# Extended Long Wave Hindcast inside Port Solutions to Minimize Resonance

^{*}

## Abstract

**:**

## 1. Introduction

_{LW}and lon wave period T

_{LW}) is obvious: (1) for the correct assessment of coastal morphodynamics influenced by long period oscillations [4,5,6]; and for harbor agitation [7,8,9].

_{LW}and T

_{LW}are defined as follows:

## 2. Methodology for Long Wave Assessment

#### 2.1. Overview

^{®}) measurements. A distance of 1.3 km separates both locations, so changes due to refraction and shoaling should be expected; as the short wave propagates from Funwave to the AWAC location. After several tests, negligible differences were observed.

**Figure 2.**Methodological framework to assess and reconstruct time series for wave + bound long wave spectrum.

#### 2.2. Bound Long Wave Prediction

^{2}; k

_{n}is the wave number for spectral component n, in 1/m; k

_{m}is the wave number for spectral component m, in 1/m; Δθ is the angular difference between each individual energy component; k

_{n}is the wave number vector associated with the bound long wave, in 1/m; ω

_{j}= ω

_{n}− ω

_{m}is the angular frequency difference for each individual energy component; and h is the bathymetry depth at each wave spectrum location, in m. Figure 3 shows an example of the application of the equations described above, combining short wave energy components for a spectrum selected randomly from the 27 August 2007 inoperability event (provided by the MWPA). Initial spectral characteristics are: significant wave height of H

_{s}= 3.49 m, peak period T

_{p}= 13.75 s, mean period T

_{z}= 7.49 s and mean propagation direction (in nautical) θ = 236°. After applying Equations (1) and (2), the obtained long wave height and mean period are: H

_{LW}= 0.26 m and T

_{LW}= 43 s. This methodology was applied in for the infragravity and resonance wave hindcast in some ports in the north of Spain, obtaining good H

_{LW}and T

_{LW}predictions [12].

**Figure 3.**Modified full amplitude spectra for the 27 August 2007 inoperability event at the AWAC location. Bound long wave energy indicated with a dashed-line circle.

## 3. Validation and Diagnosis

#### 3.1. Validation

_{LW}and period T

_{LW}. They are compared to data measured during 2004 at the AWAC location (provided by the MWPA; see Figure 1).

**Figure 4.**Comparison of long wave time series obtained for H

_{LW}and T

_{LW}, for the AWAC location, during August and September 2004. Predicted (line); measured (points).

_{LW}is well predicted along the whole instrumental record. For T

_{LW}, it can be observed that predicted values present a smoother behavior in time, not matching all of the temporal variations shown in the records. Average trends and the general envelope of this variable on time is well predicted by the methodology proposed. Still, T

_{LW}predicted results can be considered to be a good approximation taking the advantage of having long-term time series of infragravity waves inside the harbors.

_{LW}and T

_{LW}time series for the following locations: Berths 2 to 3, 3 to 4, 5 to 6 and 7, Beacons 17 and 20 and the Seal Rocks locations (data provided by the MWPA).

_{LW}predictions inside the basin provide appropriate values and similar time evolution. Overall good predictions and trends can be seen, but for some locations, it seems that post-processing for T

_{LW}is different from one location to another (measured T

_{LW}data would respond to a zero crossing infragravity wave period (25 to 150 s) or to a spectral peak period of infragravity waves (25 to 150 s), according to MWPA information). It is expected that if H

_{LW}is well predicted, long wave periods within the full spectra will be realistic.

**Figure 5.**Comparison of long wave time series obtained for H

_{LW}and T

_{LW}for Berths 2 to 3, 3 to 4, 5 to 6 and 7, Beacons 17 and 20 and the Seal Rocks point. Predicted (line); measured (points).

#### 3.2. Diagnosis

_{LW}Berth 2 to 7. Figure 7 shows a box-plot of the monthly performance of H

_{LW}for the 12 years evaluated at the same points.

- H
_{LW}within the port (Berths 2 to 7) is always lower than the external forcing at the AWAC location. - Berths 2 to 7 show a similar agitation response.
- Mean values of H
_{LW}, from 0.02 m for the months of January to April and November to December, and of 0.05 m for the rest of the year. - Each month, the 12-year analyzed H
_{LW}shows values of 0.1 and 0.2 m (75% percentile of between), depending on the season. - Berth 4 is the most vulnerable zone to long wave oscillations, as higher H
_{LW}values were presented by the numerical records. - Exceedances at Berth 4 can reach maximum values around 0.4 m.
- Approximately 30% of the year (2600 h per year), H
_{LW}values are exceeded over 0.1 m (as an average value at all of the berthing locations). - Between 5% and 1% of the year (between 440 and 90 h per year), the threshold exceed 0.2 m (depending on the port area).

_{LW}inside the basin never exceed the AWAC records (if this location is considered as the outer boundary forcing). However, a detailed analysis using isolated frequency bands within the spectrum does suggest a modest degree of frequency-specific amplification (not necessarily shown by the total H

_{LW}values).

## 4. Potential Solutions

_{LW}acts as a forcing of the system, independently of the short wave propagation interaction after the reef.

- A1, construction of a new oblique breakwater of 400 m connected to the eastern breakwater.
- A2, construction of a new oblique, exterior and detached breakwater of 780 m, located 600 m from Geraldton Harbor.
- A3, construction of an extension of 1000 m of the eastern breakwater.
- A4, construction of a new oblique breakwater of 300 m perpendicular to the mouth of the harbor.
- A5, 250 m breakthrough of the eastern breakwater towards the beach.
- A6, 150 m breakthrough of Berth Zone 6 towards the fishing boat harbor.
- A7, extension of 300 m for the western breakwater.

_{LW}time series for August to September 2004 for Berths 2 to 3 and Berths 5 to 6 (an inoperability event did occur around 25 August 2004), showing the response of the harbor under each of the alternatives proposed.

**Figure 9.**Comparison of HLW for the different harbor layouts proposed for year 2004 at Berths 2 to 3 and 5 to 6. A1, Alternative 1.

_{LW}(for A0).

A1 | A2 | A3 | A4 | A5 | A6 | A7 |
---|---|---|---|---|---|---|

3.8 | −19.2 | 19.1 | −4.1 | 26.7 | 0.7 | −31.2 |

_{LW}presented in Figure 8 show, as expected, that each of the proposed geometries yields a different harbor response, sometimes bigger (A1, A3, A5 and A6) and other times lower (A2, A4 and A7).

## 5. Evaluation of Long Wave-Induced Currents

_{LW}events inside the harbor; 1-hour long sea state.

**Figure 10.**Snapshot for the maximum long wave-induced current of the 27 August 2007 inoperability event at Geraldton Harbor, obtained with the MANOLO model.

- 60-year hindcast analysis.
- Calibration of the short wave hindcast in the AWAC location.
- Simultaneous short + long wave propagation and analysis of alternatives.
- Evaluation of the effects of each alternative at the beach and in the near harbors.
- Evaluation of the non-linear effects of the energy transfer mechanism from high to low frequencies due to the reef.
- Reconstruction of the whole statistics of flow currents using the Boussinesq tool, for the present geometry and for each possible solution proposed.
- Evaluation of the statistics, occurrence probability and operability for short and long waves for each of the final solutions evaluated.

## Acknowledgments

## Conflicts of Interest

## References

- Munk, W.H. Surf beats. Trans. Am. Geophys. Union
**1949**, 30, 849–854. [Google Scholar] - Tucker, M. Surf beats: Sea waves of 1 to 5 min. period. Proc. R. Soc. Lond. A
**1950**, 202, 565–573. [Google Scholar] [CrossRef] - Longuet-Higgins, M.S.; Stewart, R.W. Radiation stress and mass transport in gravity waves, with application to “surf beats”. J. Fluid Mech.
**1962**, 13, 481–504. [Google Scholar] [CrossRef] - Roelvink, J.A.; Stive, M.J.F. Bar-generating cross-shore flow mechanisms on a beach. J. Geophys. Res. Oceans
**1989**, 94, 4785–4800. [Google Scholar] [CrossRef] - Baldock, T.E.; Alsina, J.A.; Caceres, I.; Manoonvoravong, P.; Pham, K.S. Influence of surf-beat on beach morphology and sediment transport. In Proceedings of the 34th IAHR World Congress 33rd Hydrology and Water Resources Symposium, Brisbane, Australia, 26 June–1 July 2011; pp. 973–980.
- Baldock, T.E.; Manoonvoravong, P.; Pham, K.S. Beachface morphology and surf beat sediment transport in laboratory scale surf and swash zones. J. Coast. Res.
**2007**, 1, 631–635. [Google Scholar] - Bellotti, G. Transient response of harbors to long waves under resonance conditions. Coast. Eng.
**2007**, 54, 680–693. [Google Scholar] [CrossRef] - Kofoed-Hansen, H.; Kerper, D.R.; Sorensen, O.R.; Kirkegaard, J. Simulation of long wave agitation in ports and harbours using a time-domain Boussinesq model. In Proceedings of the Fifth COPRI International Conference on Ocean Wave Measurement and Analysis-WAVES, Madrid, Spain, 3–7 July 2005; p. 77.
- McComb, P.J.; Johnson, D.L.; Brett, B.J. Numerical study of options to reduce swell and long wave penetration at port Geraldton. In Proceedings of the 19th Australasian Coastal and Ocean Engineering Conference 2009 and the 12th Australasian Port and Harbour Conference 2009 (Coast and Ports 2009): In a Dynamic Environment, Wellington, New Zealand, 16–18 September 2009; pp. 490–496.
- Sharma, J.; Dean, R. Development and evaluation of a procedure for simulating a random directional second order sea surface and associated wave forces. In Ocean Engineering Report; University of Delaware: Newark, DE, USA, 1979. [Google Scholar]
- Okihiro, M.; Guza, R.T.; Seymour, R.J. Bound infragravity waves. J. Geophys. Res. Oceans
**1992**, 97, 11453–11469. [Google Scholar] [CrossRef] - Diaz-Hernandez, G.; Mendez, F.J.; Losada, I.J.; Camus, P.; Medina, R. A nearshore long-term infragravity wave analysis for open harbours. Coast. Eng.
**2015**, 97, 78–90. [Google Scholar] [CrossRef] - Berkhoff, J.C.W. Computation of Combined Refraction-Diffraction; Delft Hydraulics Laboratory: Delft, The Netherlands, 1972. [Google Scholar]
- GIOC. Manual del programa en elementos finitos msp para el estudio de agitación portuaria. In Grupo de Ingeniería Oceanográfica y de Costas. Documento Técnico y Manual de Usuario; Universidad de Cantabria: Santander, Spain, 2000. [Google Scholar]
- Nwogu, O. Alternative form of Boussinesq equations for nearshore wave propagation. J. Waterw. Port Coast. Ocean Eng.
**1993**, 119, 618–638. [Google Scholar] [CrossRef] - Woo, S.-B.; Liu, P.L.-F. Finite-element model for modified Boussinesq equations. I: Model development. J. Waterw. Port Coast. Ocean Eng.
**2004**, 130, 1–16. [Google Scholar] [CrossRef] - Woo, S.-B.; Liu, P.L.-F. Finite-element model for modified Boussinesq equations II. Applications to Nonlinear Harbor Oscillations. J. Waterw. Port Coast. Ocean Eng.
**2004**, 130, 1–16. [Google Scholar] [CrossRef] - Losada, I.J.; Gonzalez-Ondina, J.M.; Diaz-Hernandez, G. Numerical modeling of nonlinear resonance of semi-enclosed water bodies: Description and experimental validation. Coast. Eng.
**2008**, 55, 21–34. [Google Scholar] [CrossRef] - Camus, P.; Mendez, F.J.; Medina, R. A hybrid efficient method to downscale wave climate to coastal areas. Coast. Eng.
**2011**, 58, 851–862. [Google Scholar] [CrossRef] - Camus, P.; Mendez, F.J.; Medina, R.; No, A.S.C. Analysis of clustering and selection algorithms for the study of multivariate wave climate. Coast. Eng.
**2011**, 58, 453–462. [Google Scholar] [CrossRef] - Camus, P.; Mendez, F.J.; Medina, R.; Tomas, A.; Izaguirre, C. High resolution downscaled ocean waves (DOW) reanalysis in coastal areas. Coast. Eng.
**2013**, 72, 56–68. [Google Scholar] [CrossRef] - Kennard, R.W.; Stone, L.A. Computer aided design of experiments, american statistical association and american society for quality. Technometrics
**1969**, 11, 137–148. [Google Scholar] [CrossRef]

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Diaz-Hernandez, G.; Lara, J.L.; Losada, I.J.
Extended Long Wave Hindcast inside Port Solutions to Minimize Resonance. *J. Mar. Sci. Eng.* **2016**, *4*, 9.
https://doi.org/10.3390/jmse4010009

**AMA Style**

Diaz-Hernandez G, Lara JL, Losada IJ.
Extended Long Wave Hindcast inside Port Solutions to Minimize Resonance. *Journal of Marine Science and Engineering*. 2016; 4(1):9.
https://doi.org/10.3390/jmse4010009

**Chicago/Turabian Style**

Diaz-Hernandez, Gabriel, Javier L. Lara, and Inigo J. Losada.
2016. "Extended Long Wave Hindcast inside Port Solutions to Minimize Resonance" *Journal of Marine Science and Engineering* 4, no. 1: 9.
https://doi.org/10.3390/jmse4010009