1 PHYSICAL AND NUMERICAL MODELLING OF ...

PHYSICAL AND NUMERICAL MODELLING OF WAVE TRANSFORMATION OVER A SUBMERGED RUBBLE-MOUND STRUCTURE Scott Baker1, Ioan Nistor1, Andrew Cornett2, Pedro Lomonaco3 Physical and numerical modelling of the interaction of irregular waves with a large-scale three-dimensional submerged structure was performed, with the purpose of understanding the structure’s influence on the wave and hydrodynamic field, the wave-induced velocities along the structure crest, as well as on the wave-induced currents. Extensive processing and analysis was performed for a multitude of data and experimental scenarios, including – but not limited to – wave heights, wave periods, wave energy spectra, energy transfer functions, wave reflection, and wave-induced velocities.

INTRODUCTION

Submerged rubble-mound structures are widely used for coastal defence against severe hydrodynamic conditions generated by the combined action of waves and currents. Understanding energy dissipation and wave transformation over submerged structures is essential in assessing their structural reliability and in determining their impacts on the environment. The objective of this research program was to investigate and quantify, both experimentally and numerically, the wave transformation and hydrodynamic field induced by the presence of a steeply-sloped, deeply submerged structure with a varying cross-section and varying submergence depth. The project is a component of an extensive collaborative research program established between the Department of Civil Engineering at the University of Ottawa, Canada, and the Canadian Hydraulics Centre (CHC) of the National Research Council of Canada. PHYSICAL MODELLING

The large scale three-dimensional physical model of the submerged structure was designed and constructed in the Coastal Basin at the Canadian Hydraulics Centre in Ottawa, Canada. The basin measures 63 m long by 14 m wide by 1.5 m in height, and is equipped with a computer controlled multi-mode wave generator capable of producing irregular long-crested waves with significant wave heights of up to approximately 0.35 m at model scale. The

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Department of Civil Engineering, University of Ottawa, 161 Louis Pasteur, CBY A-115, Ottawa, Ontario, K1N 6N5, Canada 2 Canadian Hydraulics Centre, National Research Council 1200 Montreal Road, Building M32, Ottawa, Ontario, K1A 0R6, Canada 3 Environmental Hydraulics Institute, University of Cantabria, Avda de los Castros, 39005 Santander, Spain

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2 basin is fitted with highly efficient wave absorbers for minimizing undesired wave reflections back into the model area. The physical modelling study was conducted at an undistorted 1 to 50 length scale (based on Froude scaling). A 7.2 m wide central testing channel was created by constructing two parallel solid vertical walls and leaving two 3.4 m wide side-channels on either side of the central channel. A rigid model bathymetry was constructed within the central testing channel, which included a 0.32 m deep by 6 m long trench that was filled with fine sand used to simulate the seabed beneath the submerged structure. Two thrusters were placed in each of the side channels in order to generate reversing currents within the central channel (simulating tidal currents). Steady currents could be generated flowing both with and against the direction of wave propagation. Test cases involving currents will not be discussed in the present paper. Wave conditions in the model were measured at 10 locations, distributed up-wave, down-wave, and along the crest of the submerged structure using capacitance wire gauges. The arrangement of the wave gauges remained constant throughout the calibration and testing stages so that further comparison of the impact of the structure on the wave field could be properly assessed. The magnitude and direction of the orbital velocities and currents were measured using two 2-axis electromagnetic current meters (ECM) installed along the channel centerline up-wave and down-wave from the structure, and three 3-axis acoustic Doppler velocimeters (ADV) placed above the structure crest. Similarly, the location of the current meters remained constant throughout the calibration and testing phases. Once the structure was constructed, the locations of the ADVs were set approximately 5 cm above the longitudinallyvarying crest elevation of the submerged structure. A series of tests were conducted prior to constructing the submerged structure in order to calibrate and verify the waves and currents within the central test channel. Once the undisturbed tests were competed, dredging works were replicated in the mobile sand bed and the model structure was constructed. The submerged rubble-mound structure had a longitudinally varying freeboard, from approximately half the water depth at the high end (-14.8 m), sloping down to just above the seabed (-30.3 m) at the lower end (see Figure 1).

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Figure 1. Physical model of the submerged structure in CHC’s Coastal Basin.

Once the structure was completed, a series of tests were carried out with varying significant wave heights, wave periods, and water levels (see Table 1). The generated waves were irregular and long-crested, defined by the JONSWAP spectrum, with a γ parameter of 3.3. Each time series of waves had a duration corresponding to a 5 hour storm at full scale (approximately 43 minutes at model scale), and each wave train consisted of more than 1000 individual waves. Table 1. Test Series – Extreme (storm) wave conditions

Test

Wave Height (m)

Wave Period (s)

Case 0 Case 1 Case 2 Case 3 Case 4

4.5 4.5 6.0 6.0 7.0

16.2 16.2 20.1 20.1 20.1

Water Level from MSL (m) -1.55 -1.55 -1.72 -5.00 -5.00

Storm Duration (hrs)

Presence of Tunnel

5 5 5 5 5

No Yes Yes Yes Yes

NUMERICAL SIMULATIONS

Numerical modelling was undertaken to verify and compare the computational results with the data collected during the experiments. To properly simulate the propagation and transformation of waves over a steeply sloping submerged structure, a highly non-linear numerical model was required. In this study, the 2DH (two-dimensional horizontal) numerical model WaveSim (Nwogu 1993, 1996) was employed. WaveSim is an extended Boussinesq-type model, based on the depth-integrated mass and momentum equations for nonlinear dispersive waves. The model is capable of simulating the nonlinear transformation of irregular multidirectional waves in water of varying depth, incorporating at the same time the effects of shoaling, refraction, diffraction,

4 full/partial reflection and transmission, bottom friction, nonlinear wave-wave interactions, wave breaking and runup, and wave-induced currents. The computational domain (see Figure 2) was a replica of the central test channel from the physical modelling study. The domain included the initial bathymetry and the submerged structure. Since currents were not simulated, the lateral channels were omitted from the computational domain. The numerical wave generator was placed at the left side of the computational domain, with 200 m long sponge layers placed behind the wave generator and also downwave of the submerged structure in order to absorb all outgoing wave energy and prevent any undesirable reflections from the front and back walls.

Figure 2. Overview of the computational domain.

The computational domain was discretized using grid steps of ∆y = 5.25 m by ∆x = 14.4 m (prototype) yielding a grid with 245 steps in the direction of wave propagation and 25 steps in the transverse direction. A time step of 0.1 s was found to maintain stability of the numerical solution. The model’s strong non-linearity and wave-breaking options were both utilized for all the numerical simulations. The same test conditions listed above (refer to Table 1) were simulated using the numerical model so that direct comparisons of the computational and experimental results could be performed. RESULTS

The authors performed significant processing and analysis on both the experimental and numerical data sets. This included comparisons of the wave statistics and spectra, the transfer function (describing changes in spectral shape across the structure), and orbital velocities between the physical and numerical results. The numerical simulations alone were used to investigate the spatial distribution of significant wave height around the structure, the wave-induced current field, and level of wave reflection. For the undisturbed test condition (before the structure was constructed, refer to Table 1 -- Case 0) the comparison of the wave spectra showed that the experimental and numerical results matched very well. When the submerged structure was included in the physical and numerical model, a significant change in the wave conditions was observed. The gauges located up-wave of the structure measured higher waves than was observed during the undisturbed case due to wave reflections from the submerged structure. As expected, the readings

5 showed that the influence of the structure was more significant at the right side of the channel, where the submergence depth was smaller (the structure was taller). A similar trend was observed for the gauges located at the structures crest (see Figure 3). Figure 3a shows the measured wave spectra at the left side of the channel, where the submergence depth was greatest (the structure was shorter). Only a small increase in measured wave height was observed in this location. However, Figure 3d demonstrates a significant increase in the measured wave height, for the location where the submergence depth was smallest. The submerged structure forces the approaching waves to undergo shoaling as they pass over it.

Figure 3. Comparison of wave spectra above the crest of the submerged structure from numerical simulations and physical experiments of Test Case 3.

6 The wave heights observed at all the down-wave located gauges, for both the physical and numerical model were nearly identical, suggesting, as expected, that the submerged structure increases wave energy dissipation with decreasing submergence depth. A transfer function provides a measure of the transfer of energy into and out of a system. Transfer functions were defined relating the wave spectra measured down-wave from the submerged structure to spectra measured on the up-wave side. These transfer functions describe the frequency-dependent changes in wave energy due to the presence of the submerged structure. In this case, a distinct pattern in energy transfer across the structure was revealed by the analysis of variance spectra of the wave conditions. Specifically, a significant reduction in energy is observed at the spectral peak frequency fp, and a significant increase in energy is observed at roughly 1.8 times the spectral peak frequency (see Figure 4).

Figure 4. Comparison of transfer functions from numerical simulations and physical experiments of Test Case 3.

Figures 4a and 4b show the up-wave and down-wave spectra respectively, while Figure 4c shows the computed transfer function. Although the results were much more clearly visible in the numerical modelling results, the “W” shape of the computed transfer function was repeatedly observed in both the

7 numerical and physical modelling results. Also, as expected, the “W” shape was accentuated where the structure freeboard was least, that is, where more energy transfer occurred. Orbital velocities were measured above the structure’s crest at three locations. The influence of the submerged structure was consistently observed in both the physical and numerical model. Figure 5 shows the cumulative distributions of orbital velocities for the three measurement locations.

Figure 5. Comparison of orbital velocities above the crest of the submerged structure from physical experiments and numerical simulations of Test Case 4.

The dotted lines show the measured velocities during the undisturbed case before the structure was introduced. In Figure 5a, where the crest of the submerged structure was almost even with the sea floor, there is little difference between the measured and simulated velocities with and without the structure. However, in Figure 5c, both the physical measurements and numerical

8 simulations show that velocities measured over the crest of the structure increased with increasing crest elevation. As the wave heights increased with each progressive test case, the observed orbital velocities also increased in magnitude. A reflection analysis was also performed using data from the numerical simulations. For the undisturbed case, no wave reflection was observed since there were no obstructions in the path of the incident waves. However, once the structure was included, a steady increase in reflected wave energy was observed as the freeboard of the structure decreased. In other words, the reflected wave energy was roughly proportional to the submergence depth (height) of the structure. Figure 6 shows an example of the incident and reflected wave trains in front of the part of the structure with lowest freeboard (greatest height) for Test Case 4. The overall reflection coefficient for this case was 35%.

Figure 6. Wave reflection analysis from numerical simulations of Test Case 4.

These results confirm some of the findings of previous researchers. Twu et al. (2001) conducted research on deeply submerged breakwaters and developed an equation for calculating wave reflection from such structures. In general, the reflection coefficients computed from the numerical simulations in this study agree very well with the relationship proposed by Twu et al. The spatial distribution of time-averaged wave height around the submerged structure was also examined. The numerical simulations clearly showed the formation of a partial standing wave field in front of the submerged structure, with peaks occurring approximately every half-wavelength. The numerical results also showed that the longitudinally sloping submerged structure induced a circular time-averaged residual current with flow in the direction of wave propagation over the lower part of the structure, balanced by flow in the opposite direction over the higher part (see Figure 7).

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Submerged structure

Wave propagation Figure 7. Circular time-averaged current.

Although the WaveSim model has its limitations, the numerical model provided an excellent tool for studying the wave field transformation over a steeply-sloped, three-dimensional submerged structure. Weston et al. (2004) modelled wave groups passing over a shoal and observed the release of free waves as the wave groups returned to deeper water. This phenomenon was clearly reproduced in the present numerical simulations as well. As particularly large waves passed over the submerged structure, the rapid change in water depth induced the waves to steepen and take on a highly non-linear shape associated with the growth of high-frequency harmonics. A portion of this high-frequency energy was released as free waves on the downwave side of the structure. Burcharth et al. (2006) observed that the freeboard has a large influence in regards to the initiation of damage for low-crested structures. The pattern of damage observed in the physical model study was entirely consistent with this finding. A significant increase in observed damage to the outer armour layer was observed as the freeboard of the structure decreased (as the crest elevation increased). CONCLUSIONS

Submerged structures are increasingly being considered for use in coastal engineering applications. However, past research has focused on low-crested structures while relatively few studies have specifically dealt with deeply submerged structures. In addition, unlike this study, most previous research considered structures with uniform cross-section and constant submergence

10 depth (Van der Meer & Daemen (1994), d'Angremond et al. (1996), Seabrook & Hall (1998), Briganti et al. (2003), etc.). The present study showed that the wave-structure interactions were intense and significantly affected the local hydrodynamic conditions. The submerged structure induced significant transformations to the wave characteristics and generated substantial orbital velocities at the crest of the structure. As expected, the maximum increases in wave height and wave-induced velocities were observed where the submergence depth of the structure was smallest (where the structure crest was highest). The present study showed that even deeply submerged structures can have complex and important effects on waves and orbital velocities. These effects can be important considerations for the design of the submerged structure itself, the design of other structures nearby, and the assessment of the structure’s impact on the surrounding marine environment. The three-dimensional sloping nature of the submerged structure considered herein spawned a circular residual current that would not occur in cases with a uniform crest elevation. ACKNOWLEDGMENTS

The authors wish to express their gratitude to the Canadian Hydraulics Centre, National Research Council Canada, for providing the experimental facilities and to the Natural Sciences and Engineering Research Council of Canada (NSERC) for its partial financial support for this project. REFERENCES

Baker, S. 2007. Physical and Numerical Modelling of Wave Interaction with a 3-D Submerged Structure, M.A.Sc. Thesis, Department of Civil Engineering, University of Ottawa, 223 pp. Briganti, R., Van der Meer, J., Buccino, M., & Calabrese, M. 2003. Wave Transmission Behind Low-Crested Structures, Proceedings of the Conference on Coastal Structures, 580-592. Burcharth, H.F., Kramer, M., Lamberti, A., & Zanuttigh, B. 2006. Structural Stability of Detached Low Crested Breakwaters, Coastal Engineering, 53, 381-394. d'Angremond, K., Van der Meer, J.W., & de Jong, R.J. 1996. Wave Transmission at Low-Crested Structures, Proceedings of the 25th International Conference on Coastal Engineering, 2418-2427. Nwogu, O. 1993. Alternative Form of Boussinesq Equations for Nearshore Wave Propagation, Journal of Waterway, Port, Coastal and Ocean Engineering, 119(6), 618-638. Nwogu, O. 1996. Numerical Prediction of Breaking Waves and Currents with a Boussinesq Model, Proceedings of the 25th International Conference on Coastal Engineering, 4807-4820.

11 Seabrook, S.R., & Hall, K.R. 1998. Wave Transmission at Submerged Rubblemound Breakwaters, Proceedings of the 26th International Conference on Coastal Engineering, 2000-2013. Twu, S.-W., Liu, C.-C., & Hsu, W.-H. 2001. Wave Damping Characteristics of Deeply Submerged Breakwaters, Journal of Waterway, Port, Coastal, and Ocean Engineering, 127(2), 97-105. Van der Meer, J.W., & Daemen, I.F.R. 1994. Stability and Wave Transmission at Low-Crested Rubble-Mound Structures, Journal of Waterway, Port, Coastal, and Ocean Engineering, 120(1), 19 pp. Weston, B.P., Taylor, P.H., Borthwick, A.G.L., Hunt, A.C., & Stansby, P.K. 2004. Boussinesq Modelling of Wavegroup Propagation over a Shallow Shoal and the Release of Second Order and Higher Harmonics. Proceedings of the 29th International Conference on Coastal Engineering, 1277-1289.

12 KEYWORDS – ICCE 2008 PHYSICAL AND NUMERICAL MODELLING OF WAVE TRANSFORMATION OVER A SUBMERGED RUBBLE-MOUND STRUCTURE Scott Baker, Ioan Nistor, Andrew Cornett, Pedro Lomonaco Abstract #76 Breakwaters Coastal structures Deeply submerged structures Numerical modelling Physical modelling Wave transformation Wave reflection