Full transmission through perfect-conductor subwavelength hole arrays

Light transmission through 2D subwavelength hole arrays in perfect-conductor films is shown to be complete (100%) at some resonant wavelengths even for arbitrarily narrow holes. Conversely, the reflection on a 2D planar array of non-absorbing scatterers is shown to be complete at some wavelengths regardless how weak the scatterers are. These results are proven analytically and corroborated by rigorous numerical solution of Maxwell's equations. This work supports the central role played by dynamical diffraction during light transmission through subwavelength hole arrays and it provides a systematics to analyze more complex geometries and many of the features observed in connection with transmission through hole arrays.Comment: 5 pages, 4 figure

Influence of Mild Bottom Slopes on the Overtopping Flow over Mound Breakwaters under Depth-Limited Breaking Wave Conditions

[EN] The crest elevation of mound breakwaters is usually designed considering a tolerable mean wave overtopping discharge. However, pedestrian safety, characterized by the overtopping layer thickness (OLT) and the overtopping flow velocity (OFV), is becoming more relevant due to the reduction of the crest freeboards of coastal structures. Studies in the literature focusing on OLT and OFV do not consider the bottom slope effect, even if it has a remarkable impact on mound breakwater design under depth-limited breaking wave conditions. Therefore, this research focuses on the influence of the bottom slope on OLT and OFV exceeded by 2% of incoming waves, hc,2% and uc,2%. A total of 235 2D physical tests were conducted on conventional mound breakwaters with a single-layer Cubipod® and double-layer rock and cube armors with 2% and 4% bottom slopes. Neural networks were used to determine the optimum point to estimate wave characteristics for hc,2% and uc,2% calculation; that point was located at a distance from the model toe of three times the water depth at the toe (hs) of the structure. The influence of the bottom slope is studied using trained neural networks with fixed wave conditions in the wave generation zone; hc,2% slightly decreases and uc,2% increases as the gradient of the bottom slope increases.This research was funded by Ministerio de Economia y Competitividad and the Fondo Europeo de Desarrollo Regional (FEDER) under grant BIA2015-70436-R and RTI2018-101073-B-I00. The first author was also financially supported by the Ministerio de Educacion, Cultura y Deporte through the FPU program (Formacion de Profesorado Universitario) under grant FPU16/05081.Mares-Nasarre, P.; Gómez-Martín, ME.; Medina, JR. (2020). Influence of Mild Bottom Slopes on the Overtopping Flow over Mound Breakwaters under Depth-Limited Breaking Wave Conditions. Journal of Marine Science and Engineering. 8(1):1-16. https://doi.org/10.3390/jmse8010003S11681www.overtopping-manual.comMolines, J., & Medina, J. R. (2016). Explicit Wave-Overtopping Formula for Mound Breakwaters with Crown Walls Using CLASH Neural Network–Derived Data. Journal of Waterway, Port, Coastal, and Ocean Engineering, 142(3), 04015024. doi:10.1061/(asce)ww.1943-5460.0000322Nørgaard, J. Q. H., Lykke Andersen, T., & Burcharth, H. F. (2014). Distribution of individual wave overtopping volumes in shallow water wave conditions. Coastal Engineering, 83, 15-23. doi:10.1016/j.coastaleng.2013.09.003Molines, J., Herrera, M. P., Gómez-Martín, M. E., & Medina, J. R. (2019). Distribution of individual wave overtopping volumes on mound breakwaters. Coastal Engineering, 149, 15-27. doi:10.1016/j.coastaleng.2019.03.006Mares-Nasarre, P., Argente, G., Gómez-Martín, M. E., & Medina, J. R. (2019). Overtopping layer thickness and overtopping flow velocity on mound breakwaters. Coastal Engineering, 154, 103561. doi:10.1016/j.coastaleng.2019.103561Herrera, M. P., Gómez-Martín, M. E., & Medina, J. R. (2017). Hydraulic stability of rock armors in breaking wave conditions. Coastal Engineering, 127, 55-67. doi:10.1016/j.coastaleng.2017.06.010Van Gent, M. R. A. (2003). WAVE OVERTOPPING EVENTS AT DIKES. Coastal Engineering 2002. doi:10.1142/9789812791306_0185Schüttrumpf, H., Möller, J., & Oumeraci, H. (2003). OVERTOPPING FLOW PARAMETERS ON THE INNER SLOPE OF SEADIKES. Coastal Engineering 2002. doi:10.1142/9789812791306_0178Gent, M. R. A. van. (2001). Wave Runup on Dikes with Shallow Foreshores. Journal of Waterway, Port, Coastal, and Ocean Engineering, 127(5), 254-262. doi:10.1061/(asce)0733-950x(2001)127:5(254)Van der Meer, J. W., Hardeman, B., Steendam, G. J., Schuttrumpf, H., & Verheij, H. (2011). FLOW DEPTHS AND VELOCITIES AT CREST AND LANDWARD SLOPE OF A DIKE, IN THEORY AND WITH THE WAVE OVERTOPPING SIMULATOR. Coastal Engineering Proceedings, 1(32), 10. doi:10.9753/icce.v32.structures.10Lorke, S., Scheres, B., Schüttrumpf, H., Bornschein, A., & Pohl, R. (2012). PHYSICAL MODEL TESTS ON WAVE OVERTOPPING AND FLOW PROCESSES ON DIKE CRESTS INFLUENCED BY WAVE-CURRENT INTERACTION. Coastal Engineering Proceedings, 1(33), 34. doi:10.9753/icce.v33.waves.34Herrera, M. P., & Medina, J. R. (2015). Toe berm design for very shallow waters on steep sea bottoms. Coastal Engineering, 103, 67-77. doi:10.1016/j.coastaleng.2015.06.005Gómez-Martín, M. E., & Medina, J. R. (2014). Heterogeneous Packing and Hydraulic Stability of Cube and Cubipod Armor Units. Journal of Waterway, Port, Coastal, and Ocean Engineering, 140(1), 100-108. doi:10.1061/(asce)ww.1943-5460.0000223Argente, G., Gómez-Martín, M., & Medina, J. (2018). Hydraulic Stability of the Armor Layer of Overtopped Breakwaters. Journal of Marine Science and Engineering, 6(4), 143. doi:10.3390/jmse6040143Gómez-Martín, M., Herrera, M., Gonzalez-Escriva, J., & Medina, J. (2018). Cubipod® Armor Design in Depth-Limited Regular Wave-Breaking Conditions. Journal of Marine Science and Engineering, 6(4), 150. doi:10.3390/jmse6040150Battjes, J. A., & Groenendijk, H. W. (2000). Wave height distributions on shallow foreshores. Coastal Engineering, 40(3), 161-182. doi:10.1016/s0378-3839(00)00007-7Victor, L., van der Meer, J. W., & Troch, P. (2012). Probability distribution of individual wave overtopping volumes for smooth impermeable steep slopes with low crest freeboards. Coastal Engineering, 64, 87-101. doi:10.1016/j.coastaleng.2012.01.003Verhagen, H. J., van Vledder, G., & Arab, S. E. (2009). A PRACTICAL METHOD FOR DESIGN OF COASTAL STRUCTURES IN SHALLOW WATER. Coastal Engineering 2008. doi:10.1142/9789814277426_0241Van Gent, M. R. A., van den Boogaard, H. F. P., Pozueta, B., & Medina, J. R. (2007). Neural network modelling of wave overtopping at coastal structures. Coastal Engineering, 54(8), 586-593. doi:10.1016/j.coastaleng.2006.12.001Molines, J., Herrera, M. P., & Medina, J. R. (2018). Estimations of wave forces on crown walls based on wave overtopping rates. Coastal Engineering, 132, 50-62. doi:10.1016/j.coastaleng.2017.11.00

Design and construction of the western breakwater for the outer port at Punta Langosteira (A Coruña, Spain)

This paper describes the design process, hydraulic stability tests and construction of the Cubipod® armored Western breakwater at Punta Langosteira (Outer Port of A Coruña, Spain), located on the Atlantic coast of Spain. The environmental, geotechnical, economic and logistic conditions favored randomly-placed Cubipods for single-layer armoring of the trunk. 3D hydraulic stability tests were carried out to validate the final design of the Western Breakwater; two models were tested with single- and double-layer Cubipod armors in the trunk and roundhead, respectively. Single-layer 25- and 30-tonne Cubipod® armors were used for the trunk section and a double-layer 45-tonne Cubipod® armor was used for the roundhead. During this project, new challenges were overcome, such as constructing a transition between single and double-layer armors, and manufacturing and handling of 45-tonne Cubipods. The transition in the armor thickness was solved by modifying the filter thickness under the main armor, to ensure a homogeneous external armor profile. Breakwater construction finished in November 2016 with no significant problem or delay in the original schedule

Armor Porosity and Hydraulic Stability of Mound Breakwaters

Armor porosity significantly affects construction costs and hydraulic stability of mound breakwaters; however, most hydraulic stability formulas do not include armor porosity or packing density as an explicative variable. 2D hydraulic stability tests of conventional randomly-placed double-layer cube armors with different armor porosities are analyzed. The stability number showed a significant 1.2-power relationship with the packing density, similar to what has been found in the literature for other armor units; thus, the higher the porosity, the lower the hydraulic stability. To avoid uncontrolled model effects, the packing density should be routinely measured and reported in small-scale tests and monitored at prototype scale.The authors are grateful for financial support from the Spanish Ministerio de Economía y Competitividad and FEDER (Grant BIA2012-33967) and CDTI (CUBIPOD and CLIOMAR Projects). The second author was funded through the FPU program (Formación del Profesorado Universitario, Grant AP2010-4366) by the Spanish Ministerio de Educación, Cultura y Deporte

Design and construction of the western breakwater for the outer port at Punta Langosteira (A Coruña, Spain)

This paper describes the design process, hydraulic stability tests and construction of the Cubipod® armored Western breakwater at Punta Langosteira (Outer Port of A Coruña, Spain), located on the Atlantic coast of Spain. The environmental, geotechnical, economic and logistic conditions favored randomly-placed Cubipods for single-layer armoring of the trunk. 3D hydraulic stability tests were carried out to validate the final design of the Western Breakwater; two models were tested with single- and double-layer Cubipod armors in the trunk and roundhead, respectively. Single-layer 25- and 30-tonne Cubipod® armors were used for the trunk section and a double-layer 45-tonne Cubipod® armor was used for the roundhead. During this project, new challenges were overcome, such as constructing a transition between single and double-layer armors, and manufacturing and handling of 45-tonne Cubipods. The transition in the armor thickness was solved by modifying the filter thickness under the main armor, to ensure a homogeneous external armor profile. Breakwater construction finished in November 2016 with no significant problem or delay in the original schedule

The Performance Evolution of Match Play Styles in the Spanish Professional Basketball League

The aim of this study is to analyse the performance evolution of all, and the dominant, team’s performances throughout an eight-season period within the Spanish professional basketball league. Match-related statistics were gathered from all regular season matches (n = 2426) played during the period 2009−2010 to 2016−2017. The non-metric multidimensional scaling model was used to examine the team’s profiles across seasons and for the most successful (playoff) teams. The main results showed that: 3-point field goals made (effect size, d = 0.61; 90% confidence interval, CI = 0.23; 1.37) and missed (d = 0.72; 90% CI = 0.35; 1.46), and assists (d = 1.27; 90% CI = 0.82; 1.86) presented a positive trend with an increased number of actions across the seasons; 2-point field goals made (d = 0.21; 90% CI = −1.25; 2.02) and missed (d = 0.27; 90% CI = −0.52; 0.92) were decreased; free throws made and missed, rebounds, fouls, blocks, steals and turnovers showed a relatively stable performance. The matrix solution (stress = 0.22, rmse (root mean squared error) = 7.9 × 104, maximum residual = 5.8 × 103) indicated minimal season-to-season evolution with the ordination plot and convex hulls overlapping. The two most dominant teams exhibited unique match patterns with the most successful team’s pattern, a potential benchmark for others who exhibited more dynamic evolutions (and less success). The current findings identified the different performances of teams within the Spanish professional basketball league over eight seasons with further statistical modelling of match play performances useful to identify temporal trends and support coaches with training and competition preparations

Numerical Study of Wave Forces on Crown Walls of Mound Breakwaters with Parapets

[EN] The influence of parapets on crown walls of mound breakwaters on wave forces has not been extensively analyzed in the literature. In this study, numerical experiments were carried out using the open-source platform OpenFOAM(R) to evaluate the influence of nine crown wall geometries with and without parapets. The OpenFOAM(R) model was validated with laboratory experiments. Dimensionless horizontal forces and overturning moments due to horizontal forces increase when there is a parapet. Dimensionless up-lift forces provide similar results, regardless of the existence of a parapet. Crown walls with parapets increase the horizontal wave forces and overturning moments due to horizontal wave forces by a factor of two.This research was funded by (1) Universitat Politecnica de Valencia (Grant SP20180111, Primeros Proyectos de Investigacion (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia de la Universitat Politecnica de Valencia) and (2) Spanish Ministerio de Ciencia, Innovacion y Universidades (Grant RTI2018-101073-B-I00).Molines, J.; Bayón, A.; Gómez-Martín, ME.; Medina, JR. (2020). Numerical Study of Wave Forces on Crown Walls of Mound Breakwaters with Parapets. Journal of Marine Science and Engineering. 8(4):1-15. https://doi.org/10.3390/jmse8040276S11584Molines, J., Bayon, A., Gómez-Martín, M. E., & Medina, J. R. (2019). Influence of Parapets on Wave Overtopping on Mound Breakwaters with Crown Walls. Sustainability, 11(24), 7109. doi:10.3390/su11247109Martinelli, L., Ruol, P., Volpato, M., Favaretto, C., Castellino, M., De Girolamo, P., … Sammarco, P. (2018). Experimental investigation on non-breaking wave forces and overtopping at the recurved parapets of vertical breakwaters. Coastal Engineering, 141, 52-67. doi:10.1016/j.coastaleng.2018.08.017Nørgaard, J. Q. H., Andersen, T. L., & Burcharth, H. F. (2013). Wave loads on rubble mound breakwater crown walls in deep and shallow water wave conditions. Coastal Engineering, 80, 137-147. doi:10.1016/j.coastaleng.2013.06.003Molines, J., Herrera, M. P., & Medina, J. R. (2018). Estimations of wave forces on crown walls based on wave overtopping rates. Coastal Engineering, 132, 50-62. doi:10.1016/j.coastaleng.2017.11.004Van Gent, M. R. A., & van der Werf, I. M. (2019). Influence of oblique wave attack on wave overtopping and forces on rubble mound breakwater crest walls. Coastal Engineering, 151, 78-96. doi:10.1016/j.coastaleng.2019.04.001Castellino, M., Sammarco, P., Romano, A., Martinelli, L., Ruol, P., Franco, L., & De Girolamo, P. (2018). Large impulsive forces on recurved parapets under non-breaking waves. A numerical study. Coastal Engineering, 136, 1-15. doi:10.1016/j.coastaleng.2018.01.012Issa, R. . (1986). Solution of the implicitly discretised fluid flow equations by operator-splitting. Journal of Computational Physics, 62(1), 40-65. doi:10.1016/0021-9991(86)90099-9Patankar, S. ., & Spalding, D. . (1972). A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. International Journal of Heat and Mass Transfer, 15(10), 1787-1806. doi:10.1016/0017-9310(72)90054-3Jacobsen, N. G., van Gent, M. R. A., Capel, A., & Borsboom, M. (2018). Numerical prediction of integrated wave loads on crest walls on top of rubble mound structures. Coastal Engineering, 142, 110-124. doi:10.1016/j.coastaleng.2018.10.004Jensen, B., Jacobsen, N. G., & Christensen, E. D. (2014). Investigations on the porous media equations and resistance coefficients for coastal structures. Coastal Engineering, 84, 56-72. doi:10.1016/j.coastaleng.2013.11.004Hirt, C. ., & Nichols, B. . (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201-225. doi:10.1016/0021-9991(81)90145-5Berberović, E., van Hinsberg, N. P., Jakirlić, S., Roisman, I. V., & Tropea, C. (2009). Drop impact onto a liquid layer of finite thickness: Dynamics of the cavity evolution. Physical Review E, 79(3). doi:10.1103/physreve.79.036306Jacobsen, N. G., van Gent, M. R. A., & Wolters, G. (2015). Numerical analysis of the interaction of irregular waves with two dimensional permeable coastal structures. Coastal Engineering, 102, 13-29. doi:10.1016/j.coastaleng.2015.05.004Higuera, P., Lara, J. L., & Losada, I. J. (2014). Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part II: Application. Coastal Engineering, 83, 259-270. doi:10.1016/j.coastaleng.2013.09.002Higuera, P., Lara, J. L., & Losada, I. J. (2013). Realistic wave generation and active wave absorption for Navier–Stokes models. Coastal Engineering, 71, 102-118. doi:10.1016/j.coastaleng.2012.07.002Higuera, P., Lara, J. L., & Losada, I. J. (2013). Simulating coastal engineering processes with OpenFOAM®. Coastal Engineering, 71, 119-134. doi:10.1016/j.coastaleng.2012.06.002Higuera, P., Lara, J. L., & Losada, I. J. (2014). Three-dimensional interaction of waves and porous coastal structures using OpenFOAM®. Part I: Formulation and validation. Coastal Engineering, 83, 243-258. doi:10.1016/j.coastaleng.2013.08.010Bayon-Barrachina, A., & Lopez-Jimenez, P. A. (2015). Numerical analysis of hydraulic jumps using OpenFOAM. Journal of Hydroinformatics, 17(4), 662-678. doi:10.2166/hydro.2015.041Bayon, A., Valero, D., García-Bartual, R., Vallés-Morán, F. ​José, & López-Jiménez, P. A. (2016). Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump. Environmental Modelling & Software, 80, 322-335. doi:10.1016/j.envsoft.2016.02.018Bayon, A., Toro, J. P., Bombardelli, F. A., Matos, J., & López-Jiménez, P. A. (2018). Influence of VOF technique, turbulence model and discretization scheme on the numerical simulation of the non-aerated, skimming flow in stepped spillways. Journal of Hydro-environment Research, 19, 137-149. doi:10.1016/j.jher.2017.10.002Romano, A., Bellotti, G., Briganti, R., & Franco, L. (2015). Uncertainties in the physical modelling of the wave overtopping over a rubble mound breakwater: The role of the seeding number and of the test duration. Coastal Engineering, 103, 15-21. doi:10.1016/j.coastaleng.2015.05.00

Heterogeneous packing and hydraulic stability of cube and cubipod armor units

This paper describes the heterogeneous packing (HEP) failure mode of breakwater armor. HEP reduces packing density in the armor layer near and above the mean water level and increases packing density below it. With HEP, armor units may move in the armor layer, although they are not actually extracted from it. Thus, when HEP occurs, armor-layer porosity is not constant, and measurements obtained with conventional methods may underestimate armor damage. In this paper, the Virtual Net method is proposed to calculate armor damage considering both armor-unit extraction and HEP. The Cubipod concrete armor unit is then described as a solution to the effects of HEP on conventional cubic block armor. The hydraulic stability of cube and Cubipod armor units was compared in two-dimensional laboratory experiments. Cube and Cubipod armor layers were tested in two wave flumes under nonbreaking and non-overtopping conditions. The hydraulic stability was higher for double-layer Cubipod armor than for single-layer Cubipod armor, which had a higher hydraulic stability tan conventional double-layer cube armor.The authors are grateful for the financial support of CDTI (CUBIPOD Project), SATO Construction Co. (OHL Group), and Puertos del Estado (Convenio de Diques). The authors also thank Debra Westall for revising the manuscript.Gómez-Martín, ME.; Medina, JR. (2014). Heterogeneous packing and hydraulic stability of cube and cubipod armor units. Journal of Waterway, Port, Coastal, and Ocean Engineering. 140(1):100-108. doi:10.1061/(ASCE)WW.1943-5460.0000223S100108140

Hydraulic stability of rock armors in breaking wave conditions

[EN] Armor layers of mound breakwaters are usually designed with empirical formulas based on small-scale tests in non-breaking wave conditions. However, most rubble mound breakwaters are constructed in the depth-induced breaking zone, where they must withstand design storms having some percentage of large waves breaking before reaching the structure; in these cases, the design formulas for non-breaking wave conditions are not fully valid. To characterize double-layer rock armor damage in breaking wave conditions, 2D physical model tests were carried out with a bottom slope m=1/50. In order to develop a simple method to determine the wave parameters in the depth-induced breaking zone, experimental wave measurements were compared to the numerical estimations given by the SwanOne model. An analysis was conducted to select the best characteristic wave height to estimate rock armor damage when dealing with depth-induced breaking waves; the spectral significant wave height, Hm0, estimated at a distance of 3hs seaward from the structure toe, was found to be the most adequate. A new hydraulic stability formula is proposed for double-layer rock armors in breaking wave conditions, considering the observed potential 6-power relationship between the equivalent dimensionless armor damage and the Hm0 at 3hs seaward distance from the structure toe.The authors acknowledge the financial support from the Spanish Ministry of Economy and Competitiveness (grants BIA2012-33967 and BIA2015-70436-R). The first author was financially supported through the FPU program (Formacion del Profesorado Universitario) funded by the Spanish Ministry of Education (Ministerio de Educacion, Cultura y Deporte) FPU13/01872. The authors thank Debra Westall for revising the manuscript.Herrera Gamboa, MP.; Gómez-Martín, ME.; Medina, JR. (2017). Hydraulic stability of rock armors in breaking wave conditions. Coastal Engineering. 127:55-67. https://doi.org/10.1016/j.coastaleng.2017.06.010S556712

Hydraulic stability of cube-armored mound breakwaters in depth-limited breaking wave conditions

[EN] Armor erosion due to wave attack has been studied intensively since it is considered the main failure mode of mound breakwaters. Cube-armored mound breakwaters in depth-limited breaking wave conditions are common in practice but have received limited attention in the literature. In this study, 2D physical tests were performed on non-overtopped double-layer randomly-placed cube-armored mound breakwater models with armor slope cot¿ = 1.5 and bottom slope m = 2% in breaking wave conditions. Using the experimental results, a new hydraulic stability formula was derived with a coefficient of determination R2 = 0.85 based on a power relationship between the armor damage and the stability number and the dimensionless water depth. A lower hydraulic stability was found for the front slope of non-overtopped cube-armored structures in breaking wave conditions when compared to formulas given in the literature.The authors acknowledge the support from grant RTI2018-101073B-I00 funded by MCIN/AEI/10.13039/501100011033 and "ERDF A way of making Europe", the Spanish Ministry of Economy and Competitiveness under grant BIA2012-33967, the Generalitat Valenciana under the grant AEST/2021/045 and FEDER. The authors thank Debra Westall for revising the manuscript.Mares-Nasarre, P.; Molines, J.; Gómez-Martín, ME.; Medina, JR. (2022). Hydraulic stability of cube-armored mound breakwaters in depth-limited breaking wave conditions. Ocean Engineering. 259:1-13. https://doi.org/10.1016/j.oceaneng.2022.11184511325