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E.ON Technologies E.ON Technologies (Ratcliffe) Limited, Technology Centre, Ratcliffe-on-Soar, Nottinghamshire, NG11 0EE T+44 (0) 2476 192900 F+44 (0) 115 902 4012 [email protected] www.eon.com/technology

ENT/12/CNS/PM/796/R

June 2014

EIC/Renewables-PN11260: ETI ReDAPT - MA1001 PM14 MD5.2:

FALLS OF WARNESS 3D MODEL VALIDATION REPORT by

K Gunn & C Stock-Williams EXECUTIVE SUMMARY As part of the ReDAPT project, a 3D hydrodynamic model of the Falls of Warness area has been built, using the MIKE3 software. Here, a one-month simulation using this model is validated against data collection campaigns at four locations within the model. Statistical parameters to assess the performance of the model are extracted for time-domain comparisons of tidal height, depth-averaged velocity and shear profile. Harmonic analysis is also used, to provide further insight into discrepancies and potential sources of modelling error. It is found that tidal heights and depth-averaged current are reproduced very well in all the locations tested. Shear profiles are found to exhibit similar trends and to reproduce certain aspects of the site data. However, two particular tendencies are identified in the model: the prediction of separated flood and ebb profiles in sites with simple profiles; and the underestimation of twisted and reverse sheared flows in complex sites. As a result, the MIKE3 model results generated as part of MD5.1 and MD5.2 have been used to provide information about the spatial variability of the shear profile around the location of the tidal turbine. This will inform CFD modelling being conducted elsewhere in ReDAPT. Prepared by Approved for publication Master report signed by C Stock-Williams & P Bartlam, 13 June 2014 K Gunn & C Stock-Williams P Bartlam Renewables Modelling Software & Modelling

mailto:[email protected]

LEGAL NOTICES Neither E.ON, nor any person acting on its behalf, makes any warranty, express or implied, with respect to the use of any information, method or process disclosed in this document or that such use may not infringe the rights of any third party or assumes any liabilities with respect to the use of, or for damage resulting in any way from the use of, any information, apparatus, method or process disclosed in the document. Telephone +44 (0) 2476 192900 (please ask for customer administration) Fax +44 (0) 115 902 4001 E-mail [email protected]

Other Participants: None

mailto:[email protected]

ENT/12/CNS/PM/796/R

CONTENTS

Page 1 INTRODUCTION ............................................................................................................ 1 1.1 Background to this Report .............................................................................................. 1 1.2 Acceptance Criteria for MD5.2 ........................................................................................ 1 2 DATA .............................................................................................................................. 2 2.1 MIKE Model .................................................................................................................... 2 2.2 Validation Data ............................................................................................................... 3 3 VALIDATION PROCESS ................................................................................................ 5 3.1 Time Series .................................................................................................................... 5 3.2 Harmonic Analysis .......................................................................................................... 6 4 RESULTS ....................................................................................................................... 7 4.1 Tidal Height Validation .................................................................................................... 7 4.1.1 Testing for a Standing Wave ........................................................................................ 7 4.1.2 Time-Domain Analysis .................................................................................................... 8 4.1.3 Spectral Analysis .......................................................................................................... 12 4.2 Velocity: Two-Dimensional Validation ........................................................................... 17 4.2.1 Time-Domain Analysis .................................................................................................. 17 4.2.2 Spectral Analysis .......................................................................................................... 22 4.3 Velocity: Three-Dimensional Validation ......................................................................... 27 4.3.1 Generalised Shear Profiles ........................................................................................... 27 4.3.2 Sites with Power-Law Profiles ....................................................................................... 28 4.3.3 Sites with Complex Profiles Initial Understanding ...................................................... 31 4.3.4 Sites with Complex Profiles Characterisation and Mapping ....................................... 32 4.3.5 Sites with Complex Profiles Direct Comparison .......................................................... 35 4.3.6 Shear Profile Data for CFD Modelling ........................................................................... 39 5 SUMMARY AND CONCLUSIONS ................................................................................ 42 6 REFERENCES ............................................................................................................. 43

ENT/12/CNS/PM/796/R

NOMENCLATURE ADP Acoustic Doppler Profiler, used predominantly to measure current speeds through the water column and surface elevation. DHI Danish Hydraulics Institute, developer of MIKE numerical hydrodynamic modelling software. EMEC European Marine Energy Centre, location of TGL turbine being tested under ReDAPT. MIKE numerical hydrodynamic modelling software, which can be used to model tidal flows (and waves) either in 3D (MIKE3) or depth-averaged 2D (MIKE21). MSL mean sea level.

1 ENT/12/CNS/PM/796/R

1 INTRODUCTION 1.1 Background to this Report DHI has constructed a 3D hydrodynamic model of the Falls of Warness, where the European Marine Energy Centre (EMEC) tidal current test site is located. That work, for MD5.1 of ReDAPT, used boundary conditions from within a pre-existing 2D model of the Orkney Islands, built under contract for EMEC. In the MD5.1 report, DHI presented calibration and initial validation of the model results against EMECs own ADPs and the D1 ADP deployment conducted as part of ReDAPT. Here, data from several ADPs deployed as part of ReDAPT during July-August 2011 are used, in order to complete validation of the 3D model. New results have been generated by DHI covering the same period as the new ADP data. In Section 2, the data sources are described both for the hydrodynamic model and the ADPs. In Section 3, the validation process is explained; Section 4 gives the results of its application to the data from Section 2. Finally, a summary and conclusions are given in Section 5. 1.2 Acceptance Criteria for MD5.2 The Acceptance Criteria for MD5.2 are as follows:

Delivery of the report detailing how the boundary conditions were constructed and showing acceptable agreement between model and measurements. Report will include:

Data set of results that is accurate and that is accepted by EDF for their

modelling activities.

Re-iterate EDFs requirements, for example the location of the boundary conditions, length of time covered by the model run.

Identify any issues/assumptions and how these were addressed.


2 DATA 2.1 MIKE Model The MIKE3 model described in the ReDAPT report for deliverable MD5.1 has been re-run by DHI, on behalf of EMEC. These results were supplied to E.ON for the purposes of validation, along with model set-up files. Since E.ON has access to MIKE licences, it was possible to view the set-up files and extract data as required for this validation study. Figure 2.1 shows the extent of the model.

Figure 2.1: Extent of Falls of Warness MIKE Model The 3D model, as run by DHI, is summarised in Table 2.1. Table 2.1: MIKE3 Falls of Warness Model Run Summary

Simulation Time 24/7/2011 00:00 to 27/8/2011 00:00 Output Timestep 30 minutes Mesh size 11802 nodes, 22203 elements. Number of vertical layers 10 equidistant sigma layers.

Boundary Conditions

Flather (velocities and heights) at all seven mesh boundaries from larger 2D model. These are specified as 10 vertical layers with identical flow speeds. Constant roughness height (0.017m).

Initial Conditions Soft-start (3600s sinus) on boundaries. Flat water at MSL inside model. A 2D model run was also provided, which is summarised in Table 2.2.


Table 2.2: MIKE21 Falls of Warness Model Run Summary

Simulation Time 24/7/2011 00:00 to 27/8/2011 00:00 Output Timestep 5 minutes Mesh size 11802 nodes; 22203 elements. Number of vertical layers Depth-averaged.

Boundary Conditions Flather (velocities and heights) at all seven mesh boundaries from larger 2D model. Constant roughness height (0.017m).

Initial Conditions Soft-start (3600s sinus) on boundaries. Flat water at MSL inside model. 2.2 Validation Data The model has been calibrated against ADP data provided by EMEC, and initial validation was against the D1 deployment conducted as part of ReDAPT. The ADP data provided to E.ON to support validation is summarised in Table 2.3. The locations of the ADPs are given in Figure 2.2. As can be seen, GN is actually a tidal gauge rather than an ADP, meaning that no current velocities are available; however, tidal height data is available at high precision. Table 2.3: Data around the Falls of Warness supplied to E.ON for MD5.2

TGL

Location 59.13N 2.82W Date of first

usable reading 25 June 2011 14:00

Relevant Parameters

Current velocity; water depth

Date of last usable reading

25 July 2011 20:30

Mean Water Depth 42.271

Measurement frequency 1 second

GS


usable reading 27 July 2011 20:20

Relevant Parameters



23 August 2011 12:00

Mean Water Depth 32.107m


GN



Relevant Parameters Water depth


20 August 2011 12:50


Measurement frequency 0.5 seconds

D1


usable reading 23 June 2011 12:10

Relevant Parameters



26 July 2011 14:10



D2



Relevant Parameters



24 August 2011 11:20




Figure 2.2: Admiralty Chart showing Location of ADPs Deployed around Falls of Warness All data was averaged to 10 minute intervals to facilitate the validation exercise. The data was then Quality Checked to remove data before stable deployment and after retrieval. Bad data during deployment (as identified during pre-processing by EMEC) was also removed.

Figure removed to comply with copyright


3 VALIDATION PROCESS Model validation will be achieved by comparing key parameters: Current speed and direction, depth-averaged or at different depths. Water depth or surface elevation. Vertical shear profile of current velocity. These comparisons will be performed as described in the following sub-sections. 3.1 Time Series One method of validating a model is to compare time series of the key parameters. Comparison can be made graphically, using scatter plots or quantile-quantile plots as in the MD5.1 report. Alternatively, statistical measures can be calculated to represent graphs as single numbers. Measures in standard use include: Bias the mean of the residuals. RMS Error the square root of the mean of the squared errors. Scatter the standard deviation of the residuals. Correlation co-efficient. Defining as the measured data, and as the modelled data, these can be calculated for a set of data with members as follows: Bias (absolute)* Bias Index

RMS Error (absolute)

Scatter (absolute)* Scatter Index*

Correlation co-efficient*

In this study, the four asterisked parameters will be used to assess the data. This is because they are the easiest to interpret for a general audience and the least susceptible to data manipulation.


3.2 Harmonic Analysis Comparing the time series data as described above can often fail to identify the cause of errors in the data. For example, if the model produces a tidal height signal which has a phase error with the site data, a plot of site tidal height against model modal height will show a circular pattern. This shows there is an error, but the fact that it results only from a phase error (whereas the magnitude may be correct) is easily missed. A preferred method is to perform a harmonic analysis on the two data sets. By performing such an analysis: extracting the same tidal harmonics form both model and site data; it is possible to create scatter plots of: Magnitude (speed or height)

o For both semi-major and semi-minor axis for speed. Phase; and direction. It is then possible to see, at a glance, what the nature of modelling errors is. For this work, an ENT in-house harmonic analysis code has been used, which is based on the Matlab implementation of T Tide by R. Pawlowicz1. Further analysis is then performed using standard methods2. In all cases the most appropriate tidal harmonic constituents have been selected to represent the data sets to be compared.

1 R. Pawlowicz, B. Beardsley, and S. Lentz, "Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE", Computers and Geosciences 28 (2002), 929-937. 2 D. T. Pugh, Tides, Surges and Mean Sea-Level Wiley, ISBN 0 471 91505 X, (1987).


4 RESULTS 4.1 Tidal Height Validation 4.1.1 Testing for a Standing Wave One concern often present when producing a model carefully calibrated to one location, as is the case here, is a misrepresentation of the spatial flow field. In other words, the model produces correct data at the desired location, but due to other errors (in the model inputs or physics) sites away from that location are incorrectly modelled. One example of particular concern in the Falls of Warness is the potential for a standing wave effect to exist across the channel. This would potentially result in the model being correct at the centre of the standing wave (where the EMEC site is) but with large errors at the ends of the channel. In order to test for this phenomenon the two G instrument (GN and GS) were deployed as far to the ends of the Falls of Warness channel as possible. By comparing the tidal heights at three points: the two G sites and one central one (in this case the D site), it is possible to detect the standing wave effect. In particular, if all three points in the model match the ADP data equally well, it can be inferred that the standing wave does not exist. As can be seen from tables 2.2 and 2.3, the three ReDAPT ADP deployments concurrent with the MIKE model run are GN, GS and D2. The overlapping data have been interpolated to a common timestep to enable the scatter plots in Figure 4.1 to be created.

Figure 4.1a: Data from the D2 Deployment

Figure 4.1b: Data from the GN Deployment

Figure 4.1c: Data from the GS Deployment

Figure 4.1: Comparison of Water Surface Elevation for Three Locations


It is clear from the comparisons in Figure 4.1 that the model has found a good fit all three sites. Although the D, GN and GS fits are extremely good, suggesting no standing wave effect, it is possible that this effect occurs at some frequency other than the M2 and is therefore hidden by the M2 signal. To evaluate if a standing wave exists at another frequency it is necessary to perform harmonic analysis on these data. This is discussed further in Section 4.1.3. 4.1.2 Time-Domain Analysis The four parameters chosen in Section 3.1 to assess the model performance are: 1. Absolute Bias in metres, this shows whether the model overall under-predicts or over-

predicts the water surface elevation. 2. Absolute Scatter in metres, this shows how scattered the differences between the model

and the measured data are. 3. Scatter Index non-dimensional, this is the ratio of scatter to bias (and will therefore have

the same sign as the bias). 4. Correlation coefficient a value close to +1 is ideal. Figures 4.2 to 4.4 show the time-series plots equivalent to the scatter plots in Figure 4.1. The associated Tables 4.1 to 4.3 give the values calculated for the four validation parameters at each site.


Figure 4.2: Comparison of Surface Elevation Records for GN Location Table 4.1: Time Domain Validation Parameters for GN Location

Parameter Value

Absolute bias -0.047

Absolute scatter 0.104

Scatter Index -2.226

Correlation coefficient 0.994


Figure 4.3: Comparison of Surface Elevation Records for GS Location

Table 4.2: Time Domain Validation Parameters for GS Location

Parameter Value




Correlation coefficient 0.992 The last four days of all three of these graphs show a rise in the measured surface elevation in comparison with the model data. This is very likely to be due to an atmospheric event (low pressure storm) and so this discrepancy should be ignored for the purposes of validation and the values in the tables given leniency. From this data, it is clear that the MIKE3 model reproduces the surface elevation at all three locations in the Falls of Warness well. The slightly lower goodness of fit for the D site is perhaps a function of the complexity of the flow around the EMEC site.


Figure 4.4: Comparison of Surface Elevation Records for D Location Table 4.3: Time Domain Validation Parameters for D Location

Parameter Value




Correlation coefficient 0.985


4.1.3 Spectral Analysis The tidal components in Table 4.4 were selected for the harmonic analysis, since they produce a reasonable fit to all 4 of the sites tested (GN, GS, D and TGL). For the D site, the data from both D1 and D2 were used to improve the certainty in the results. Table 4.4: Tidal Components used in the Tidal Height Analysis

Component Period (hours)

O1 25.82

P1 24.07

K1 23.93

N2 12.66

M2 12.42

S2 12.00

K2 11.97

M4 6.21 The resulting amplitudes and phases can be seen in Figures 4.5 to 4.8 (a graphical representation including confidence intervals derived for the fit to each harmonic), and Tables 4.5 to 4.8 (a tabulated version of the amplitudes and phases calculated for each harmonic).


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100

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O1

P1

K1N2

M2

S2

K2M4

Amplitude

Model (m)

Site

(m)

0 45 90 135 180 225 270 315 3600

45

90

135

180

225

270

315

360Phase

Model ()S

ite (

)

O1

P1

K1

N2M2

S2K2

M4

Figure 4.5: Spectral Comparison for Site D. The Red Lines Indicate the 95% Confidence Intervals

Table 4.5: Tabulated Spectral Comparison for Site D

Component Amplitude Phase

Site Model Site Model

M2 0.7385 0.8091 278.58 289.49

S2 0.2008 0.2832 300.57 324.93

N2 0.1355 0.1634 257.70 267.88

K1 0.1286 0.1063 162.81 163.92

K2 0.1250 0.0883 272.29 322.87

O1 0.0985 0.0892 10.17 19.60

M4 0.0870 0.0854 246.20 302.27

P1 0.0049 0.0376 201.29 149.79


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O1

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N2

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S2

K2M4

Amplitude

Model (m)

Site

(m)

0 45 90 135 180 225 270 315 360

0

45

90

135

180

225

270

315

360Phase

Model ()

Site

()

O1

P1

K1

N2M2

S2K2M4

Figure 4.6: Spectral Comparison for Site GN. The Red Lines Indicate the 95% Confidence Intervals

Table 4.6: Tabulated Spectral Comparison for Site GN



M2 1.1021 1.0546 258.38 256.94

S2 0.4139 0.3993 291.28 292.65

N2 0.2165 0.2149 245.13 229.94

K2 0.1055 0.0945 294.09 288.85

O1 0.1032 0.0866 2.72 9.36

K1 0.0970 0.1108 134.36 149.96

M4 0.0905 0.0586 304.38 305.47

P1 0.0701 0.0379 103.86 137.79


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M4

Amplitude

Model (m)

Site

(m)

0 45 90 135 180 225 270 315 3600

45

90

135

180

225

270

315

360Phase

Model ()

Site

()

O1

P1

K1

N2M2

S2K2

M4

Figure 4.7: Spectral Comparison for Site GS. The Red Lines Indicate the 95% Confidence Intervals

Table 4.7: Tabulated Spectral Comparison for Site GS



M2 0.7934 0.8154 309.04 305.62

S2 0.2482 0.2836 336.32 343.85

N2 0.1506 0.1716 296.83 286.09

K2 0.1225 0.0857 337.35 337.38

O1 0.1016 0.0876 25.07 25.93

K1 0.0848 0.0949 177.22 162.42

M4 0.0678 0.0487 293.57 321.95

P1 0.0371 0.0509 85.20 140.76


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100

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100

O1P1

K1

N2

M2

S2

K2 M4

Amplitude

Model (m)

Site

(m)

0 45 90 135 180 225 270 315 3600

45

90

135

180

225

270

315

360

405Phase

Model ()

Site

()

O1

P1K1

N2

M2

S2

K2

M4

Figure 4.8: Spectral Comparison for site TGL. The Red Lines Indicate the 95% Confidence Intervals

Table 4.8: Tabulated Spectral Comparison for Site TGL



M2 0.8192 0.8825 303.77 281.07

S2 0.2786 0.3231 344.29 316.65

N2 0.2396 0.1768 273.02 256.20

M4 0.1098 0.1034 335.06 309.91

K2 0.1030 0.0835 19.10 314.26

P1 0.0995 0.0370 142.37 146.67

O1 0.0923 0.0892 19.08 15.42

K1 0.0472 0.1099 149.74 160.08 As can be seen, the components with greater amplitude are fitted with better confidence; and the amplitude of the largest component (M2) is within 10% of the value obtained from the measurements for all the sites. Referring back to the standing wave discussion in Section 4.1.1, this effect would reveal itself in phase-locking of one or more harmonic constituents along the channel. Harmonic analysis should reveal this: since the phase of the affected constituents would be the same at different measured sites. The closest constituent to being phase-locked is O1, which has a maximum difference between the measured phases at the four sites of 22. Since this has an amplitude of around 1/10 of the M2 constituent, it is clear why this does not show up on the time-series analysis in Section 4.1.1.


The TGL site will now be highlighted, since it is the intended location of the installed turbine, and will be modelled elsewhere in ReDAPT using CFD. The three most important (semi-diurnal) constituents have amplitudes which are, respectively, 5% and 11% over-predicted, and 28% under-predicted. The phases are between 11 and 25 out. Considering the inaccuracies of performing harmonic analysis on relatively short time-series of data and the likely skewing of the site measured data by the storm at the end of the deployment period, these results should be taken to be an example of a model doing a good job of predicting variations in tidal surface elevation over a site. 4.2 Velocity: Two-Dimensional Validation In a model designed for use relating to tidal current turbines, it is clearly important that the model is able to accurately predict velocities and heights simultaneously. Validation of tidal currents will first consider two-dimensional characteristics before attempting to compare 3D flows. ADPs were only successfully deployed at three sites: D and TGL near the site, and GS to the south. It should be noted that the D1 deployment data have previously been used in the construction and initial validation of the model by DHI, thus a good fit is expected for that location. 4.2.1 Time-Domain Analysis The velocity data are reduced to two dimensions by depth-averaging. This reduces the 3D model back to an equivalent MIKE21 model, although the results may not be the same due to complexities in the vertical shear which could be modelled successfully in the 3D model. Scatter plots comparing the measured and modelled data directly are shown in Figures 4.9, 4.10 and 4.11 for the GS, D and TGL sites respectively (note that for the TGL site the model and ADP data from different time periods). As can be seen, the TGL location has the most complex flow (both in the measured and modelled data).

Figure 4.9: Velocity Scatter Plot for Site GS


Figure 4.10: Velocity Scatter Plot for Site D

Figure 4.11: Velocity Scatter Plot for Site TGL


Numerical comparison is affected by further resolving ADP and model velocities to principal axes for flood and ebb. These were identified by choosing the maxima of histograms of the flow direction data, binned to one degree intervals. Principal axes identified are shown in Table 4.9. As can be seen, the model predicts both principal directions at the D2, GS and TGL locations very well. Table 4.9: Comparison of Flood and Ebb Flow Directions

Site D2 GS TGL Direction ADP Model ADP Model ADP Model

Flood 150 147 154 153 137 139 Ebb 314 312 334 337 321 320

The principal directions for the appropriate data set were used to create depth-averaged speed data sets. The flood directions were defined negative to create the graphs of GS and D2 in Figures 4.12 and 4.13, although it has no effect on the validation parameters shown in Tables 4.10 and 4.11. The TGL site has been omitted in this analysis due to the lack of concurrent data. The correlation coefficient has been calculated using the cosine of the angles, to avoid differences of greater than 180 skewing the result.


Figure 4.12: Comparison of Resolved Depth-Averaged Speed and Direction Records for D Location

Table 4.10: Time Domain Validation Parameters for D Location

Parameter Value

Speed (m/s)

Absolute Bias 0.127 Absolute Scatter 0.305

Scatter Index 2.395 Correlation Coefficient 0.987

Direction (degrees)

Absolute Bias 1.471 Absolute Scatter 21.013

Scatter Index 14.282 Correlation Coefficient 0.949


Figure 4.13: Comparison of Resolved Depth-Averaged speed and Direction Records for GS location

Table 4.11: Time Domain Validation Parameters for GS Location

Parameter Value

Speed (m/s)

Absolute Bias -0.052 Absolute Scatter 0.281

Scatter Index -5.373 Correlation Coefficient 0.982

Direction (degrees)

Absolute Bias -8.120 Absolute Scatter 47.698

Scatter Index -5.874 Correlation Coefficient 0.933


This clearly shows that the depth-averaged currents at these two sites are reproduced extremely well by the model. The more complex directional behaviour at the GS location results in a greater bias in the direction, which is not apparent from the simple choice of a principal direction. For greater insight, however, it is necessary to turn to spectral analysis, which will allow comparisons with non-overlapping datasets. 4.2.2 Spectral Analysis As with the tidal height data analysis, the most instructive method of validating the model is in the spectral domain. A further complication is present when applying such methods to velocities as both magnitude and direction must be considered. The approach generally taken is to resolve the velocities to a principal direction. However, since this discards any information about the elliptical nature of the flow, this is not used here. Instead, the east and north components of the flow are analysed separately. This results in a phase and magnitude for each harmonic constituent. These values can then be manipulated, as described by Pugh (1987), to provide the following for each harmonic constituent: Semi-major axis (the maximum magnitude of the flow); Semi-minor axis (the minimum magnitude of the flow); Inclination of the ellipse (the bearing of the semi-major axis); and either Time of zero phase (the time that the flow was first equal to the positive semi-major axis);

or phase at time zero. In the figures below, scatter plots of the constituent values are first shown, as for Section 4.1.4, followed by a comparison of the resultant tidal ellipse values (one per constituent). For the tidal ellipse plots the figures have the phase at time equals zero marked. Initially, it is worth examining the results for site D (Figure 4.14), for which validation has already been attempted in the MD5.1 report.


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Site(m/s)

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el (m

/s)

O1

K1

MU2 N2

M2

S2

3MS4

M4 MS4

M6 ST42

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ST42

80 90 100 110 120 130 14080

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150Inclination of Ellipse

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el (

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K1 MU2 N2 M2 S2

3MS4 M4 MS4

M6 ST42

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0.5

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2.5Time of zero phase

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el (H

rs)

O1 K1

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M2

S2

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M6

ST42

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/s)

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MU2 N2 M2

S2 3MS4 M4 MS4 M6

ST42

(a) Scatter Plots of Spectral Parameters

-0.1 0 0.1-0.05

0

0.05

O1

-0.1 0 0.1

-0.05

0

0.05

K1

-0.2 0 0.2

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MU2

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-101

M2

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00.020.04

3MS4

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M4

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MS4

-0.05 0 0.05-0.05

0

0.05 M6

-0.1 0 0.1-0.05

0

0.05

ST42

SiteModel

(b) Tidal Ellipses for Each Used Component

Figure 4.14: Harmonic Analysis Results for Depth-Averaged Velocities at Site D


Figure 4.14 confirms the conclusion in Section 4.2.2, that the model has produced an excellent fit to the ADP data at this site. The semi-major axes for all components have been predicted well, as have the directions and the phases. The semi-minor axes give a poorer correlation. However, as can be seen from Figure B, the magnitudes of the semi-minor axes are much smaller than the semi-major. Figures 4.15 and 4.16 repeat the same analysis for the GS and TGL sites respectively. Once again, the earlier conclusions are confirmed: there is excellent agreement with the ADP data. The same general trends are seen at this site as for D, with the only exception being that the model seems to have been less accurate in determining the direction of flow of several of the less-important tidal constituents. This is likely to be the result of inaccurate bathymetry.


10-2

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101

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100

101

Site(m/s)

Mod

el (m

/s)

K1

2N2 N2

M2

S2

N4 M4 MK4

Semi-major Axis

10-4

10-3

10-2

10-1

10-4

10-3

10-2

10-1

Site(m/s)

Mod

el (m

/s)

Semi-minor Axis

K1

2N2

N2

M2 S2

N4

M4 MK4

110 120 130 140 150110

120

130

140


Site ()

Mod

el (

)

K1 2N2

N2 M2 S2

N4

M4

MK4

0 0.5 1 1.5 20

0.5

1

1.5

2Time of zero phase

Site(Hrs)

Mod

el (H

rs)

K1

2N2

N2

M2

S2

N4

M4

MK4

10-2

10-1

100

101

10-2

10-1

100

101

Site(m/s)

Mod

el (m

/s)

K1

2N2 N2

M2

S2

N4 M4 MK4

Semi-major Axis

10-4

10-3

10-2

10-1

10-4

10-3

10-2

10-1

Site(m/s)

Mod

el (m

/s)

Semi-minor Axis

K1

2N2

N2

M2 S2

N4

M4 MK4


-0.05 0 0.05-0.05

0

0.05

K1

-0.2 -0.1 0 0.1 0.2

-0.1

0

0.1

2N2

-0.2 0 0.2

-0.2

-0.1

0

0.1

0.2

N2

-1 0 1

-1

-0.5

0

0.5

1

M2

-0.5 0 0.5

-0.5

0

0.5

S2

-0.05 0 0.05-0.05

0

0.05 N4

-0.1 -0.05 0 0.05 0.1-0.1

-0.05

0

0.05

0.1

M4

-0.1 0 0.1

-0.1

-0.05

0

0.05

0.1

MK4

SiteModel


Figure 4.15: Harmonic Analysis Results for Velocities at Site GS


10-2

10-1

100

101

10-2

10-1

100

101

Site(m/s)

Mod

el (m

/s)

O1

K1 ST1

2N2

N2

M2

L2

S2

3MS4 M4

MS4

Semi-major Axis

10-3

10-2

10-1

100

10-3

10-2

10-1

100

Site(m/s)

Mod

el (m

/s)

Semi-minor Axis

O1

K1

ST1

2N2 N2

M2

L2

S2

3MS4

M4 MS4

130 135 140 145 150120

130

140

150


Site ()

Mod

el (

)

O1 K1

ST1 2N2

N2 M2

L2

S2

3MS4

M4

MS4

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5Time of zero phase

Site(Hrs)

Mod

el (H

rs)

O1 K1

ST1

2N2

N2

M2 L2

S2

3MS4 M4

MS4

10-2

10-1

100

101

10-2

10-1

100

101

Site(m/s)

Mod

el (m

/s)

O1

K1 ST1

2N2

N2

M2

L2

S2

3MS4 M4

MS4

Semi-major Axis

10-3

10-2

10-1

100

10-3

10-2

10-1

100

Site(m/s)

Mod

el (m

/s)

Semi-minor Axis

O1

K1

ST1

2N2 N2

M2

L2

S2

3MS4

M4 MS4


-0.1 0 0.1

-0.05

0

0.05

O1

-0.1 0 0.1

-0.05

0

0.05

K1

-0.05 0 0.05-0.04-0.02

00.020.04

ST1

-0.2 0 0.2

-0.1

0

0.1

2N2

-0.5 0 0.5-0.5

0

0.5 N2

-2 0 2

-1

0

1

M2

-0.5 0 0.5

-0.20

0.2

L2

-1 0 1

-0.5

0

0.5

S2

-0.02 0 0.02

-0.01

00.01

3MS4

-0.1 0 0.1

-0.05

0

0.05

M4

-0.02 0 0.02

-0.010

0.01

MS4

SiteModel


Figure 4.16: Harmonic Analysis Results for Velocities at the TGL Site


4.3 Velocity: Three-Dimensional Validation One of the primary aims of the 3D model was to produce understanding of the flow shear profile. Inspection of the ADP data has revealed that the velocity vertical shear profiles at all the ADP sites are quite complex. This section will seek to understand the key elements of that complexity and demonstrate how well the MIKE3 model has reproduced it. 4.3.1 Generalised Shear Profiles Initially, it is worth examining the general form the flow profiles take. One simplistic approach is to first resolve the flow to a principal direction (here chosen as the inclination of the M2 tidal ellipse as identified in Section 4.2.2). The flow conditions at each time step can then be binned into a set of depth-averaged flow speed ranges, and the profile derived for each of these bins. Having performed this analysis it has been found that the sites can be classified as having simple profiles or complex profiles. The simple flow profiles are characterised by taking a form similar to the well-known power law (see Section 4.3.2 for details). Sites D (Figure 4.17) and GS fit into this category. Furthermore, as can be seen in Figure 4.17, the flow profiles are similar in both flood and ebb.

0 0.5 1 1.5 2 2.5 3 3.50

5

10

15

20

25

30

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)

Flood

Ebb

0.0-0.20.2-0.40.4-0.60.6-0.80.8-1.01.0-1.21.2-1.41.4-1.61.6-1.81.8-2.02.0-2.22.2-2.42.4-2.62.6-2.82.8-3.03.0-3.23.2-3.4

Figure 4.17: Mean Flow Profiles for Site D Conversely, the TGL site has complex flow profiles as seen in Figure 4.18. These flow profiles show a considerable difference between flood and ebb. These profiles also do not fit the power law formula, since the maximum flow speed often occurs well below the surface. Since the model run does not overlap sufficiently with the ADP deployment at this site, it is necessary to conduct a different analysis for this site: see Section 4.3.3.


0 0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)

Flood

Ebb

0.0-0.20.2-0.40.4-0.60.6-0.80.8-1.01.0-1.21.2-1.41.4-1.61.6-1.81.8-2.02.0-2.22.2-2.42.4-2.62.6-2.82.8-3.03.0-3.23.2-3.4

Figure 4.18: Mean Flow Profile for the TGL Site

4.3.2 Sites with Power-Law Profiles In order to attempt numerical validation, two shear profile equations have been fitted to the sites with simple profiles in order to analyse the validity of the model. Direct comparisons are again made between the site data and ADP data, since they are concurrent, by interpolating both ADP and model data to identical time steps. The shear profile is then calculated for each time step. The parameters of the power law profile for the model and the ADP can then be compared on a scatter plot. The power law takes the form:

where is an arbitrary depth and here is chosen to be the middle of the water column. The flow at that height ( ) and the shear exponent ( ) are obtained by fitting a straight line to:

To quantify how well the power law fitted the true flow profile, the R2 value for each fit was also calculated. If both model and ADP data have similar flow profiles, not only should the power from the flow profile be correlated, but also the R2 value. Results for this analysis are presented in Figures 4.19 and 4.20 for the GS and D2 data respectively.


0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

Site

Mod

el

Ebb, R2 >= 0.9

Flood, R2 >= 0.9

Ebb, R2 < 0.9

Flood, R2 < 0.9

Figure 4.19: Scatter Plot of Calculated from Model and ADP Vertical Data Profiles for Site GS

The model has clearly failed to produce a good representation of the true shear profile of the flow, since there is no 1:1 agreement. The ADP data for both sites show that , in reality, is between approximately 6 and 10, with no difference between ebb and flood. The model data, conversely, is primarily in two groups (at = 8 and 9 for GS, and = 9 and 10 for D) with a clear pattern of different profiles for ebb and flood. This artefact between ebb and flood is of particular concern as it could, if believed, easily drive design features of a tidal turbine. Referring back to Figure 4.17 for site D, the lack of a distinct difference between ebb and flood profiles in the ADP data, as presented here, may come as a surprise. This is a result of the large variability in the data overwhelming a rather small difference in flow profiles.


0 2 4 6 8 10 12 14 160

2

4

6

8

10

12

14

16

Site

Mod

el

Ebb, R2 >= 0.9

Flood, R2 >= 0.9

Ebb, R2 < 0.9

Flood, R2 < 0.9

Figure 4.20: Scatter Plot of Calculated from Model and ADP Vertical Data Profiles for Site D

Figure 4.21 compares the values for ebb and flood in the form of a histogram. It can be seen that, for the model, different shear exponents have clearly been found. However, only a very small difference exists in the distributions of flow profiles for the ADP data and even this difference may not be statistically significant. It is only when these differences are aggregated by averaging large numbers of these profiles together (as was performed for Figure 4.17) that a slight difference in flow profiles becomes visible. Calculating the mean on its own is, therefore, not sufficient to identify temporal variation in flow profiles. Instead, this more detailed analysis shows that the model has clearly predicted a differing flood and ebb profile which the ADP data cannot be said to exhibit.


5 6 7 8 9 10 11 120

50

100

150

200Site

Freq

uenc

y

5 6 7 8 9 10 11 120

50

100

150

200

5 6 7 8 9 10 11 120

50

100

150

200Model

Freq

uenc

y

5 6 7 8 9 10 11 120

50

100

150

200

Ebb Flood

Figure 4.21: Distributions of Flow Profiles Produced by the Model and ADP Data in Ebb and Flood for Site D

4.3.3 Sites with Complex Profiles Initial Understanding As has already been discussed, the complex sites cannot be analysed with power-law profiles, therefore an alternative method has to be found. First, a survey of the forms the complex flow takes will be assessed. Figure 4.22 shows all of the data used to create the 1.0 1.2m/s mean flow profile in Figure 4.18. During the flood portion of the tide, the mean flow profile seems to give a good representation of the data (although, as already pointed out, it does not present information on variability). However, the ebb data displays at least two extremely different flow profiles, originating from different directions. As a result, the mean flow profile misrepresents the data used to create it. At sites such as this one, the flow follows a highly elliptical path (i.e. the direction of flow during accelerating and decelerating portions of the tidal cycle are not the same). Therefore, simply choosing a speed bin without reference to the tidal cycle would be inadequate.

0.8 1 1.2 1.4 1.60

5

10

15

20

25

30

35Ebb

Hei

ght a

bove

sea

bed

(m)

Flow speed (m/s)

Dire

ctio

n (d

eg)

315

320

325

330

335

0.8 1 1.2 1.4 1.60

5

10

15

20

25

30

35Flood

Hei

ght a

bove

sea

bed

(m)

Flow speed (m/s)

Dire

ctio

n (d

eg)

115

120

125

130

135

140

145

150

155

Figure 4.22: Flow Profiles for the TGL Sites with Flows between 1 and 1.2m/s. The Black Line is the Mean Flow Profile. The Colour Shows the Direction of Flow.


To contend with these complex flow profiles, two analyses are undertaken. First, a polynomial is fitted to the flow profile at each time step, in order to create a map of flow profiles for the whole measurement period. This makes it to see whether flows from different directions and of different speeds are well matched between the model and the ADP data. Second, the actual ADP and model data are compared for specific flow conditions. This shows what aspects of a flow profile the model is able to find, and what aspects have been missed. This is performed only for a single speed bin. 4.3.4 Sites with Complex Profiles Characterisation and Mapping A polynomial is to be fitted to the shear profiles in order to capture the features apparent in the data. Normalisation of the height above the sea bed and the velocity data is first performed so that the order of the polynomial can be determined. The height becomes:

where is the depth; thus at the sea bed and 1 at the free surface. The velocities are normalised by the depth averaged speed:

Figure 4.23 shows these normalised properties plotted horizontally. A quadratic function was determined to be the most appropriate:

A least-squares fitting of this function for both model and ADP data was performed; however, scatter plots were not able to be used, due to the different time period covered by the data. Instead, flow speed maps of the resulting coefficients are presented in Figure 4.24 for the TGL site and, for comparison, Figure 4.25 for site D. These figures show the same velocity plot as shown in Figures 4.9 to 4.11, but rotated so that the speed in the principal direction is on the x-axis, allowing the width of the elliptical form to be increased and thereby separating the accelerating and decelerating portions of the tide. The colour of the mark is then the value of the coefficient.

Figure 4.23: Illustration of the Normalised Variables used in fitting a Polynomial Flow Profile


-4 -3 -2 -1 0 1 2 3 4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Model

Major Velocity (m/s)

N

E

S

W

-4 -3 -2 -1 0 1 2 3 4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Site


Min

or V

eloc

ity (m

/s)

N

E

S

W

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

(a) Quadratic Coefficient ( )

-4 -3 -2 -1 0 1 2 3 4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Model


N

E

S

W

-4 -3 -2 -1 0 1 2 3 4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Site


Min

or V

eloc

ity (m

/s)

N

E

S

W

-0.1

0

0.1

0.2

0.3

0.4

(b) Linear Coefficient ( )

-4 -3 -2 -1 0 1 2 3 4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Model


N

E

S

W

-4 -3 -2 -1 0 1 2 3 4-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Site


Min

or V

eloc

ity (m

/s)

N

E

S

W

1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.1

(c) Constant Coefficient ( )

Figure 4.24: Fitted Shear Profile coefficients for the TGL Site


-4 -3 -2 -1 0 1 2 3 4-0.2

0

0.2

0.4

0.6

0.8

1

Model


N

E

S

W

-4 -3 -2 -1 0 1 2 3 4-0.2

0

0.2

0.4

0.6

0.8

1

Site


Min

or V

eloc

ity (m

/s)

N

E

S

W

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

(a) Quadratic Coefficient ( )

-4 -3 -2 -1 0 1 2 3 4-0.2

0

0.2

0.4

0.6

0.8

1

Model


N

E

S

W

-4 -3 -2 -1 0 1 2 3 4-0.2

0

0.2

0.4

0.6

0.8

1

Site


Min

or V

eloc

ity (m

/s)

N

E

S

W

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

(b) Linear Coefficient ( )

-4 -3 -2 -1 0 1 2 3 4-0.2

0

0.2

0.4

0.6

0.8

1

Model


N

E

S

W

-4 -3 -2 -1 0 1 2 3 4-0.2

0

0.2

0.4

0.6

0.8

1

Site


Min

or V

eloc

ity (m

/s)

N

E

S

W

0.94

0.96

0.98

1

1.02

1.04

1.06

(c) Constant Coefficient ( )

Figure 4.25: Fitted Shear Profile Coefficients for Site D


Comparison of these two sets of graphs confirms that the TGL site is indeed much more complex than Site D. The flow profile varies depending on the direction of the flow in a manner such that just looking at single sets of speeds would conflate very different flow regimes. The profiles are also very different in ebb and flood, which is not seen in the data for Site D: where the flow profile only seems to take a different form as the velocity tends to zero. From a model validation perspective, it is clear that basic trends have been predicted well by the MIKE model. For Site D, it is clear that both ebb and flow correctly have a similar profile form. Similarities in the form of the maps are also visible for the TGL site; although the patterns are clearly not identical, particularly around velocities of -2m/s. As discussed in Section 4.3.2, the value of the power-law exponent is incorrectly predicted to be different for flood and ebb tides at Site D. However, the similarity of the ADP and model analysis in Figure 4.25 when compared to the far greater variation for the TGL site puts into perspective the performance of the model. 4.3.5 Sites with Complex Profiles Direct Comparison More valuable information can be derived from direct comparison of flow profiles in a certain speed bin, but after having split them up into flood, ebb, accelerating and decelerating flow: in order to try to account for the complexity shown in Figure 4.24. To this end, the data for one speed bin, 1.0 - 1.2m/s, has been plotted for both the TGL site and site D. The data have been selected based on absolute depth averaged speed. Ebb and flood have been separated by considering the directions of the principal axis, and accelerating and decelerating flow by assessing a smoothed differential of the flow resolved to the principal direction. These flow profiles, showing both absolute speed and direction at each depth, have then been normalised by dividing them by the depth-averaged speed and multiplying by the bin centre (1.1m/s). The TGL site results are shown in Figure 4.26. Some features of the flow profiles have clearly been well represented. For example, all the flow conditions except accelerating ebb flow match up very well in both direction and overall form. Accelerating flood flow appears to break down into three flow regimes: Flow from 180 with an un-sheared flow about 10m; Flow from 150 with an un-sheared flow about 10m; and Flow from 140 with a heavily sheared flow. The model appear to differentiate much more strongly between the second and third of these. The accelerating ebb flow has produced the worst discrepancy. Although the model has managed to predict that the flow speed is maximum at approx 10-15m, then decreasing to the surface, it has substantially underestimated the reversed shear profile above 15m. It has been observed that this is a trend for all instances with a heavily reversed shear profile, and so is likely to be a difficult profile for MIKE to recreate. The ADP data also shows two distinct shear profiles in the accelerating ebb flow, which are not present in the model data. The model has found a much better agreement for the D site. As all four of the flow conditions show a simple shear profile, the model has represented them well. The model has performed


particularly well in identifying the range of profiles measured during decelerating ebb flow. On the other hand, the model predicts two distinct flow profiles for accelerating flood flow, which is not apparent from the ADP data. The fact that one of these flow profiles has an extremely different form to all other data at this site probably accounts for the separation in ebb and flood profiles shown in Figures 4.20 and 4.21.


0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)

Ebb, Accelerating (53)

Dire

ctio

n (d

eg)

310

320

330

340

350

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)

Flood, Accelerating (50)

Dire

ctio

n (d

eg)

100

110

120

130

140

150

160

170

180

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)

Ebb, Decelerating (26)

Dire

ctio

n (d

eg)

310

320

330

340

350

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)

Flood, Decelerating (83)

Dire

ctio

n (d

eg)

100

110

120

130

140

150

160

170

180

(a) ADP Data

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

310

320

330

340

350

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

100

110

120

130

140

150

160

170

180

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

310

320

330

340

350

0.7 0.8 0.9 1 1.1 1.2 1.3 1.40

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


D

irect

ion

(deg

)

100

110

120

130

140

150

160

170

180

(b) Model Data

Figure 4.26: The 1.0-1.2m/s Speed Bin for the TGL Site. The Number in Brackets in Each Title is the Number of Samples in the Figure.


0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

300

305

310

315

320

325

330

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

135

140

145

150

155

160

165

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

300

305

310

315

320

325

330

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

135

140

145

150

155

160

165

(a) ADP Data

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

300

305

310

315

320

325

330

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

135

140

145

150

155

160

165

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

15

20

25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


Dire

ctio

n (d

eg)

300

305

310

315

320

325

330

0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.60

5

10

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30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


D

irect

ion

(deg

)

135

140

145

150

155

160

165

(b) Model Data

Figure 4.26: The 1.0-1.2m/s Speed Bin for Site D. The Number in Brackets in Each Title is the Number of Samples in the Figure.


4.3.6 Shear Profile Data for CFD Modelling The ReDAPT CFD modelling of MD1 will be based on flow measurements obtained by the measurement campaign of MD3. The target flow-speeds for this campaign are bins of 0.2 m/s width, centered at 1.8 m/s and 2.8 m/s (see TGL TRN316 [4]). To inform the inputs to CFD models, the methodology of Section 4.3.5 is therefore applied to the following two velocity ranges: 1.7-1.9 m/s and 2.7-2.9 m/s. The first step is to compare model and ADP for these flow speed bins. Figures 4.27 and 4.28 show similar trends as for the 1.0-1.2m/s speed bin: particularly the under-estimation of the reversed shear profile above the maximum velocity in accelerating ebb flow. Two additional discrepancies between the model and the ADP data are worth commenting upon, since they were not present to the same degree in the 1.0-1.2m/s flow profiles: 1. In accelerating flood flow at 1.7-1.9m/s there is a flow deficit at approx 12m in some of the

shear profiles. It is beloved that this is a result of the operation of the TGL 500kW turbine, however the authors have not had confirmation of the times when the device was operational.

2. The flow in both the accelerating and decelerating ebb conditions at 2.7-2.9m/s shows a

considerable amount of directional twist in the ADP data, with the flow at the sea bed being at 335, decreasing to 315 at the sea surface. This is a twist of 20. The model, however, has only produced a twist of about 5. This is a trend seen elsewhere to a lesser degree in the data.

Second, data from the model will be extracted for different locations without validation data in order to inform the CFD modelling in the following ways: 1. An important input to the CFD model is definition of a representative flow-field across a

vertical plane approximately 5 diameters upstream of the turbine (~100 m) and with a width of approximately 4 diameters (~ 80 m). It is important to understand: a) The form of the depth variation in velocity profile at, or near, the TGL turbine location

during flood and ebb tides. Based on the information in previous sections, this comprises 8 profiles corresponding to accelerating and decelerating profiles for both flood and ebb tide for bins with centres 1.8 m/s and 2.8 m/s. A table indicating the number of profiles extracted from the model for each of the 8 flow states will be provided.

b) The spatial variation of the velocity profile in the 'streamwise' direction. A

comparison between the TGL location and points on a plane of about 80m width and 100m upstream along the directions of the principal headings given in Table 4.9 will be provided.

2. Whilst this analysis provides information on predicted mean flow, information on the flow

profile and turbulence characteristics will be obtained from the MD3 measurement campaign.


1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.10

5

10

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20

25

30

35

Flow speed (m/s)

Hei

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315

320

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335

340

345

1 1.5 2 2.50

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1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.10

5

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315

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335

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1 1.5 2 2.50

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Flow speed (m/s)

Hei

ght a

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(m)


Dire

ctio

n (d

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120

125

130

135

140

145

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155

(a) ADP Data

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.10

5

10

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35

Flow speed (m/s)

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ght a

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(m)


Dire

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n (d

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315

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330

335

340

345

1 1.5 2 2.50

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35

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Hei

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Dire

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eg)

120

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155

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.10

5

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35

Flow speed (m/s)

Hei

ght a

bove

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bed

(m)


Dire

ctio

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eg)

315

320

325

330

335

340

345

1 1.5 2 2.50

5

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35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


D

irect

ion

(deg

)

120

125

130

135

140

145

150

155

(b) Model Data

Figure 4.27: The 1.7-1.9m/s Speed Bin for the TGL Site.

The Number in Brackets in Each Title is the Number of Samples in the Figure.


2 2.5 3 3.50

5

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35

Flow speed (m/s)

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ght a

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Dire

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315

320

325

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335

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.60

5

10

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35

Flow speed (m/s)

Hei

ght a

bove

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(m)


Dire

ctio

n (d

eg)

132

134

136

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140

142

2 2.5 3 3.50

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ght a

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(m)


Dire

ctio

n (d

eg)

315

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330

335

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.60

5

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Flow speed (m/s)

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ght a

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Dire

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142

(a) ADP Data

2 2.5 3 3.50

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335

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.60

5

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2 2.5 3 3.50

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35

Flow speed (m/s)

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ght a

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(m)


Dire

ctio

n (d

eg)

315

320

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330

335

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.60

5

10

15

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25

30

35

Flow speed (m/s)

Hei

ght a

bove

sea

bed

(m)


D

irect

ion

(deg

)

132

134

136

138

140

142

(b) Model Data

Figure 4.28: The 2.7-2.9m/s Speed Bin for the TGL Site.

The Number in Brackets in Each Title is the Number of Samples in the Figure.


5 SUMMARY AND CONCLUSIONS Data produced by the new 3D model of the Falls of Warness have been compared to ADP and tidal gauge data from four locations. Time-domain analyses have been carried out on concurrent data, and spectral analysis for all the locations. Tidal height (surface elevation), depth-averaged velocities and shear profiles have all been investigated the latter have been reduced to a set of polynomial coefficients which will be useful for MD1. The key conclusions reached regarding the depth averaged performance of the Mike 3 model are: 1. Tidal height data is well-reproduced by the model at all locations tested throughout the

Falls of Warness. 2. No standing wave phenomenon has been observed in the Falls of Warness. 3. Depth-averaged velocity data is well-reproduced. With regard the 3 dimensional effects of flow, the following general comments need to be considered when interpreting data from the model: For each site, general trends in flow profile are correct in the model. General trends in the variation of shear profile with site and region of the tidal cycle are

reproduced by the model. General trends in the variation of the profile with direction are reproduced by the model. The near-bed profile is nearly always steeper than measured, this might be improved with

calibrated bed roughness coefficients or finer model resolution.

The model underestimates the amount by which flows can twist through the water column.

The model underestimates the amount by which shear profiles can be reversed above the

depth of maximum flow speed, particularly at the TGL location. The lack of variability in profiles from the model could lead one to overestimate the

importance of certain flow features (see particularly the accelerating flood flow in Figure 4.26).

The overall conclusion is that the model will be used to investigate spatial variation in mean shear profiles over a range of flood and ebb conditions, in order to inform the CFD modelling as part of ReDAPT. In future, site data should be used to carefully validate results at any new site and check for discrepancies. Care must be taken to account for the model underestimating complex flow features (such as twist or reversed shear) or over-estimating differences in simpler flow profiles.


6 REFERENCES [1] NOAA, NOS Standards for Evaluating Operational Nowcast and Forecast Hydrodynamic

Model Systems (2003) NOAA Technical Report NOS CS 17. [2] PAWLOWICZ R, Beardsley B, and Lentz S, (2002) "Classical tidal harmonic analysis

including error estimates in MATLAB using T_TIDE", Computers and Geosciences 28, 929-937.

[3] PUGH D T, Tides, Surges and Mean Sea-Level (1987) Wiley, ISBN 0 471 91505 X. [4] SELLAR B, STALLARD T & THOMSON M, TRN316: Targeted Turbulence

Characterisation (2012) TGL.

CNS-PM-796-R-C10151 004-KG_CSW reissue to ETI.PDF1 INTRODUCTION1.1 Background to this Report1.2 Acceptance Criteria for MD5.2

2 DATA2.1 MIKE Model2.2 Validation Data

3 VALIDATION PROCESS3.1 Time Series3.2 Harmonic Analysis

4 RESULTS4.1 Tidal Height Validation4.1.1 Testing for a Standing Wave4.1.2 Time-Domain Analysis4.1.3 Spectral Analysis

4.2 Velocity: Two-Dimensional Validation4.2.1 Time-Domain Analysis4.2.2 Spectral Analysis

4.3 Velocity: Three-Dimensional Validation4.3.1 Generalised Shear Profiles4.3.2 Sites with Power-Law Profiles4.3.3 Sites with Complex Profiles Initial Understanding4.3.4 Sites with Complex Profiles Characterisation and Mapping4.3.5 Sites with Complex Profiles Direct Comparison4.3.6 Shear Profile Data for CFD Modelling

5 SUMMARY AND CONCLUSIONS6 REFERENCES

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