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Wave Transmission and Wave Induced Currents around a Reef Breakwater

Shirin SHUKRIEVA*, Valeri PENCHEV** * Bulgarian Academy of Sciences - BSHC Varna, Bulgaria, 9003 Varna, kv. Asparuhovo, 1 William Froude St., P.O. Box 58, Bulgaria, e-mail: sh.shukrieva @bshc.bg ** Black Sea Coastal Association - Varna, Bulgaria, v.penchev @coresbg.eu

Keywords: waves, currents, reef breakwater, numerical modelling Abstract

This paper presents a numerical approach for simulating the processes of wave transmission and associated wave induced set-up, as well as wave driven currents in the neighborhood of a reef breakwaters, using MIKE 21 BW and MIKE 3 FM numerical models. Two dimensional numerical simulations have been carried out for a virtual submerged reef placed on a gentle slope, as well as for a reef planned to be placed at certain area along the Bulgarian Black Sea coast.

Numerical simulation results have been compared to physical model data on wave height transformation and orbital wave velocities. Several submergence cases and wave spectra have been applied in the physical model. Numerical results from the simulations have been also compared to some published test data. A good correspondence has been concluded which encourages the author for further development of the approach.

1. INTRODUCTION

Reef breakwaters are applied to cause breaking of waves at a distance from the beaches, and this way to reduce wave energy flux. They are permanently submerged detached breakwaters most often constructed as rubble mound structures. Construction of a reef breakwater is a sensitive engineering solution where that needs the knowledge of relationships linking basic parameters such as depth of submergence (freeboard) and crest width to wave transmission and set-up behind the structure.

Wave transmission, reflection, and wave overtopping at low-crested structures have been studied extensively with 2-D physical models by Ahrens (1987 and 2001), Seabrook and Hall (1998), Van der Meer (1991), Penchev et al. 1986 and 2001, and other. Most of these studies concerned narrow-crested, emergent structures with little variation in experiment parameters for a given study. It is now widely accepted that main parameters influencing wave transmission at a reef breakwater are the relative depth of submergence dS / HS (where dS = structure submergence, HS = unreflected incident wave height), and the relative crest width B/L (where B = crest width of the structure; and L = wavelength). Detailed diagrams for evaluation of wave transmission behind low-crested structures have been proposed by Tanaka (1976) based on wave tests that included both submerged and emerged crests as well as a broad range of wave crests. Later, a number of empirical formulae have been suggested (Van der Meer 1991; d’Angremond, Van der Meer and de Jong 1996; Seabrook and Hall 1998; Ahrens 1987 and 2001; Siladharma and Hall 2003; Friebel and Harris 2004). A critical evaluation of the above formulae by Wamsley, Hanson

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and Craus (2002), Pilarczyk (2003), Penchev (2005), Penchev et al. (2007), has concluded that different formulae refer to different conditions - fully submerged or emerging, short or broad-crested structures, monochromatic or irregular, breaking or non-breaking waves. These formulae can be used for preliminary design, however their area of application is restricted, in general - to the ranges suggested by authors.

Numerical models that solve the unsteady Reynolds-Averaged Navier-Stokes Equations (RANSE) are being used to simulate spilling and plunging waves over submerged obstacles, or over a sloping bed VOF (volume of fluid) technique to track the discontinuous free surface (Lin and Liu, 1998; Lomonaco et al. 2004; Penchev and Scheffermann, 2005 and 2006). Parabolic mild slope models as well as 2D Boussinesq models have been used to calculate waves and wave driven currents around low crested structures by Johnson et al. (2005). Commercial 2DH model MIKE 21 is tested in predicting parameters relevant to the design process as set-up, overtopping and returning flows by Zanuttigh and Lamberti (2006). As the dominant mechanism for dissipating wave energy over a submerged breakwater is depth-limited wave breaking (while available models for energy dissipation due to wave breaking are developed for beaches and gentle slopes), a method for numerical modelling wave breaking over submerged structures has been developed by Johnson (2005), where wave breaking is split into two parts: 1) depth-limited breaking and 2) steepness limited breaking.

It is worth to note that even the best numerical wave model would not provide appropriate results for wave disturbance if the hydrodynamic properties of the reef breakwater (reflection and transmission coefficients, energy dissipation factor, and porosity factor) are not well defined in advance.

The present study is focused on the modelling of waves and currents around reef breakwaters using MIKE 21 BW and MIKE 3 FM.

2. BASIC MODEL PARAMETERS

2.1 Breakwater properties

An impermeable submerged breakwater (rubble mound structure covered with concrete plate revetments) has been considered for this study. 2D numerical simulations have been carried out for 2 basic cases:

a) a virtual submerged reef placed on a gentle slope 1:40 b) a reef breakwater designed to be placed at certain area along the Bulgarian

Black Sea coast (real bathymetry)

Virtual reef breakwater characteristics are presented on Figure 1. The fully submerged detached breakwater is placed parallel to the shoreline at 200 m from the shoreline, and at 5m water depth, with the following dimensions:

crest length of 350 m crest width 18 m side slopes 1:3 both offshore and onshore direction submergence of 1.2 m bellow still water level

The size of the numerical model is 1200 m x 1500 m (Figure 1). It consists of two sections: a 360 m wide horizontal section with a depth of 15 m and plain sloping beach of 1:40 between the horizontal section and the shoreline.

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a) cross section

b) 3D view c) bathymetry

Figure 1. Reef breakwater characteristics.

Analogue reef breakwater dimensions and size were used for the reef to be placed at a real area at the Black sea coast. Bathymetry of the area is shown on Figure 2.

Figure 2. Bathymetry of a reef breakwater designed to be placed along the Bulgarian Black Sea coast

2.2 Wave climate

The wave climate was reproduced by both regular and irregular waves with the following parameters:

Regular unidirectional waves - H = 1 m, T = 8 s and direction is from East; Irregular one-dimensional waves: HS = 0.5 m, TP = 8 s and wave direction from East (BW) HS = 1.0 m, TP = 8 s and wave direction from East (BW and SW) HS = 2.0 m, TP = 8 s oblique waves (SW)

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Higher waves have been tried to be simulated in BW at relatively low depth of submergence of the reef, but unfortunately simulations were unstable as discussed further bellow in this paper.

The above wave conditions have been applied for both Boussinesq and Spectral Wave models. The internal wave generation has been used to create wave series which have been applied to a generation line at the eastern boundary in Boussinesq model of MIKE 21.

2.3 Water levels and currents

In order to simplify the simulations no current and water level variations have been included. The latest corresponds to the environmental conditions at the Black sea which is a tideless sea without any strong permanent littoral currents.

2.4 Sea bed

A mean sand diameter D50 of 0.2 mm has been selected for the constant slope model (Figure 1).

For the real area from the Black sea coast the mean sand diameter D50 varies from 0.2 - 0.5 mm. Bathymetry of the area is shown on Figure 2.

3. BOUSSINESQ WAVE MODEL

The objective of the 2D BW model simulations was to calculate wave disturbance as well as wave driven currents behind the reef.

The numerical model covers an area of 1200 m x 1500 m, grid cell size is 3 m, the depth varies from 15 m to 0.5 m. The model consists of two sections: a 360 m wide horizontal section with 15 m water depth and a plane sloping beach 1:40. A fully submerged breakwater is placed at 5 m water depth parallel to the shoreline with dimensions as shown on Figure 1.

The onshore side of the breakwater is located 200 m from the shoreline. An absorbing beach is placed on the offshore side of the reef breakwater.

Simulation period covers 15 minutes real time, a time step of 0.125 s has been considered in accordance with the maximum Courant number limitations. Wave climate conditions have been simulated as presented above.

As a result the following parameters have been calculated and analysed:

wave heights surface elevation flow velocity components

Main results are illustrated on Figures 3 to 6

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a) Significant wave height distribution, Hs [m]

b) Mean surface elevation, [m]

c) Velocity distribution

Figure 3. Example results from irregular waves simulations.

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a) Wave height distribution, H [m]

b) Mean surface elevation, [m]

c) Velocity direction

Figure 4. Example results from regular waves simulations.

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4. MIKE 3 FM

The objective of the MIKE 3 FM model simulations was to calculate wave driven currents behind the reef using radiation stresses calculated by MKE 21 wave models (in this particular case MIKE SW was used).

The virtual reef breakwater model domain covers an area of 1200 m x 1500 m with a maximum water depth 24 m. The computational unstructured mesh consists of nearly 7000 triangular elements and 5000 nodes, with 10 layers in the vertical domain are used. The triangular elements are coarser in offshore direction and refined for the reef breakwater area and the shoreline (Figure 5-a).

a) virtual reef breakwater

b) reef breakwater over a real bathymetry

Figure 5. Reef breakwater, flexible mesh bathymetry.

The simulations cover 30 minutes real time duration, irregular waves have been simulated in this case with significant wave height Hs = 1 m, Tp = 8 s, waves are coming from south. The horizontal eddy viscosity type has been set to the Smagorinsky formulation with a constant value of 0.28. The vertical eddy viscosity type has been presented by k-ε formulation. The bed resistance type has been set to roughness height with a constant value of 0.28. Wave radiations have been set as varying in time and in the domain as calculated with the MIKE 21 SW. The results from simulations are shown on Figures 6 to 9.

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Figure 6. Significant wave height, Hs, [m]

Figure 7. Wave set-up, [m]

Figure 8. Velocity distribution [m/s]

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Figure 9. Current speed and direction, [m/s]

The second case study model for a reef breakwater (placed over a real bathymetry on the Black sea) has an area of approximately 3 168 000 m2 (Figure 5b). The duration time of the simulations is 50 minutes, irregular waves have been simulated in this case with significant wave height Hs = 2 m, Tp= 8 s, waves are coming from South-East.

Some results from the numerical simulations, as described above, are illustrated on Figures 10 to 13.

Figure 10. Significant wave height distribution [m].

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Figure 11. Wave set-up distribution [m].

Figure 12. Mean wave period, [sec]

Typical flow velocity distribution of wave driven currents is shown on Figure 13a and vertical profile of the currents is presented on Figure 13b.

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a) plan view

b) cross section

Figure 13. Current speed and flow direction, [m/s]

A comparison between physical model data and numerical simulations of wave height disturbance (Hs) for submerged breakwaters with similar geometry and wave climate conditions is presented on Figure 14. Test data are taken from physical model tests as presented in Table 1. In general, good correspondence between physical and numerical model data has been concluded, which encourages the authors in their further study on this issue.

Table 1. Model set-up characteristics of the tested submerged breakwaters

Author Water depth h (m)

Crest width B (m)

Submergence dS (m)

Wave period Tm (s)

Wave height Hs (m)

dS / Hs

Present BW model 5 18 1.2 8 1.0 1.2

Johnson et al. (2005) 0.25 1.00 0.05 2.4 0.06 0.83

Penchev et al. (2001) 1.00 3.60 0.25 2.69 0.25 1.00

Penchev et al. (2001) 0.60 1.00 0.10 2.5 0.14 0.7

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0

0.25

0.5

0.75

1

1.25

1.5

-3 -2 -1 0 1 2 3 4 5

X/B

Hs(x

) /

Hs,i

-0.5

0

0.5

1

1.5

z /

h

MIKE BW Simulations

Johnson et al. (2005)

Penchev et al. (2001)

Penchev (2006)

Figure 14. Numerical vs physical model data for wave disturbance behind reef breakwaters with close geometry and wave climate conditions

4. Problems and challenges.

In general, most of the simulations within the present study were successful, and provided very promising results on wave-structure interaction. However, some technical and practical problems have been detected during simulations, and in particular when applying the BW model. These difficulties are discussed here below.

Some limitations occur when the depth of submergence of the structure is close to the incoming wave height: negative water depth occurs in some cells at the top of the reef that leads to abnormal completion of simulations. Filtering layers to reduce high frequencies, as well as moving shoreline option could be applied in some cases, however this does not solve the problem completely.

It should be noted that drying of the reef crown is a real natural phenomena (it has been detected also in physical model tests), and therefore it needs special attention.

The above phenomenon is related mainly to the wave breaking problem. The available wave breaking model integrated in BW model (incl. roller form factor and celerity) does not provide reliable description of breaking process over a submerged breakwater (reef). An improved depth-limited breaking model is required, as suggested in previous study of Johnson et al. (2005).

It should be noted also that application of BW model for short waves (hmax /Lo > 0.22), as typical for some areas at Black Sea coast, needs the inclusion of “deep water” terms, that requires substantially more CPU time. Therefore, this leads to some restricted application for some climate conditions.

Finally, the main challenge remains the application of MIKE 21 BW at low submergences and higher waves, where more attention should be paid to clarify the above discussed issues.

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5. Conclusions

A numerical approach to simulate wave disturbance and wave driven currents around reef breakwaters is demonstrated within the present study, and is proposed to facilitate appropriate design of this type of coastal structures.

2D waves in the vicinity of coastal structures have been simulated using Boussinesq Wave module of MIKE 21. Concurrently, another approach has been tried, where radiation stresses calculated by the wave models have been used as input to the hydrodynamic model (MIKE 3 FM) to simulate wave induced currents around reef structures.

The analysis of computational results from the above models, as well as the comparison of numerical results with test data for various types of reef, different geometry parameters, and broad band of wave climate conditions, has shown promising results that encourage author for further research, development, and use of presented approaches for practical design of reef breakwaters. As it has been discussed above, more attention should be paid to possibility to improve MIKE 21 BW for application at low submergences and high waves. REFERENCES

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