.1.2 are extracted from each 5-minute or 3-191 minute data block. Finally, assuming symmetry in short time period data, the fluctuation192 in the current direction is parameterized by opening angles between two percentiles193 equidistant from the median value (99.9-0.1, 97.7-2.3, 95-5,. . . ). In this case, most of194 the 5-minute or 3-minute data blocks are “contaminated” with the current directions195 6 collected from very low velocity magnitude points, resulting on opening angles much196 wider than those to be considered for tidal turbine designing purposes. In order to avoid197 this kind of contamination in the samples, instantaneous flow directions corresponding198 with velocity magnitudes lower than 0.5 m/s are excluded for the current direction199 analysis. A graphic summary of the procedure for the extraction of opening angles is200 presented in Fig 2, showing the opening angles between percentiles 99.9 and 0.1 and201 between percentiles 70 and 30.202 Figure 2: Graphic representation of opening angles extraction with pct 99.9 - pct 0.1 opening angle (blue), pct 70 - pct 30 opening angle (green) and 0.5 m/s threshold (red) 7 2.3.4 Turbulence intensity and prediction of velocity magnitude fluctuation203 Laboratory tests have demonstrated the influence of turbulence intensity (TI) conditions204 to the converter devices in terms of fatigue [13]. Furthermore, higher turbulence intensity205 values lead to a reduction in the velocity deficit downstream, with the maximum deficit206 point closer to the converter [14]; and a small reduction in the averaged flapwise and207 edgewise blade root bending moments, though fluctuations increase [15]. For this reason,208 turbulence intensity is a key parameter for tidal stream energy converters design.209 Turbulence intensity is defined for a given period of time as the ratio of standard devi-210 ation to averaged velocity magnitude (see Eq 2). Thus, when current velocity approaches211 zero, very high and unrepresentative values are obtained for turbulence intensity. This212 effect was observed and analyzed in previous similar studies, neglecting turbulence in-213 tensity results for defined “slack conditions” range for which tidal energy extraction is214 expected to be null [25]. In the present study, the upper limit for this range can be set215 at 0.7 m/s, a typical cut-in speed for tidal stream energy turbines [26], discarding all216 the 3-minute or 5-minute data blocks for which mean velocity is lower.217 TI =σV ¯ V(2) Besides its effect on the converter behavior, summarized in the first paragraph in Sec-218 tion 2.3.4, in the present study turbulence intensity is used as a means for the prediction219 of the different percentiles of velocity magnitude. The election of turbulence intensity220 as the parameter used for this purpose is based on two reasons. First, the dimension-221 less nature of turbulence intensity, which makes the direct comparison with velocities222 possible. Second, the capability of numerical methods for its prediction. Turbulence223 intensity can be estimated from numerical model results for turbulent kinetic energy by224 tke =3 2(Uavg ·T I)2[19]. For a short period of time, in this case 5 (ADCP) or 3 (ADV)225 minutes, the direct correlation between a certain percentile αof velocity magnitude and226 turbulence intensity proposed in the present study is defined by Eq 3:227 Vpα= (MFM·TI + 1) ·¯ V(3) Where Vpαis the velocity magnitude value for a certain percentile, MFMis a mul-228 tiplier factor for that velocity magnitude percentile, and TI and ¯ Vare the turbulence229 intensity and averaged velocity magnitude, respectively, for a 3-minute or 5-minute pe-230 riod. Physically, in a flow with no turbulence, velocity fluctuation is null. This is231 represented in the equation with the “+1” term.232 The method to establish the MFMfor each percentile starts assuming and evaluat-233 ing a theoretical normal distribution. If this does not fit the measured data, alternative234 values are calculated empirically. The procedure is as follows. From a first lineal ap-235 proach, for which all the 3-minute (ADV) or 5-minute (ADCP) samples with mean236 velocity higher than 0.7 m/s are used, the 1% farthest poins are discarded in order to237 avoid outliers, calculating the final equations with the lineal regression of the remaining238 99% points. The resulting 52 approaches (P1, P2, 22 layers in P3 and 28 layers in P4)239 are evaluated individually comparing them with the measured data at its corresponding240 8 Figure 9: Median value of the 52 prediction levels (Median PL) for margins of error of 0.1 m/s, 0.15 m/s and 0.25 m/s considering a normal distribution for velocity magnitude fluctuation and minimum prediction levels (Min PL) for a margin of error of 0.15 m/s using ADCP and ADV or underestimation of percentile 99.9 and percentile 0.1 (and by extension to the other360 percentiles) assuming a normal distribution can be discarded.361 Figure 10: Absolute errors box plot for percentiles 99.9 (pct 99.9) and 0.1 (pct 0.1) of velocity magnitude with the normal distribution assumption 15 3.3 Prediction of current direction fluctuation362 Time history for the same period as for turbulence intensity in Fig 6 is presented in363 Fig 11 for transverse turbulence intensity. Except for the more pronounced difference364 between ebb and flood tide conditions in P3 at 3 meter from the bottom or in P4 at both365 representative depths, results are very similar to those presented in Fig 6. Regarding the366 vertical profiles, shown in Fig 4 and Fig 5, TTI curves for ebb and flood in P3 are similar,367 decreasing from the bottom to approximately 12 m from the seabed and remaining almost368 constant for upper layers. In P4, during flood tide TTI gradually decreases from the369 bottom to the surface, while for ebb tide it is constant throughout the whole water370 column. The same characteristics were observed for the variations in current direction371 for a 3-minute or 5-minute period (Fig 4 and Fig 5), confirming the expected relation372 between transverse turbulence intensity and current direction fluctuation.373 Figure 11: Transverse turbulence intensity time history for a tidal cycle in P1 (3m), P2 (3m), P3 (3m, 15m) and P4 (3m, 15m) As for velocity magnitude, the adaptability of current direction fluctuation in a short374 period of time to a normal distribution is evaluated with skewness and kurtosis analysis.375 Results obtained for skewness evaluation are shown in Fig 12, with coefficients slightly376 deviatioed from zero for all the cases (|S|<0.05), and without a uniform tendency (pos-377 itive skew in P4 and the lower layers in P3 and negative skew in the upper layers in P3,378 P1 and P2). In addition to the evaluation of the adaptability to a normal distribution,379 this also confirms symmetry in current direction fluctuation for a short period data and380 validates the assumption established in Section 2.3.3.381 Regarding kurtosis, Fig 13 shows values clearly higher than 3 for all the 52 cases,382 based on which a leptokurtic distribution more outlier-prone than normal can be con-383 cluded. Substituting MFDin Eq 5 by the theoretical σmultiplier factor in a normal384 distribution for every analyzed opening angle, despite the good adaptability for central385 16 Figure 12: Groeneweld and Meeden skewness factor box plot for velocity direction short samples measured in P1, P2, P3 and P4 angles (55-45 to 90-10), flow direction fluctuation does not fit well with a normal distri-386 bution for the widest angles (see Fig 14). Thus, alternative MFDmust be found for the387 correlation between transverse turbulence intensity and opening angle. The prorated388 values obtained empirically for each opening angle following the procedure described in389 Section 2.3.4 and Section 2.3.5 are presented in Table 2.390 Figure 13: Kurtosis factor box plot for velocity direction short samples measured in P1, P2, P3 and P4 The multiplier factors for the different angles are consistent with the leptokurtic391 distribution concluded from the kurtosis analysis, with MFDhigher than those in a392 normal distribution for the three widest angles. This approximation fits more than 75%393 of 3-minutes or 5-minutes samples with a margin of error of 15% and more than 92% if394 we consider a margin of 25% from the measured value for the 0.1-99.9 angle. Considering395 absolute error, results are also clearly better than those observed when compared with396 the normal distribution, increasing the median of prediction levels for 1◦, 2◦and 5◦in 14,397 18 and 21 percentage points. For the 2.3-97.7 angle, the proposed approximation fits398 more than 77% of samples with a 5% margin of error, increasing to almost 100% for399 higher margins, as shown in Table 2. For narrower opening angles, with empirical MFD 400 very close to a normal distribution, error conclusions are similar to those presented in401 17 Figure 14: Median value of the 52 prediction levels for margins of error of 1◦, 2◦and 5◦considering a normal distribution for velocity direction fluctuation and minimum prediction levels for a margin of error of 2◦using ADCP and ADV Table 2: Multiplying factor, absolute and relative prediction levels for the different analyzed opening angles Angle MFD(Theo. Normal Distribution) PL abs 5◦(min-max) PL abs 10◦(min-max) PL rel 15% (min-max) PL rel 15% (min-max) 99.9-0.1 6.79 (6.00) 0.55-0.89 0.82-0.98 0.75-0.97 0.92-0.99 97.7-2.3 4.17 (4.00) 0.93-1.00 0.98-1.00 0.98-1.00 0.99-1.00 95-5 3.38 (3.29) 0.97-1.00 0.99-1.00 0.99-1.00 0.99-1.00 90-10 2.60 (2.56) 0.99-1.00 0.99-1.00 0.98-1.00 0.99-1.00 85-15 2.08 (2.07) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00 84.1-15.9 2.01 (2.00) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00 80-20 1.68 (1.68) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00 75-25 1.37 (1.35) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00 70-30 1.08 (1.05) 0.99-1.00 0.99-1.00 0.97-1.00 0.98-1.00 65-35 0.81 (0.77) 0.99-1.00 1.00-1.00 0.97-1.00 0.98-1.00 60-40 0.54 (0.51) 0.99-1.00 1.00-1.00 0.97-1.00 0.98-1.00 55-45 0.27 (0.25) 1.00-1.00 1.00-1.00 0.98-1.00 0.99-1.00 Fig 14. Focusing in the widest angle, for which the highest difference with the measured402 data is found, a deeper error analysis is presented in Fig 15. For all the 52 cases, median403 values are close to zero, with a highest median relative error of 4.82% in the eighth layer404 in P3 and a lower of -4.97% in P2. Thus, as for the velocity magnitude fluctuation405 prediction method, overestimation or underestimation can be discarded.406 4 Discussion407 The new methods are evaluated by comparing the results from the estimation by Eq408 3 and Eq 5 with measured data for velocity magnitude percentiles and opening angles,409 respectively.410 Regarding velocity magnitude fluctuation, Fig 16 shows a comparison of velocity411 magnitude measured and estimated values for the 0.1 and 99.9 percentiles during the412 18 Figure 15: Absolute and relative errors box plot for pct 99.9 - pct 0.1 opening angle estimation with the empirical multiplying factor measuring period in P2. Even in the worst scenario (percentiles with the lower prediction413 levels and the measuring point with the highest median error), red line shows a very good414 agreement with measured data, giving an idea of the high accuracy of this estimation415 method. In Fig 16, it is also notable the important difference between flood and ebb,416 with good results for both tide directions, which shows the capability of this method for417 diverse flow conditions.418 Similarly, a comparison of measured and estimated values for the three widest angles419 in P2 is shown in Fig 17, for which values corresponding with 3-minute averaged velocity420 lower than 0.7 m/s are discarded. As in Fig 16, the difference between ebb and flood421 tides is notable, getting a very good correlation for both flow conditions. Since these422 three opening angles show the lowest prediction levels according to information provided423 in Table 2, a better agreement is expected for narrower angles and other spatial cases.424 For current direction fluctuation prediction by numerical modelling, a turbulence425 anisotropic ratio (σs:σt:σv) needs to be assumed. As presented in Section 2.3.5, Nezu426 and Nakagawa [27], based on an experimental study with two-dimensional channel flows427 at relatively low Reynolds numbers, proposed the ratios 1:0.71:0.55. Regarding data428 measured in strong tidal channels, Milne et al [8] observed 1:0.75:0.56 ratios for current429 velocities around 2 m/s. The ratios calculated from the data measured for the present430 study for the 3-minute data blocks representative of flood conditions at 1 m/s shown431 in Table 1 are 1:0.85:0.45 for P1 and 1:0.78:0.58 for P2. Concerning the data measured432 by ADCP, vertical averaged ratios are 1:0.79:0.40 for P3 and 1:0.98:0.41 for P4. Except433 for P4, both the ratios shown in [8] and measured in the present study agree relatively434 19 Figure 16: Comparison of measured (blue) data and estimation (red) values for percentiles 99.9 (pct 99.9) and 0.1 (pct 0.1) of velocity magnitude Figure 17: Comparison of measured (blue) data and estimation (red) values for opening angles 99.9-0.1, 97.7-2.3 and 95-5 well with those proposed by Nezu and Nakagawa [27], with the expected deviations from435 the theoretical ratios due to the differences in bathymetry and Reynolds numbers. In436 the case of P4, due to the shallower and narrower nature of the channel, the irregular437 shape of the coastline (multiple small capes and gulfs) and the variable depth (hills and438 valleys in various directions), the fluctuation in the transverse component of velocity439 20 becomes more important. These differences in the turbulence anisotopic ratios must be440 considered when applying this method to the prediction of current direction fluctuation441 by numerical modelling.442 5 Conclusions443 Within the journey towards tidal energy stream commercial exploitation, one of the main444 topics is the adaptability of laboratory devices to sea water and flow conditions. In this445 regard, some converters have had to face issues related to biofouling, marine corrosion446 or turbulence conditions. Concerning this last topic, notable turbulence-related high447 frequency fluctuations in velocity magnitude and direction have been observed by in-448 situ measurements. The present paper analyzes this fluctuation and introduces a new449 method for its estimation based on short data samples measured by two ADVs and two450 ADCPs at 4 different locations with diverse flow conditions in the waters of Goto Islands,451 Japan.452 Dividing measured data into 3-minutes (ADV) and 5-minutes (ADCP) samples, mag-453 nitude fluctuation is well adapted to a theoretical normal distribution. With this as-454 sumption, more than 80% percentiles 0.1 and 99.9 can be predicted within a margin455 of error of 0.15 m/s. This percentage increases to values very close to 100% for more456 centered percentiles (2.3, 97.7, 5, 95,. . . ). For direction fluctuation, data samples show457 a leptokurtic distribution, which implies a greater importance of outliers. Thus, the458 normal distribution assumption showed good results for central opening angles (from459 percentiles 45-55 to percentiles 10-90), whilst for wider angles there is an underestima-460 tion problem. The three widest angles (5-95, 2.3-97.7, 0.1-99.9) were treated empirically,461 obtaining slope trends of 3.38, 4.17 and 6.79, respectively, instead of 3.29, 4 and 6 of the462 theoretical normal distribution. With these new factors, more than 75% of the 99.9-0.1463 and more than 98% of 97.7-2.3 opening angles can be estimated with a 15% margin464 of error. These results demonstrate the validity of this method for the estimation of465 this kind of fluctuation, regardless of measuring device, frequency sampling, location or466 depth.467 The importance of this work lies not only in the understanding of this kind of fluc-468 tuations, but also in the relation of these with turbulence intensity for magnitude and469 transverse turbulence intensity for direction. Since both parameters can be calculated470 indirectly by numerical models, the conclusions extracted from this paper represent a471 significant step towards tidal stream energy commercialization. Reducing the need for472 in-situ measurements, this new prediction method allows a higher accuracy in energy473 resource prediction (residuals from harmonic analysis up to 5 kW/m2have been ob-474 served in a tidal site with maximum velocity of 3 m/s [10]) and an important advance475 concerning converters design, since high frequency fluctuations in velocity have an im-476 portant effect on the device stabilization [12] and on the dynamic loading conditions on477 the blades, support structures and seabed connections [11].478 21 Acknowledgements479 The authors would like to thank the Ministry of Environment of Japan for permission480 to publish of the data used in this study, which were obtained through the project for481 Promotion of Realization of Tidal Current Power Generation supported by the ministry482 in 2014 and 2015.483 References484 [1] Foreman M.G.G,Manual for tidal heights analysis and prediction. 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