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Shallow water wave propagation over curved wave guides

Published online by Cambridge University Press:  07 August 2025

Edgardo Rosas Open the ORCID record for Edgardo Rosas [Opens in a new window] ,
Fabián Sepúlveda-Soto  and
Claudio Falcón Open the ORCID record for Claudio Falcón [Opens in a new window]
Edgardo Rosas*
Affiliation:
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla, Santiago 4873, Chile Laboratoire Gulliver (UMR 7083), CNRS, ESPCI Paris, PSL Research University, Paris, France
Fabián Sepúlveda-Soto*
Affiliation:
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla, Santiago 4873, Chile Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago, Chile
Claudio Falcón*
Affiliation:
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla, Santiago 4873, Chile
*
Corresponding authors: Claudio Falcón, cfalcon@uchile.cl; Edgardo Rosas, edgardo.rosas@espci.fr; Fabián Sepúlveda-Soto, fsepulveda@dim.uchile.cl
Corresponding authors: Claudio Falcón, cfalcon@uchile.cl; Edgardo Rosas, edgardo.rosas@espci.fr; Fabián Sepúlveda-Soto, fsepulveda@dim.uchile.cl
Corresponding authors: Claudio Falcón, cfalcon@uchile.cl; Edgardo Rosas, edgardo.rosas@espci.fr; Fabián Sepúlveda-Soto, fsepulveda@dim.uchile.cl
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Abstract

We report on the experimental and theoretical characterisation of shallow water wave guiding along a curved wave guide. A curved beam of fixed height and width positioned at the bottom of a wave tank generates an effective step-like perturbation which can guide surface water waves. We construct a linear wave theory for this wave propagation and characterise the parameter region where wave guiding can develop, as well as the possible guided modes, their profile and propagation constant. The theoretical analysis is supported by experimental surface wave data. A good agreement is found between experimental data and theoretical predictions, which gives insight into the possible harnessing of wave-guiding phenomena for energy harvesting.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave-structure interactions

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 1016 , 10 August 2025 , A64
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© The Author(s), 2025. Published by Cambridge University Press

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References

Accatino, L. & Bertin, G. 1990 Modal analysis of curved waveguides. In 20th European Microwave Conference 90, vols 1 and 2, pp. 1246–1250.Google Scholar
Anton, S.R. & Sodano, H.A. 2007 A review of power harvesting using piezoelectric materials (2003–2006). Smart Mat. Struct 16, R1–R21.10.1088/0964-1726/16/3/R01CrossRefGoogle Scholar
Arthur, R.S., Munk, W.H. & Isaacs, J.D. 1955 The direct construction of wave rays. Trans. Am. Geophys. Union 33, 855–865.Google Scholar
Berglund, W. & Gonipath, A. 2000 WKB analysis of bend losses in optical waveguides. J. Lightwave Technol. 18, 1161–1166.10.1109/50.857763CrossRefGoogle Scholar
Boyd, C.M. & Smith, S.L. 1983 Plankton, upwelling, and coastally trapped waves off Peru. Deep-Sea Res. I 30, 723–742.10.1016/0198-0149(83)90019-5CrossRefGoogle Scholar
Bresch, D. & Desjardins, B. 2003 Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic. Model. Commun. Math. Phys. 238, 211.10.1007/s00220-003-0859-8CrossRefGoogle Scholar
Brink, K.H. 1991 Coastal-trapped waves and wind-driven currents over the continental shelf, Ann. Rev. Fluid Mech. 23, 389–412.Google Scholar
Brink, K.H. 2006 Coastal-trapped waves with finite bottom friction. Dyn. Atmos. Ocean 41, 172–190.10.1016/j.dynatmoce.2006.05.001CrossRefGoogle Scholar
Bryan, K.R. & Bowen, A.J. 1993 Edge wave trapping and amplification on barred beaches. J. Geophys. Res. Oceans 101, 6543–6552.CrossRefGoogle Scholar
Buchwald, V.T. 1968 Long waves on oceanic ridges. Proc. R. Soc. Lond. A 308, 343–354.Google Scholar
Buchwald, V.T. & Adams, J.I. 1969 The propagation of continental shelf waves. Proc. R. Soc. A 305, 235–250.Google Scholar
Bühler, O. 2014 Waves and mean flows, Cambridge monographs on mechanics, 2nd edn.CrossRefGoogle Scholar
Cai, D.P., Lu, Y.H., Chen, C.C., Lee, C.C., Lin, C.E. & Yen, T.J. 2015 High Q-factor microring resonator wrapped by the curved waveguide. Sci. Rep. 5, 10078.10.1038/srep10078CrossRefGoogle ScholarPubMed
Caldwell, D.R., Cutchin, D.L. & Longuet-Higgins, M.S. 1972 Some model experiments on continental shelf waves. J. Mar. Res. 30, 39–55.Google Scholar
Chamberlain, P.G. & Porter, D. 1999 Scattering and near-trapping of water waves by axisymmetric topography. J. Fluid Mech. 388, 335–354.CrossRefGoogle Scholar
Chen, J., et al. 2015 Networks of triboelectric nanogenerators for harvesting water wave energy: a potential approach toward blue energy. ACS Nano 9, 3324–3331.CrossRefGoogle ScholarPubMed
Cho, Y.H. & Galan, J.M. 2004 Investigation of guided wave scattering in curved waveguides KEM (Volumes 270–273), 447–452.Google Scholar
Codiga, D.L., Renouard, D.P. & Fincham, A.M. 1999 Experiments on waves trapped over the continental slope and shelf in a continuously stratified rotating ocean, and their incidence on a canyon. J. Mar. Res. 57, 585–612.Google Scholar
Collin, R.E. 1990 Field Theory of Guided Waves. 2nd edn. Wiley-IEEE Press.10.1109/9780470544648CrossRefGoogle Scholar
Craik, A.D.D. 1988 Wave Interactions and Fluid Flows (Cambridge Monographs On Mechanics). Cambridge University Press.Google Scholar
De Freitas, P.P., Paiva, A.de M., Cirano, M., Mill, G.N., da Costa, V.S., Gabioux, M. & França, B.R.L. 2021 Coastal trapped waves propagation along the southwestern Atlantic continental shelf. Continental Shelf Res. 226, 104496.10.1016/j.csr.2021.104496CrossRefGoogle Scholar
Demma, A., Cawley, P. & Lowe, M.J.S. 2002 Guided waves in curved pipes (in review of progress in quantitative evaluation. (ed. D.O. Thompson & D.E. Chimenti), vol. 21, pp. 157–164.Google Scholar
di Leoni, P.C., Cobelli, P.J. & Mininni, P.D. 2014 Wave turbulence in shallow water models. Phys. Rev. E 89, 063025.CrossRefGoogle Scholar
Dodd, N., Stoker, A.M., Calvete, D. & Sriariyawat, A. 2008 On beach cusp formation. J. Fluid Mech. 597, 145–169.Google Scholar
Drivdal, M., Weber, J.E.H. & Debernard, J.B. 2016 Dispersion relation for continental shelf waves when the shallow shelf part has an arbitrary width: application to the shelf west of Norway. J. Phys. Oceanogr. 46, 537–549.10.1175/JPO-D-15-0023.1CrossRefGoogle Scholar
Elgar, S., Herbers, T.H.C. & Guza, R.T. 1994 Reflection of ocean surface gravity waves from a natural beach. J. Phys. Oceanogr. 24, 1503–1511.10.1175/1520-0485(1994)024<1503:ROOSGW>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Evans, D.V. & Linton, C.M. 1993 Edge waves along periodic coastlines. Q. J. Mech. Appl. Maths 46, 643–656.CrossRefGoogle Scholar
Falkovich, G. 2011 Fluid Mechanics: A Short Course for Physicists. Cambridge University Press.Google Scholar
Fong, J. & Lowe, M.J.S. 2004 Curvature effect on the properties of guided waves in plates (in review of progress in quantitative evaluation. (ed. D.O. Thompson & D.E. Chimenti), vol. 23, pp. 126–133.Google Scholar
Grant, I., Stewart, N. & Padilla-Perez, I.A. 1990 Topographical measurements of water waves using the projection moire method. Appl. Opt. 20, 3981–3983.CrossRefGoogle Scholar
Howd, P.A., Bowen, A.J. & Holman, R.A. 1992 Edge waves in the presence of strong longshore currents. J. Geophys. Res 97, 11357–11371.10.1029/92JC00858CrossRefGoogle Scholar
Hsiao, S.-C., Shih, M.-Y. & Wu, N.-J. 2018 Simulation of propagation and run-up of three dimensional landslide-induced waves using a meshless method. Water-SUI 10, 552.Google Scholar
Huthnance, J.M. 1975 On trapped waves over a continental shelf. J. Fluid Mech. 69, 689.Google Scholar
Igeta, Y., Yamazaki, K. & Watanabe, T. 2014 Amplification of coastal-trapped waves resonantly generated by wind around Sado Island, Japan. J. Oceanogr. 71, 41–51.CrossRefGoogle Scholar
Inall, M.E., Nilsen, F., Cottier, F.R. & Daae, R. 2015 Shelf/fjord exchange driven by coastal-trapped waves in the Arctic. J. Geophys. Res. Oceans 120, 8283–8303.10.1002/2015JC011277CrossRefGoogle Scholar
Johnson, R.S. 2005 Some contributions to the theory of edge waves. J. Fluid Mech. 24, 81–97.10.1017/S0022112004002538CrossRefGoogle Scholar
Johnson, R.S. 2007 Edge waves: theories past and present. Proc. R. Soc. Lond. A 365, 2359–2376.Google ScholarPubMed
Krause, M. 2011 Finite-difference mode solver for curved waveguides with angled and curved dielectric interfaces. J. Lightwave Technol. 29, 691–699.10.1109/JLT.2011.2106763CrossRefGoogle Scholar
Kurkin, A. & Pelinovsky, E. 2002 Focusing of edge waves above a sloping beach. Eur. J. Mech. B Fluids 21, 561–577.10.1016/S0997-7546(02)01201-3CrossRefGoogle Scholar
Laforge, N., et al. 2019 Observation of topological gravity-capillary waves in a water wave crystal. New J. Phys. 21, 083031.CrossRefGoogle Scholar
Liao, F. & Wang, X.H. 2018 A study of low-frequency, wind-driven, coastal-trapped waves along the Southeast Coast of Australia. J. Phys. Oceanogr. 48, 301–316.CrossRefGoogle Scholar
Little, B.E., Chu, S.T., Absil, P.P., Hryniewicz, J.V., Johnson, F.G., Sieferth, F., Gill, D., Van, V., King, O. & Trakalo, M. 2004 Very high-order microring resonator filters for WDM applications. IEEE Photon. Technol. Lett. 16, 2263–2265.10.1109/LPT.2004.834525CrossRefGoogle Scholar
Little, B.E., Chu, S.T., Haus, H.A., Foresi, J. & Laine, J.-P. 1997 Microring resonator channel dropping filters. J. Lightwave Technol. 15, 998–1005.10.1109/50.588673CrossRefGoogle Scholar
Liu, P.L.-F., Cho, Y.-S., Kostense, J.K. & Dingemans, M.W. 1992 Propagation and trapping of obliquely incident wave groups over a trench with currents. Appl. Ocean Res. 14, 201–213.10.1016/0141-1187(92)90015-CCrossRefGoogle Scholar
Liu, Z.H., Hara, K. & Shneider, M.N. 2023 Dynamics of electrified liquid metal surface using shallow water model. Phys. Fluids 35, 042101.Google Scholar
Long, S.R., Lai, R.J., Huang, N.E. & Spedding, G.R. 1993 Blocking and trapping of waves in an inhomogeneous flow. Dyn. Atmos. Ocean 20, 79–106.CrossRefGoogle Scholar
Longuet-Higgins, M.S. 1967 On the trapping of wave energy round islands. J. Fluid Mech. 29, 781–821.10.1017/S0022112067001181CrossRefGoogle Scholar
Longuett-Higgins, M.S. 1968 On the trapping of waves along a discontinuity of depth in a rotating ocean. J. Fluid Mech. 31, 417–434.10.1017/S0022112068000236CrossRefGoogle Scholar
Lui, W.W., Xu, C.-L., Hirono, T., Yokoyama, K. & Huang, W.-P. 1998 Full vectorial wave propagation in semiconductor optical bending waveguides and equivalent straight waveguide approximations. J. Lightwave Technol. 16, 910–914.10.1109/50.669038CrossRefGoogle Scholar
Marche, F. 2007 Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects. Eur. J. Mech. B 49, 49.CrossRefGoogle Scholar
Marcuse, D. 1971 Bending losses of the asymmetric slab waveguide. Bell Syst. Tech. J. 50, 2551–2563.10.1002/j.1538-7305.1971.tb02620.xCrossRefGoogle Scholar
Maurel, A., Cobelli, P., Pagneux, V. & Petitjeans, P. 2009 Global measurement of water waves by fourier transform profilometry. Appl. Opt. 48, 1037–1047.Google Scholar
Merrifield, M.A. 1992 A comparison of long coastal-trapped wave theory with remote-storm-generated wave events in the gulf of california. J. Phys. Oceanogr. 22, 5–18.Google Scholar
Merzon, A.E. & Zhevandrov, P.N. 1998 High-frequency asymptotics of edge waves on a beach of nonconstant slope. SIAM J. Appl. Maths 59, 529–546.CrossRefGoogle Scholar
Miller, R.N., Matano, R.P. & Palma, E.D. 2011 Shelfbreak upwelling induced by alongshore currents: analytical and numerical results. J. Fluid Mech. 686, 239–249.10.1017/jfm.2011.326CrossRefGoogle Scholar
Moisy, F., Rabaud, M. & Salsac, K. 2009 A synthetic Schlieren method for the measurement of the topography of a liquid interface. Exp. Fluids 46, 1021–1036.10.1007/s00348-008-0608-zCrossRefGoogle Scholar
Perez, N., Delplace, P. & Venaille, A. 2021 Manifestation of the Berry curvature in geophysical ray tracing. Proc. R. Soc. A. 477, 20200844.10.1098/rspa.2020.0844CrossRefGoogle Scholar
Pite, H.D. 1977 The excitation of damped waves diffracted over a submerged circular sill. J. Fluid Mech. 82, 621–641.Google Scholar
Pizarro, O. & Shaffer, G. 1998 Wind-Driven, Coastal-Trapped Waves off the Island of Gotland, Baltic Sea. J. Phys. Oceanogr. 28, 2117–2129.10.1175/1520-0485(1998)028<2117:WDCTWO>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Pruszak, Z., Róźyński, G., Szmytkiewicz, M. & SkajaField, M. 2007 Observation of edge waves and beach cusps on the South Baltic sea coast. J. Coast. Res. 234, 846–860.10.2112/04-0293.1CrossRefGoogle Scholar
Przadka, A., Cabane, B., Pagneux, V., Maurel, A. & Petitjeans, P. 2012 Fourier transform profilometry for water waves: how to achieve clean water attenuation with diffusive reflection at the water surface? Exp. Fluids 52, 519–527.10.1007/s00348-011-1240-xCrossRefGoogle Scholar
Ralph, F.M., Armi, L., Bane, J.M., Dorman, C., Neff, W.D., Neiman, P.J., Nuss, W. & Persson, P.O.G. 1998 Observations and analysis of the 10–11 June 1994 coastally trapped disturbance. Mon. Weather Rev. 126, 2435–2465.10.1175/1520-0493(1998)126<2435:OAAOTJ>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Renardy, Y. 1983 Trapping of water waves above a round sill. J. Fluid Mech. 132, 105.10.1017/S0022112083001500CrossRefGoogle Scholar
Reyes, F., Torrejón, V. & Falcón, C. 2020 Wave damping of a sloshing wave by an interacting turbulent vortex flow. Phys. Rev. E 101, 033106.10.1103/PhysRevE.101.033106CrossRefGoogle Scholar
Schmessane, A. 2016 Observation of Wood’s anomalies on surface gravity waves propagating on a channel. Phys. Rev. E 94, 031101.10.1103/PhysRevE.94.031101CrossRefGoogle ScholarPubMed
Sepúlveda-Soto, F., Guzmán-Silva, D., Rosas, E., Vicencio, R.A. & Falcón, C. 2020 Observation of broad-band water waveguiding in shallow water: a revival. Sci. Rep. 10, 18307–18316.10.1038/s41598-020-75335-8CrossRefGoogle Scholar
Shelton, J. & Trinh, P.H. 2023 Exponential asymptotics and the generation of free-surface flows by submerged line vortices. J. Fluid Mech. 958, A29.10.1017/jfm.2023.94CrossRefGoogle Scholar
Shrira, V.I. & Slunyaev, A.V. 2014 Trapped waves on jet currents: asymptotic modal approach. J. Fluid Mech. 738, 65–104.CrossRefGoogle Scholar
Shrira, V.I. & Slunyaev, A.V. 2014 Nonlinear dynamics of trapped waves on jet currents and rogue waves. Phys. Rev. E 89, 041002(R).CrossRefGoogle ScholarPubMed
Slunyaev, A.V. 2023 Extreme dynamics of wave groups on jet current. Phys. Fluids 35, 126606.10.1063/5.0180658CrossRefGoogle Scholar
Stocks, D.C. 1976 An experimental investigation of wave energy trapping. Intl J. Engng Sci. 14, 947–962.CrossRefGoogle Scholar
Takeda, M. & Mutoh, K. 1983 Fourier transform profilometry for the automatic measurement of 3-D object shapes. Appl. Opt. 22, 3977–3982.10.1364/AO.22.003977CrossRefGoogle ScholarPubMed
Tam, C.K.W. 1976 A study of sound transmission in curved duct bends by the Galerkin method. J. Sound Vib. 45, 91–104.10.1016/0022-460X(76)90669-6CrossRefGoogle Scholar
Tang, Y.M. & Grimshaw, R. 1995 A modal analysis of coastally trapped waves generated by tropical cyclones. J. Phys. Oceanogr. 25, 1577–1598.10.1175/1520-0485(1995)025<1577:AMAOCT>2.0.CO;22.0.CO;2>CrossRefGoogle Scholar
Tauber, C., Delplace, P. & Venaille, A. 2020 Anomalous bulk-edge correspondence in continuous media. Phys. Rev. Res. 2, 013147.10.1103/PhysRevResearch.2.013147CrossRefGoogle Scholar
Thyagarajan, K., Shenoy, M.R. & Ghatak, A.K. 1987 Accurate numerical method for the calculation of bending loss in optical waveguides using a matrix approach. Opt. Lett. 12, 296–298.10.1364/OL.12.000296CrossRefGoogle ScholarPubMed
Venaille, A. & Delplace, P. 2021 Wave topology brought to the coast. Phys. Rev. Res. 3, 043002.10.1103/PhysRevResearch.3.043002CrossRefGoogle Scholar
Vinogradov, D.V. & Denisov, G.G. 1990 Mode conversion in curved wave-guide with variable curvature. Izv. Vyss. Uchebnykh Zaved. Radioelektron. 33, 726–732.Google Scholar
Wang, Z.L., Jiang, T. & Xu, L. 2017 Toward the blue energy dream by triboelectric nanogenerator networks. Nano Energy 39, 9–23.10.1016/j.nanoen.2017.06.035CrossRefGoogle Scholar
Wang, G., Liang, Q., Shi, F. & Zheng, J. 2021 Analytical and numerical investigation of trapped ocean waves along a submerged ridge. J. Fluid Mech. 915, A54.CrossRefGoogle Scholar
Wang, G., Zhang, Y., Zheng, J., Fu, R. & Tao, A. 2023 Analytical investigation of trapped waves over a submerged exponential ridge. Ocean Engng 273, 114002.10.1016/j.oceaneng.2023.114002CrossRefGoogle Scholar
Weber, J.E.H. & Isachsen, P.E. 2023 Energy transfer from sub-inertial Kelvin waves to continental shelf waves at a transverse bottom escarpment. Cont. Shelf Res. 258, 104985.Google Scholar
Whitham, G.B. 2008 Linear and Nonlinear Waves. Cambridge University Press.Google Scholar
Wright, W.B., Budakian, R. & Putterman, S.J. 1996 Diffusing light photography of fully developed isotropic ripple turbulence. Phys. Rev. Lett. 76, 4528.10.1103/PhysRevLett.76.4528CrossRefGoogle ScholarPubMed
Wu, S., Wu, Y. & Mei, J. 2018 Topological helical edge states in water waves over a topographical bottom. New J. Phys. 20, 023051.10.1088/1367-2630/aa9cdbCrossRefGoogle Scholar
Yang, Z., Gao, F. & Zhang, B. 2016 Topological water wave states in a one-dimensional structure. Sci. Rep. 6, 29202.CrossRefGoogle Scholar
Zamudio, L. & López, M. 1994 On the effect of the alongshore pressure gradient on numerical simulations over the northern california continental shelf. J. Geophys. Res. 99, 16117.10.1029/94JC01116CrossRefGoogle Scholar
Zhevandrov, P. 1991 Edge waves on a gently sloping beach: uniform asymptotics. J. Fluid Mech. 233, 483.10.1017/S0022112091000563CrossRefGoogle Scholar
Zhu, S., Zhao, X., Han, L., Zi, J., Hu, X. & Chen, H. 2024 Controlling water waves with artificial structures. Nat. Rev. Phys. 6, 231–245.10.1038/s42254-024-00701-8CrossRefGoogle Scholar
Zuccoli, E., Brambley, E.J. & Barkley, D. 2024 Trapped free surface waves for a Lamb–Oseen vortex flow. J. Fluid Mech. 997, A40.10.1017/jfm.2024.645CrossRefGoogle Scholar