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Multiple-scales analysis of wave evolution in the presence of rigid vegetation

Published online by Cambridge University Press:  25 January 2022

Clint Y.H. Wong Open the ORCID record for Clint Y.H. Wong [Opens in a new window] ,
Aggelos S. Dimakopoulos ,
Philippe H. Trinh Open the ORCID record for Philippe H. Trinh [Opens in a new window]  and
S. Jonathan Chapman Open the ORCID record for S. Jonathan Chapman [Opens in a new window]
Clint Y.H. Wong*
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OxfordOX2 6GG, UK
Aggelos S. Dimakopoulos
Affiliation:
HR Wallingford, Howbery Park, WallingfordOX10 8BA, UK
Philippe H. Trinh
Affiliation:
Department of Mathematical Sciences, University of Bath, BathBA2 7AY, UK
S. Jonathan Chapman
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OxfordOX2 6GG, UK
*
†Email address for correspondence: clintwong@cantab.net
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Abstract

The study of free-surface flows over vegetative structures presents a challenging setting for theoretical, computational and experimental analysis. In this work, we develop a multiple-scales asymptotic framework for the evolution of free-surface waves over rigid vegetation and a slowly varying substrate. The analysis quantifies the balance between the competing effects of vegetation and shoaling, and provides a prediction of the amplitude as the wave approaches a coastline. Our analysis unifies and extends existing theories that study these effects individually. The asymptotic predictions are shown to provide good agreement with full numerical simulations (varying depth) and published experimental results (constant depth).

JFM classification

Waves/Free-surface Flows: Wave-structure interactions Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: Coastal engineering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A3
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Ablowitz, M.J. 2011 Nonlinear Dispersive Waves: Asymptotic Analysis and Solitons. Cambridge University Press.CrossRefGoogle Scholar
Anderson, M.E. & Smith, J.M. 2014 Wave attenuation by flexible, idealized salt marsh vegetation. Coast. Engng 83, 82–92.CrossRefGoogle Scholar
Augustin, L.N., Irish, J.L. & Lynett, P. 2009 Laboratory and numerical studies of wave damping by emergent and near-emergent wetland vegetation. Coast. Engng 56 (3), 332–340.CrossRefGoogle Scholar
Bentley, A., Bootland, N., Wathen, A.J. & Kees, C.E. 2017 Implementation details of the level set two-phase Navier–Stokes equations in Proteus. Tech. Rep. TR2017-10. Department of Mathematical Sciences, Clemson University, Clemson, South Carolina, USA.Google Scholar
Bradley, K. & Houser, C. 2009 Relative velocity of seagrass blades: implications for wave attenuation in low-energy environments. J. Geophys. Res.: Earth 114 (1), 1–13.Google Scholar
Chang, C.W., Liu, P.L.F., Mei, C.C. & Maza, M. 2017 Periodic water waves through a heterogeneous coastal forest of arbitrary shape. Coast. Engng 122 (July 2016), 141–157.CrossRefGoogle Scholar
Chapman, S.J. & Farrell, P.E. 2017 Analysis of Carrier's problem. SIAM J. Appl. Maths 77 (3), 924–950.CrossRefGoogle Scholar
Chen, H., Ni, Y., Li, Y., Liu, F., Ou, S., Su, M., Peng, Y., Hu, Z., Uijttewaal, W.S. & Suzuki, T. 2018 Deriving vegetation drag coefficients in combined wave-current flows by calibration and direct measurement methods. Adv. Water Resour. 122 (135), 217–227.CrossRefGoogle Scholar
Dalrymple, R.A., Kirby, J.T. & Hwang, P.A. 1984 Wave diffraction due to areas of energy dissipation. ASCE J. Waterway Port Coastal Ocean Engng 110 (1), 67–79.CrossRefGoogle Scholar
Dean, R.G. & Dalrymple, R.A. 1991 Water Wave Mechanics for Engineers and Scientists, Advanced Series on Ocean Engineering, vol. 2. World Scientific.CrossRefGoogle Scholar
Dimakopoulos, A.S., de Lataillade, T. & Kees, C.E. 2019 Fast random wave generation in numerical tanks. Proc. Inst. Civ. Engrs 172 (1), 1–11.Google Scholar
Fenton, J.D. 1988 The numerical solution of steady water wave problems. Comput. Geosci. 14 (3), 357–368.CrossRefGoogle Scholar
Gosselin, F.P. 2019 Mechanics of a plant in fluid flow. J. Expl Bot. 70 (14), 3533–3548.CrossRefGoogle Scholar
Kees, C.E., Akkerman, I., Farthing, M.W. & Bazilevs, Y. 2011 A conservative level set method suitable for variable-order approximations and unstructured meshes. J. Comput. Phys. 230 (12), 4536–4558.CrossRefGoogle Scholar
Keller, J.B. 1958 Surface waves on water of non-uniform depth. J. Fluid Mech. 4 (6), 607–614.CrossRefGoogle Scholar
Keulegan, G.H. & Carpenter, L.H. 1958 Forces on cylinders and spheres in a sinusoidally oscillating fluid. J. Res. Natl Bur. Stand. 60 (5), 423–440.CrossRefGoogle Scholar
Kobayashi, N., Raichle, A.W. & Asano, T. 1993 Wave attenuation by vegetation. ASCE J. Waterway Port Coastal Ocean Engng 119 (1), 30–48.CrossRefGoogle Scholar
Kuzmak, G.E. 1959 Asymptotic solutions of nonlinear second order differential equations with variable coefficients. Z. Angew. Math. Mech. 23 (3), 730–744.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics. Dover Publications.Google Scholar
Landau, L.D. & Lifshitz, E.M. 1976 Course of Theoretical Physics – Volume 1. Mechanics, 3rd edn. Pergamon.Google Scholar
Leclercq, T. & de Langre, E. 2018 Reconfiguration of elastic blades in oscillatory flow. J. Fluid Mech. 838, 606–630.CrossRefGoogle Scholar
Lei, J. & Nepf, H.M. 2019 Wave damping by flexible vegetation: connecting individual blade dynamics to the meadow scale. Coast. Engng 147, 138–148.CrossRefGoogle Scholar
Liu, P.L., Chang, C.W., Mei, C.C., Lomonaco, P., Martin, F.L. & Maza, M. 2015 Periodic water waves through an aquatic forest. Coast. Engng 96, 100–117.CrossRefGoogle Scholar
Lowe, R.J., Koseff, J.R. & Monismith, S.G. 2005 Oscillatory flow through submerged canopies: 1. Velocity structure. J. Geophys. Res.: Oceans 110 (10), 1–17.Google Scholar
Luhar, M., Infantes, E. & Nepf, H.M. 2017 Seagrass blade motion under waves and its impact on wave decay. J. Geophys. Res.: Oceans 122 (5), 3736–3752.CrossRefGoogle Scholar
Luhar, M. & Nepf, H.M. 2016 Wave-induced dynamics of flexible blades. J. Fluids Struct. 61, 20–41.CrossRefGoogle Scholar
Mattis, S.A., Kees, C.E., Wei, M.V., Dimakopoulos, A.S. & Dawson, C.N. 2019 Computational model for wave attenuation by flexible vegetation. ASCE J. Waterway Port Coastal Ocean Engng 145 (1), 04018033.CrossRefGoogle Scholar
Mei, C.C., Chan, I.C. & Liu, P.L.F. 2014 Waves of intermediate length through an array of vertical cylinders. Environ. Fluid Mech. 14 (1), 235–261.CrossRefGoogle Scholar
Mei, C.C., Chan, I.C., Liu, P.L.F., Huang, Z. & Zhang, W. 2011 Long waves through emergent coastal vegetation. J. Fluid Mech. 687, 461–491.CrossRefGoogle Scholar
Mendez, F.J. & Losada, I.J. 2004 An empirical model to estimate the propagation of random breaking and nonbreaking waves over vegetation fields. Coast. Engng 51 (2), 103–118.CrossRefGoogle Scholar
Meyer, R. 1979 Theory of water-wave refraction. In Advances in Applied Mechanics (ed. Y. Chia-Shun), pp. 53–141. Academic.CrossRefGoogle Scholar
Möller, I., et al. 2014 Wave attenuation over coastal salt marshes under storm surge conditions. Nat. Geosci. 7 (10), 727–731.CrossRefGoogle Scholar
Morris, R.L., Konlechner, T.M., Ghisalberti, M. & Swearer, S.E. 2018 From grey to green: efficacy of eco-engineering solutions for nature-based coastal defence. Glob. Change Biol. 24 (5), 1827–1842.CrossRefGoogle ScholarPubMed
Nepf, H.M. 2012 Flow and transport in regions with aquatic vegetation. Annu. Rev. Fluid Mech. 44 (1), 123–142.CrossRefGoogle Scholar
Orszaghova, J., Taylor, P.H., Borthwick, A.G. & Raby, A.C. 2014 Importance of second-order wave generation for focused wave group run-up and overtopping. Coast. Engng 94, 63–79.CrossRefGoogle Scholar
Ozeren, Y., Wren, D.G. & Wu, W. 2014 Experimental investigation of wave attenuation through model and live vegetation. ASCE J. Waterway Port Coastal Ocean Engng 140 (5), 1–12.Google Scholar
Suzuki, T., Zijlema, M., Burger, B., Meijer, M.C. & Narayan, S. 2012 Wave dissipation by vegetation with layer schematization in SWAN. Coast. Engng 59 (1), 64–71.CrossRefGoogle Scholar
Wang, B., Guo, X. & Mei, C.C. 2015 Surface water waves over a shallow canopy. J. Fluid Mech. 768, 572–599.CrossRefGoogle Scholar
Wong, C.Y.H., Trinh, P.H. & Chapman, S.J. 2020 Shear-induced instabilities of flows through submerged vegetation. J. Fluid Mech. 891, A17.CrossRefGoogle Scholar
Wu, W., et al. 2012 Investigation of surge and wave reduction by vegetation (phase II) – interaction of hydrodynamics, vegetation, and soil. Tech. Rep. 80037. University of Mississippi.Google Scholar
Zeller, R.B., Zarama, F.J., Weitzman, J.S. & Koseff, J.R. 2015 A simple and practical model for combined wave-current canopy flows. J. Fluid Mech. 767, 842–880.CrossRefGoogle Scholar