Abstract
The phase-averaged depth-integrated vegetal drag force (Fv) directly impacts the mean water level (MWL) change in vegetation. Evaluated from linear wave theory, Fv integrated along the submerged part of vegetation becomes zero due to the symmetric profile of horizontal velocity. In this study, a semianalytical model for estimating Fv on vegetation stems exposed to Stokes waves is developed based on Stokes second-order wave theory (STK). By assuming a narrow-banded wave spectral density and Rayleigh-distributed wave heights, the proposed model can be applied to random waves. STK-based formulas of the maximum depth-integrated vegetal drag force, bending moment, and bending stress are provided to assess the breakage of vegetation stems. Moreover, by taking the solutions from the stream function wave theory as references, the applicable ranges of the STK-based semianalytical model of Fv and drag-induced bending moment are determined.
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Acknowledgments
Permission to publish this paper was granted by the Chief of Engineers, USACE. Funding for this work was provided by USACE (Cooperative Agreement W912HZ-16-2-0025). Work by Q. Chen and L. Zhu was supported in part by the National Science Foundation (Grants SEES-1427389 and CCF-153956).
References
Abdolahpour, M., M. Hambleton, and M. Ghisalberti. 2017. “The wave-driven current in coastal canopies.” J. Geophys. Res. Oceans 122 (5): 3660–3674. https://doi.org/10.1002/2016JC012446.
Abreu, T., P. A. Silva, F. Sancho, and A. Temperville. 2010. “Analytical approximate wave form for asymmetric waves.” Coastal Eng. 57 (7): 656–667. https://doi.org/10.1016/j.coastaleng.2010.02.005.
Anderson, M., and J. Smith. 2014. “Wave attenuation by flexible, idealized salt marsh vegetation.” Coastal Eng. 83 (1): 82–92. https://doi.org/10.1016/j.coastaleng.2013.10.004.
Booij, N., R. C. Ris, and L. H. Holthuijsen. 1999. “A third-generation wave model for coastal regions: 1. Model description and validation.” J. Geophys. Res. Oceans 104 (C4): 7649–7666. https://doi.org/10.1029/98JC02622.
Buckley, M. L., R. J. Lowe, J. E. Hansen, and A. R. V. Dongeren. 2016. “Wave setup over a fringing reef with large bottom roughness.” J. Phys. Oceanogr. 46 (8): 2317–2333. https://doi.org/10.1175/JPO-D-15-0148.1.
Chakrabarti, A., S. R. Brandt, Q. Chen, and F. Shi. 2017. “Boussinesq modeling of wave-induced hydrodynamics in coastal wetlands.” J. Geophys. Res. Oceans 122 (5): 3861–3883. https://doi.org/10.1002/2016JC012093.
Chen, H., Q. Zou, and Z. Liu. 2017. “A coupled Rans-V of and finite element model for wave interaction with highly flexible vegetation.” Coastal Eng. Proc. 1 (35): 25. https://doi.org/10.9753/icce.v35.waves.25.
Chen, Q., and H. Zhao. 2012. “Theoretical models for wave energy dissipation caused by vegetation.” J. Eng. Mech. 138 (2): 221–229. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000318.
Dalrymple, R., J. Kirby, and P. Hwang. 1984. “Wave diffraction due to areas of energy dissipation.” J. Waterway, Port, Coastal, Ocean Eng. 110 (1): 67–79. https://doi.org/10.1061/(ASCE)0733-950X(1984)110:1(67).
Dalrymple, R. A. 1974. “A finite amplitude wave on a linear shear current.” J. Geophys. Res. 79 (30): 4498–4504. https://doi.org/10.1029/JC079i030p04498.
Dean, R. G. 1965. “Stream function representation of nonlinear ocean waves.” J. Geophys. Res. 70 (18): 4561–4572. https://doi.org/10.1029/JZ070i018p04561.
Dean, R. G., and C. J. Bender. 2006. “Static wave setup with emphasis on damping effects by vegetation and bottom friction.” Coastal Eng. 53 (2–3): 149–156. https://doi.org/10.1016/j.coastaleng.2005.10.005.
Fenton, J. 1988. “The numerical solution of steady water wave problems.” Comput. Geosci. 14 (3): 357–368. https://doi.org/10.1016/0098-3004(88)90066-0.
Guannel, G., P. Ruggiero, J. Faries, K. Arkema, M. Pinsky, G. Gelfenbaum, A. Guerry, and C.-K. Kim. 2015. “Integrated modeling framework to quantify the coastal protection services supplied by vegetation.” J. Geophys. Res. Oceans 120 (1): 324–345. https://doi.org/10.1002/2014JC009821.
Heuner, M., et al. 2015. “Ecosystem engineering by plants on wave-exposed intertidal flats is governed by relationships between effect and response traits.” PLoS One 10 (9): e0138086. https://doi.org/10.1371/journal.pone.0138086.
Hu, Z., T. Suzuki, T. Zitman, W. Uittewaal, and M. Stive. 2014. “Laboratory study on wave dissipation by vegetation in combined current–wave flow.” Coastal Eng. 88 (June): 131–142. https://doi.org/10.1016/j.coastaleng.2014.02.009.
Irish, J., L. Augustin, G. Balsmeier, and J. Kaihatu. 2008. “Wave dynamics in coastal wetlands: A state-of-knowledge review with emphasis on wetland functionality for storm damage reduction.” Shore Beach 76 (3): 52–56.
Jadhav, R. S., and Q. Chen. 2013. “Probability distribution of wave heights attenuated by salt marsh vegetation during tropical cyclone.” Coastal Eng. 82 (Dec): 47–55. https://doi.org/10.1016/j.coastaleng.2013.08.006.
Jadhav, R. S., Q. Chen, and J. M. Smith. 2013. “Spectral distribution of wave energy dissipation by salt marsh vegetation.” Coastal Eng. 77 (July): 99–107. https://doi.org/10.1016/j.coastaleng.2013.02.013.
Kobayashi, N., and B. Johnson. 1998. Computer program CSHORE for predicting cross-shore transformation of irregular breaking waves. Research Rep. CACR-98-04. Newark, DE: Center for Applied Coastal Research, Univ. of Delaware.
Le Méhauté, B. 1976. An introduction to hydrodynamics and water waves. New York: Springer-Verlag.
Liu, P. L.-F., C.-W. Chang, C. C. Mei, P. Lomonaco, F. L. Martin, and M. Maza. 2015. “Periodic water waves through an aquatic forest.” Coastal Eng. 96 (Feb): 100–117. https://doi.org/10.1016/j.coastaleng.2014.11.002.
Longuet-Higgins, M. 1952. “On the statistical distribution of the heights of sea waves.” J. Mar. Res. 11 (3): 245–266.
Lowe, R. J., J. L. Falter, J. R. Koseff, S. G. Monismith, and M. J. Atkinson. 2007. “Spectral wave flow attenuation within submerged canopies: Implications for wave energy dissipation.” J. Geophys. Res. Oceans 112 (C5): C05018.
Luhar, M., E. Infantes, A. Orfila, J. Terrados, and H. M. Nepf. 2013. “Field observations of wave-induced streaming through a submerged seagrass (Posidonia oceanica) meadow.” J. Geophys. Res. Oceans 118 (4): 1955–1968. https://doi.org/10.1002/jgrc.20162.
Luhar, M., and H. Nepf. 2016. “Wave-induced dynamics of flexible blades.” J. Fluids Struct. 61 (Feb): 20–41. https://doi.org/10.1016/j.jfluidstructs.2015.11.007.
Ma, G., J. T. Kirby, S.-F. Su, J. Figlus, and F. Shi. 2013. “Numerical study of turbulence and wave damping induced by vegetation canopies.” Coastal Eng. 80 (Oct): 68–78. https://doi.org/10.1016/j.coastaleng.2013.05.007.
Mattis, S. A., C. N. Dawson, C. E. Kees, and M. W. Farthing. 2015. “An immersed structure approach for fluid-vegetation interaction.” Adv. Water Resour. 80 (Jun): 1–16. https://doi.org/10.1016/j.advwatres.2015.02.014.
Méndez, F., I. Losada, R. Dalrymple, and M. Losada. 1989. “Effects of wave reflection and dissipation on wave-induced second order magnitudes.” In Coastal Engineering 1988, edited by B. Edge, 553–570. New York: ASCE.
Möller, I., et al. 2014. “Wave attenuation over coastal salt marshes under storm surge conditions.” Nat Geosci. 7: 727–731. https://doi.org/10.1038/ngeo2251.
Morison, J. R., J. W. Johnson, and S. A. Schaaf. 1950. “The force exerted by surface waves on piles.” J. Pet. Technol 2 (5): 149–154. https://doi.org/10.2118/950149-G.
Mullarney, J. C., and S. M. Henderson. 2010. “Wave-forced motion of submerged single-stem vegetation.” J. Geophys. Res. Oceans 115 (C12): C12061. https://doi.org/10.1029/2010JC006448.
Myrhaug, D., and L. E. Holmedal. 2011. “Drag force on a vegetation field due to long-crested and short-crested nonlinear random waves.” Coastal Eng. 58 (6): 562–566. https://doi.org/10.1016/j.coastaleng.2011.01.014.
Niklas, K. J. 2000. “Computing factors of safety against wind-induced tree stem damage.” J. Exp. Botany 51 (345): 797–806. https://doi.org/10.1093/jexbot/51.345.797.
Ozeren, Y., D. Wren, and W. Wu. 2017. “Wave setup on vegetated beach: Laboratory experiments.” Coastal Eng. Proc. 1 (35): 4. https://doi.org/10.9753/icce.v35.currents.4.
Rienecker, M. M., and J. D. Fenton. 1981. “A Fourier approximation method for steady water waves.” J. Fluid Mech. 104: 119–137. https://doi.org/10.1017/S0022112081002851.
Ruessink, B., G. Ramaekers, and L. van Rijn. 2012. “On the parameterization of the free-stream non-linear wave orbital motion in nearshore morphodynamic models.” Coastal Eng. 65 (July): 56–63. https://doi.org/10.1016/j.coastaleng.2012.03.006.
Svendsen, I. A. 2006. Introduction to nearshore hydrodynamics. Hackensack, NJ: World Scientific.
Tahvildari, N. 2016. “Numerical modeling of the interactions between nonlinear waves and arbitrarily flexible vegetation.” Coastal Eng. Proc. 1 (35): 32. https://doi.org/10.9753/icce.v35.waves.32.
van Rooijen, A. A., R. T. McCall, J. S. M. van Thiel de Vries, A. R. van Dongeren, A. J. H. M. Reniers, and J. A. Roelvink. 2016. “Modeling the effect of wave-vegetation interaction on wave setup.” J. Geophys. Res. Oceans 121 (6): 4341–4359. https://doi.org/10.1002/2015JC011392.
Vuik, V., H. Y. S. Heo, Z. Zhu, B. W. Borsje, and S. N. Jonkman. 2018. “Stem breakage of salt marsh vegetation under wave forcing: A field and model study.” Estuarine Coastal Shelf Sci. 200 (Jan): 41–58. https://doi.org/10.1016/j.ecss.2017.09.028.
Wu, W., et al. 2011. SERRI project: Investigation of surge and wave reduction by vegetation. Phase I Rep. for SERRI Project No. 80037-01. Oak Ridge, TN: Oak Ridge National Laboratory.
Wu, W.-C., and D. T. Cox. 2015. “Effects of wave steepness and relative water depth on wave attenuation by emergent vegetation.” Estuarine Coastal Shelf Sci. 164 (Oct): 443–450. https://doi.org/10.1016/j.ecss.2015.08.009.
Zhu, L., and Q. Chen. 2015. “Numerical modeling of surface waves over submerged flexible vegetation.” J. Eng. Mech. 141 (8): A4015001. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000913.
Zhu, L., and Q. Chen. 2017. “Attenuation of nonlinear waves by rigid vegetation: Comparison of different wave theories.” J. Waterway, Port, Coastal, Ocean Eng. 143 (5): 04017029. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000415.
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© 2018 American Society of Civil Engineers.
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Received: Apr 9, 2018
Accepted: Jun 29, 2018
Published online: Dec 11, 2018
Published in print: Mar 1, 2019
Discussion open until: May 11, 2019
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