ICCE 2016 Cover Image


wave attenuation
suspended vegetation canopy
analytical solution
wave and vegetation interaction

How to Cite



A generalized three-layer analytical solution for the wave attenuation by suspended and non-suspended vegetation canopy is developed in this study. The analytical solution reduces to the two-layer analytical solution by Kobayashi et al. (1993) for the non-suspended vegetation canopy rooted at the sea bed. The present theory is verified using laboratory experiments and field observations of a suspended and non-suspended as well as emerged and submerged vegetation canopy. The wave attenuation increase with the drag coefficient, blade diameter and length, canopy density and length, the elevation of the bottom of the canopy and the incident wave height. The influences of wave frequency and water depth on wave attenuation are more complex. They affect the wave attenuation mainly by changing the wave flow velocity encountered by the vegetation canopy. As a result, the canopy vertical position has significant impact on the relationship between the wave attenuation and wave frequency.


Anderson, M.E. and Smith, J.M., 2014. Wave attenuation by flexible, idealized salt marsh vegetation. Coastal Engineering, 83, 82-92.

Augustin, L.N., Irish, J.L. and Lynett, P., 2009. Laboratory and numerical studies of wave damping by emergent and near-emergent wetland vegetation. Coastal Engineering, 56(3), 332-340.

Bradley, K. and Houser, C., 2009. Relative velocity of seagrass blades: Implications for wave attenuation in low†energy environments. Journal of Geophysical Research: Earth Surface, 114(F1).

Chakrabarti, A., Chen, Q., Smith, H.D. and Liu, D., 2016. Large Eddy Simulation of Unidirectional and Wave Flows through Vegetation. Journal of Engineering Mechanics, 142(8), p.04016048.

Chen, X., Chen, Q., Zhan, J. and Liu, D., 2016. Numerical simulations of wave propagation over a vegetated platform. Coastal Engineering, 110, 64-75.

Chen, Q. and Zhao, H., 2012. Theoretical models for wave energy dissipation caused by vegetation. Journal of Engineering Mechanics, 138(2), 221-229.

Dalrymple, R.A., Kirby, J.T. and Hwang, P.A., 1984. Wave diffraction due to areas of energy dissipation. Journal of Waterway, Port, Coastal, and Ocean Engineering, 110(1), 67-79.

Dubi, A., Torum, A., 1994. Wave damping by kelp vegetation, Proceedings of 24th International Conference on Coastal Engineering, ASCE, 142-156.

Fonseca, M.S. and Cahalan, J.A., 1992. A preliminary evaluation of wave attenuation by four species of seagrass. Estuarine, Coastal and Shelf Science, 35(6), 565-576.

Horstman, E.M., Dohmen-Janssen, C.M., Narra, P.M.F., van den Berg, N.J.F., Siemerink, M. and Hulscher, S.J.M.H., 2014. Wave attenuation in mangroves: A quantitative approach to field observations. Coastal engineering, 94, pp.47-62.

Hu, Z., Suzuki, T., Zitman, T., Uittewaal, W. and Stive, M., 2014. Laboratory study on wave dissipation by vegetation in combined current-wave flow. Coastal Engineering, 88, 131-142.

Huai, W., Hu, Y., Zeng, Y. and Han, J., 2012. Velocity distribution for open channel flows with suspended vegetation. Advances in Water Resources, 49, 56-61.

Knutson, P.L., Brochu, R.A., Seelig, W.N. and Inskeep, M., 1982. Wave damping in Spartina alterniflora marshes. Wetlands, 2(1), 87-104.

Kobayashi, N., Raichle, A.W. and Asano, T., 1993. Wave attenuation by vegetation. Journal of waterway, port, coastal, and ocean engineering, 119(1), 30-48.

Koftis, T., Prinos, P. and Stratigaki, V., 2013. Wave damping over artificial Posidonia oceanica meadow: A large-scale experimental study. Coastal Engineering, 73, 71-83.

Li, C.W. and Xie, J.F., 2011. Numerical modeling of free surface flow over submerged and highly flexible vegetation. Advances in Water Resources, 34(4), 468-477

Liu, P.L.F., Chang, C.W., Mei, C.C., Lomonaco, P., Martin, F.L. and Maza, M., 2015. Periodic water waves through an aquatic forest. Coastal Engineering, 96, 100-117.

Losada, I.J., Maza, M. and Lara, J.L., 2016. A new formulation for vegetation-induced damping under combined waves and currents. Coastal Engineering, 107, 1-13.

Ma, G., Kirby, J.T., Su, S.F., Figlus, J. and Shi, F., 2013. Numerical study of turbulence and wave damping induced by vegetation canopies. Coastal Engineering, 80, 68-78.

Marsooli, R. and Wu, W., 2014. Numerical investigation of wave attenuation by vegetation using a 3D RANS model. Advances in Water Resources, 74, 245-257.

Maza, M., Lara, J.L. and Losada, I.J., 2013. A coupled model of submerged vegetation under oscillatory flow using Navier-Stokes equations. Coastal Engineering, 80, 16-34.

Mendez, F.J. and Losada, I.J., 2004. An empirical model to estimate the propagation of random breaking and nonbreaking waves over vegetation fields. Coastal Engineering, 51(2), 103-118.

Möller, I., Spencer, T., French, J.R., Leggett, D.J. and Dixon, M., 1999. Wave transformation over salt marshes: a field and numerical modelling study from North Norfolk, England. Estuarine, Coastal and Shelf Science, 49(3), 411-426.

Ota, T., Kobayashi, N. and Kirby, J.T., 2005. Wave and current interactions with vegetation. Proceedings of 29th International Conference, ASCE, 508-520.

Ozeren, Y., Wren, D.G. and Wu, W., 2014. Experimental investigation of wave attenuation through model and live vegetation. Journal of Waterway, Port, Coastal, and Ocean Engineering, 140(5), p.04014019.

Plew, D.R., Stevens, C.L., Spigel, R.H. and Hartstein, N.D., 2005. Hydrodynamic implications of large offshore mussel farms. IEEE Journal of Oceanic Engineering, 30(1), 95-108.

Plew, D.R., 2011. Depth-averaged drag coefficient for modeling flow through suspended canopies. Journal of Hydraulic Engineering, 137(2), 234-247.

Stratigaki, V., Manca, E., Prinos, P., Losada, I.J., Lara, J.L., Sclavo, M., Amos, C.L., Cáceres, I. and Sánchez-Arcilla, A., 2011. Large-scale experiments on wave propagation over Posidonia oceanica. Journal of Hydraulic Research, 49(sup1), 31-43.

Wang, Q., Guo, X.Y., Wang, B.L., Fang, Y.L. and Liu, H., 2016. Experimental measurements of solitary wave attenuation over shallow and intermediate submerged canopy. China Ocean Engineering, 30(3), 375-392.

Wu, W.C. and Cox, D.T., 2015. Effects of wave steepness and relative water depth on wave attenuation by emergent vegetation. Estuarine, Coastal and Shelf Science, 164, pp.443-450.

Zhu, L. and Chen, Q., 2015. Numerical modeling of surface waves over submerged flexible vegetation. Journal of Engineering Mechanics, 141(8), A4015001.

Zou, Q.-P., Hay, A.E. and Bowen, A.J., 2003. Vertical structure of surface gravity waves propagating over a sloping seabed: Theory and field measurements. Journal of Geophysical Research: Oceans, 108(C8), Art. No. 3265. (doi:10.1029/2002JC001432).

Authors retain copyright and grant the Proceedings right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this Proceedings.