Wave attenuation by flexible vegetation (and suspended kelp) with blade motion: Analytical solutions

Abdelrhman, 2007, Modeling coupling between eelgrass Zostera marina and water flow, Mar. Ecol. Prog. Ser., 338, 81, 10.3354/meps338081 Anderson, 2014, Wave attenuation by flexible, idealized salt marsh vegetation, Coastal Eng., 83, 82, 10.1016/j.coastaleng.2013.10.004 Augyte, 2017, Cultivation of a morphologically distinct strain of the sugar kelp, Saccharina latissima forma angustissima, from coastal Maine, USA, with implications for ecosystem services, J. Appl. Phycol., 29, 1967, 10.1007/s10811-017-1102-x Azevedo, 2019, Growth of Saccharina latissima (Laminariales, Phaeophyceae) cultivated offshore under exposed conditions, Phycologia, 58, 504, 10.1080/00318884.2019.1625610 Bak, 2018, Production method and cost of commercial-scale offshore cultivation of kelp in the Faroe Islands using multiple partial harvesting, Algal Res., 33, 36, 10.1016/j.algal.2018.05.001 Borgman, 1967, Random hydrodynamic forces on objects, Ann. Math. Stat., 38, 37, 10.1214/aoms/1177699057 Bradley, 2009, Relative velocity of seagrass blades: implications for wave attenuation in low-energy environments, J. Geophys. Res., 114, F01004 Chen, 2019, Eulerian–Lagrangian flow-vegetation interaction model using immersed boundary method and OpenFOAM, Adv. Water Resour., 126, 176, 10.1016/j.advwatres.2019.02.006 Chen, 2018, Deriving vegetation drag coefficients in combined wave-current flows by calibration and direct measurement methods, Adv. Water Resour., 122, 217, 10.1016/j.advwatres.2018.10.008 Chen, 2007, A nearshore model to investigate the effects of seagrass bed geometry on wave attenuation and suspended sediment transport, Estuaries Coasts, 30, 296, 10.1007/BF02700172 Currin, 2010, Developing alternative shoreline armoring strategies : the living shoreline approach in North Carolina, 91 Dalrymple, 1984, Wave diffraction due to areas of energy dissipation, J. Waterw. Port Coast. Ocean Eng., 110, 67, 10.1061/(ASCE)0733-950X(1984)110:1(67) Dean, 1991, Water wave mechanics for engineers and scientists, 2 Denny, 1997, Flow and flexibility II. The roles of size and shape in determining wave forces on the bull kelp Nereocystis luetkeana, J. Exp. Biol., 200, 3165, 10.1242/jeb.200.24.3165 Denny, 2002, The mechanics of wave-swept algae, J. Exp. Biol., 205, 1355, 10.1242/jeb.205.10.1355 Denny, 1998, The menace of momentum: dynamic forces on flexible organisms, Limnol. Oceanogr., 43, 955, 10.4319/lo.1998.43.5.0955 Duarte, 2017, Can seaweed farming play a role in climate change mitigation and adaptation?, Front. Mar. Sci., 4, 100 Elwany, 1995, Effects of southern California Kelp beds on waves, J. Waterw. Port Coast. Ocean Eng., 121, 143, 10.1061/(ASCE)0733-950X(1995)121:2(143) Fonseca, 2007, Biomechanical factors contributing to self-organization in seagrass landscapes, J. Exp. Mar. Biol. Ecol., 340, 227, 10.1016/j.jembe.2006.09.015 Førde, 2016, Development of bryozoan fouling on cultivated kelp (Saccharina latissima) in Norway, J. Appl. Phycol., 28, 1225, 10.1007/s10811-015-0606-5 Foster-Martinez, 2018, Wave attenuation across a tidal marsh in San Francisco Bay, Coast. Eng., 136, 26, 10.1016/j.coastaleng.2018.02.001 Fredriksson, 2020, Hydrodynamic characteristics of a full-scale kelp model for aquaculture applications, Aquac. Eng., 90, 10.1016/j.aquaeng.2020.102086 Fringer, 2019, The future of coastal and estuarine modeling: findings from a workshop, Ocean Model., 143, 10.1016/j.ocemod.2019.101458 Gaeckle, 2002, A plastochrone method for measuring leaf growth in eelgrass, Zostera marina L, Bull. Mar. Sci., 71, 1237 Gaylord, 2003, Modulation of wave forces on kelp canopies by alongshore currents, Limnol. Oceanogr., 48, 860, 10.4319/lo.2003.48.2.0860 Hansen, 2013, Seasonal growth and senescence of a Zostera marina seagrass meadow alters wave-dominated flow and sediment suspension within a coastal bay, Estuaries Coasts, 36, 1099, 10.1007/s12237-013-9620-5 Henderson, 2019, Motion of buoyant, flexible aquatic vegetation under waves: simple theoretical models and parameterization of wave dissipation, Coast. Eng., 152, 10.1016/j.coastaleng.2019.04.009 Henderson, 2017, Wave-frequency flows within a near-bed vegetation canopy, Cont. Shelf Res., 147, 91, 10.1016/j.csr.2017.06.003 Izaguirre, 2011, Global extreme wave height variability based on satellite data, Geophys. Res. Lett., 38, 10.1029/2011GL047302 Jadhav, 2013, Spectral distribution of wave energy dissipation by salt marsh vegetation, Coast. Eng., 77, 99, 10.1016/j.coastaleng.2013.02.013 Keulegan, 1958, Forces on cylinders and plates in an oscillating fluid, J. Res. Natl. Bur. Stand, 60, 423, 10.6028/jres.060.043 Kobayashi, 1993, Wave attenuation by vegetation, J. Waterw. Port Coast. Ocean Eng., 119, 30, 10.1061/(ASCE)0733-950X(1993)119:1(30) Koch, 2009, Non-linearity in ecosystem services: temporal and spatial variability in coastal protection, Front. Ecol. Environ., 7, 29, 10.1890/080126 Koehl, 1977, Mechanical adaptations of a giant kelp, Limnol. Oceanogr., 22, 1067, 10.4319/lo.1977.22.6.1067 Krause-Jensen, 2016, Substantial role of macroalgae in marine carbon sequestration, Nat. Geosci., 9, 737, 10.1038/ngeo2790 Lei, 2021, Drag force and reconfiguration of cultivated Saccharina latissima in current, Aquacult. Eng., 94, 10.1016/j.aquaeng.2021.102169 Lei, 2019, Blade dynamics in combined waves and current, J. Fluids Struct., 87, 137, 10.1016/j.jfluidstructs.2019.03.020 Lei, 2019, Wave damping by flexible vegetation: connecting individual blade dynamics to the meadow scale, Coast. Eng., 147, 138, 10.1016/j.coastaleng.2019.01.008 Losada, 2016, A new formulation for vegetation-induced damping under combined waves and currents, Coast. Eng., 107, 1, 10.1016/j.coastaleng.2015.09.011 Lowe, 2005, Oscillatory flow through submerged canopies: 1. Velocity structure, J. Geophys. Res., 110, C10016, 10.1029/2004JC002788 Luhar, M. 2012. Analytical and experimental studies of plant-flow interaction at multiple Scales. Doctoral dissertation, Massachusetts Institute of Technology. http://dspace.mit.edu/handle/1721.1/78142. Luhar, 2017, Seagrass blade motion under waves and its impact on wave decay, J. Geophys. Res.: Oceans, 122, 3736, 10.1002/2017JC012731 Luhar, 2016, Wave-induced dynamics of flexible blades, J. Fluids Struct., 61, 20, 10.1016/j.jfluidstructs.2015.11.007 Marsooli, 2017, Modeling wave attenuation by salt marshes in Jamaica Bay, New York, using a new rapid wave model, J. Geophys. Res. Oceans, 122, 5689, 10.1002/2016JC012546 Mattila, 1999, Spatial and diurnal distribution of invertebrate and fish fauna of a Zostera marina bed and nearby unvegetated sediments in Damariscotta River, Maine (USA), J. Sea Res., 41, 321, 10.1016/S1385-1101(99)00006-4 Mendez, 2004, An empirical model to estimate the propagation of random breaking and nonbreaking waves over vegetation fields, Coast. Eng., 51, 103, 10.1016/j.coastaleng.2003.11.003 Méndez, 1999, Hydrodynamics induced by wind waves in a vegetation field, J. Geophys. Res., 104, 18383, 10.1029/1999JC900119 Möller, 2006, Quantifying saltmarsh vegetation and its effect on wave height dissipation: results from a UK East coast saltmarsh, Estuar. Coast. Shelf Sci., 69, 337, 10.1016/j.ecss.2006.05.003 Möller, 2019, Applying uncertain science to nature-based coastal protection: lessons from shallow wetland-dominated shores, Front. Environ. Sci., 7, 10.3389/fenvs.2019.00049 Möller, 2002, Wave dissipation over macro-tidal saltmarshes: effects of marsh edge typology and vegetation change, J. Coast. Res., 36, 506, 10.2112/1551-5036-36.sp1.506 Morison, 1950, The force exerted by surface waves on piles, J. Pet.Technol., 2, 149, 10.2118/950149-G Mork, 1996, The effect of kelp in wave damping, Sarsia, 80, 323, 10.1080/00364827.1996.10413607 Morris, 2019, Kelp beds as coastal protection: wave attenuation of Ecklonia radiata in a shallow coastal bay, Ann. Bot., 125, 235 Mullarney, 2010, Wave-forced motion of submerged single-stem vegetation, J. Geophys. Res., 115, C12061 Mullarney, 2017, The differential response of kelp to swell and infragravity wave motion, Limnol. Oceanogr., 62, 2524, 10.1002/lno.10587 Nielsen, 2014, Growth dynamics of Saccharina latissima (Laminariales, Phaeophyceae) in Aarhus Bay, Denmark, and along the species’ distribution range, Mar. Biol., 161, 2011, 10.1007/s00227-014-2482-y Ondiviela, 2014, The role of seagrasses in coastal protection in a changing climate, Coast. Eng., 87, 158, 10.1016/j.coastaleng.2013.11.005 Ozeren, 2014, Experimental investigation of wave attenuation through model and live vegetation, J. Waterw. Port Coast. Ocean Eng., 140, 10.1061/(ASCE)WW.1943-5460.0000251 Pace, 2011, Wetlands or seawalls? Adapting shoreline regulation to address sea level rise and wetland preservation in the Gulf of Mexico, J. Land Use Environ. Law, 26, 327 Paul, 2011, Spatial and seasonal variation in wave attenuation over Zostera noltii, J. Geophys. Res., 116, C08019 Peteiro, 2006, Cultivation of the autoctonus seaweed “Laminaria saccharina” off the Galician coast (NW Spain): production and features of the sporophytes for an annual and biennial harvest, Thalassas Int. J. Mar. Sci., 22, 45 Peteiro, 2013, Biomass yield and morphological features of the seaweed Saccharina latissima cultivated at two different sites in a coastal bay in the Atlantic coast of Spain, J. Appl. Phycol., 25, 205, 10.1007/s10811-012-9854-9 Rao, 2007 Rosman, 2013, Interaction of waves and currents with kelp forests (Macrocystis pyrifera): insights from a dynamically scaled laboratory model, Limnol. Oceanogr., 58, 790, 10.4319/lo.2013.58.3.0790 Sánchez-González, 2011, Wave attenuation due to Posidonia oceanica meadows, J. Hydraul. Res., 49, 503, 10.1080/00221686.2011.552464 Sarpkaya, 1996, Oscillating flow about two and three-dimensional bilge keels, J. Offshore Mech. Arct. Eng., 118, 1, 10.1115/1.2828796 Schulze, 2019, Seasonal and spatial within-marsh differences of biophysical plant properties: implications for wave attenuation capacity of salt marshes, Aquat. Sci., 81, 65, 10.1007/s00027-019-0660-1 Sollitt, 1972, Wave transmission through permeable breakwaters, Coast. Eng. Proc., 1, 99, 10.9753/icce.v13.99 Stevens, 2001, Water motion relative to subtidal kelp fronds, Limnol. Oceanogr., 46, 668, 10.4319/lo.2001.46.3.0668 Sutton-Grier, 2015, Future of our coasts: the potential for natural and hybrid infrastructure to enhance the resilience of our coastal communities, economies and ecosystems, Environ. Sci. Policy, 51, 137, 10.1016/j.envsci.2015.04.006 Suzuki, 2012, Wave dissipation by vegetation with layer schematization in SWAN, Coast. Eng., 59, 64, 10.1016/j.coastaleng.2011.07.006 Syvitski, 2009, Sinking deltas due to human activities, Nat. Geosci., 2, 681, 10.1038/ngeo629 Tebaldi, 2012, Modelling sea level rise impacts on storm surges along US coasts, Environ. Res. Lett., 7, 10.1088/1748-9326/7/1/014032 Temmerman, 2013, Ecosystem-based coastal defence in the face of global change, Nature, 504, 79, 10.1038/nature12859 Utter, 1996, Wave-induced forces on the giant kelp Macrocystis pyrifera (Agardh): field test of a computational model, J. Exp. Biol., 199, 2645, 10.1242/jeb.199.12.2645 van Veelen, 2020, Experimental study on vegetation flexibility as control parameter for wave damping and velocity structure, Coast. Eng., 157, 10.1016/j.coastaleng.2020.103648 Vettori, 2017, Morphological and mechanical properties of blades of Saccharina latissima, Estuar. Coast. Shelf Sci., 196, 1, 10.1016/j.ecss.2017.06.033 Vuik, 2018, Stem breakage of salt marsh vegetation under wave forcing: a field and model study, Estuar Coast Shelf Sci, 200, 41, 10.1016/j.ecss.2017.09.028 Weinkle, 2018, Normalized hurricane damage in the continental United States 1900–2017, Nature Sustainability, 1, 808, 10.1038/s41893-018-0165-2 Zeller, 2014, Improved parameterization of seagrass blade dynamics and wave attenuation based on numerical and laboratory experiments, Limnol. Oceanogr., 59, 251, 10.4319/lo.2014.59.1.0251 Zhang, 2020, Flow-induced reconfiguration of aquatic plants, including the impact of leaf sheltering, Limnol. Oceanogr., 65, 2697, 10.1002/lno.11542 Zhang, 2021, Wave damping by flexible marsh plants influenced by current, Phys. Rev. Fluids, 6, 1, 10.1103/PhysRevFluids.6.100502 Zhu, 2015, Numerical modeling of surface waves over submerged flexible vegetation, J. Eng. Mech., 141, 10.1061/(ASCE)EM.1943-7889.0000913 Zhu, 2020 Zhu, 2018, Interaction between waves and hanging highly flexible kelp blades, Coast. Eng. Proc., 1, 31, 10.9753/icce.v36.papers.31 Zhu, 2020, Aquaculture farms as nature-based coastal protection: random wave attenuation by suspended and submerged canopies, Coast. Eng., 160, 10.1016/j.coastaleng.2020.103737 Zhu, 2021, Wave attenuation by suspended canopies with cultivated kelp (Saccharina latissima), Coast. Eng., 10.1016/j.coastaleng.2021.103947 Zhu, 2017, Three-layer analytical solution for wave attenuation by suspended and nonsuspended vegetation canopy, Coast. Eng. Proc., 1, 27, 10.9753/icce.v35.waves.27 Zhu, 2020, Mechanisms for the asymmetric motion of submerged aquatic vegetation in waves: a consistent-mass cable model, J. Geophys. Res.: Oceans, 125, 1, 10.1029/2019JC015517