Numerical experiments investigating the influence of drag on trajectory patterns of floating macroalgae

Ross Coppin; Christo Rautenbach; Albertus J. Smit

doi:10.1515/bot-2023-0059

Article

Numerical experiments investigating the influence of drag on trajectory patterns of floating macroalgae

Ross Coppin

Dr Ross Coppin is a Marine Scientist, holding a Doctor of Philosophy in Biodiversity and Conservation Biology from the University of the Western Cape, whose research delves into the intricate dynamics of marine ecosystems. His doctoral studies explored the trajectories of floating macroalgae, utilizing Lagrangian-based numerical experiments, and integrating geophysical fluid dynamics, oceanography, and ecology. His work sheds light on the influences of hydrodynamics and wind drag on floating macroalgae. His career spans varied roles, including serving as a Freelance Researcher for institutions, such as the University of Cape Town and the City of Cape Town, and the fisheries sector in South Africa. His freelance endeavours encompassed research, data analysis, sustainability reports, environmental impact assessments, and public participation processes; mainly in the fisheries sector.
, Christo Rautenbach

Dr Christo Rautenbach is a distinguished double PhD holder, excelling in Applied Mathematics and Physical Oceanography. With an extensive background in numerical modelling spanning over a decade, he is an expert in coastal and ocean hydro- and wave dynamics. His expertise encompasses operational physical oceanography, coastal engineering, and coastal dynamics research. As a seasoned project manager and team leader, he spearheads applied research initiatives, integrating data science and artificial intelligence methodologies.
and Albertus J. Smit

Professor Albertus J. Smit, a marine scientist, applies innovative statistical methods to vast environmental and biological datasets. His critical perspective drives research into pressing ecological and environmental issues crucial for human well-being. Aligned with national strategies, his work spans global change, marine research, and biodiversity, supporting Sustainable Development Goals. Proficient in diverse hardware, computing, and software tools, his expertise focuses on oceanic climate change. With a string of impactful publications and successful grant acquisitions, Smit’s leadership ensures program completion and fosters inclusive, transdisciplinary collaborations for actionable research outcomes.

Published/Copyright: August 23, 2024

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information Explore this Subject

From the journal Botanica Marina Volume 67 Issue 5

Abstract

Ocean currents are a crucial means of dispersing natural and human-made materials on the ocean surface. Macroalgae are among the most conspicuous natural dispersers, often called the ‘tumbleweeds of the ocean.’ Despite numerous studies on the subject, the relative influence of wind and surface currents on the trajectory of macroalgal dispersal remains uncertain. Previous studies have focused on kelp rafts of varying sizes, making it challenging to determine the impact of wind versus currents. These studies have also disregarded the macroalgae’s drag characteristics and surface area, which have been shown to impact the trajectory and accumulation of floating flotsam. This numerical study aims to shed light on the relative influence of wind and currents and the role of drag in determining the course and accumulation of macroalgae. By comparing simulations of virtual kelp ‘particles’ that incorporate drag and those without, this study focused on solitary kelp plants and considered the impact of morphological characteristics, flow-field combinations, and the presence of Stokes drift. Our results show that virtual kelp particles generally followed ocean currents, but the inclusion of drag caused deviations from purely Lagrangian particles’ trajectories and sheds light on the complex interplay of factors affecting macroalgal dispersal in the ocean.

Keywords: Lagrangian; flotsam; kelp; drift; drag; dispersal

Corresponding author: Ross Coppin, Department of Biodiversity and Conservation Biology, University of the Western Cape, Private Bag X17, Bellville 7535, South Africa, E-mail: coppinross@gmail.com

About the authors

Ross Coppin

Dr Ross Coppin is a Marine Scientist, holding a Doctor of Philosophy in Biodiversity and Conservation Biology from the University of the Western Cape, whose research delves into the intricate dynamics of marine ecosystems. His doctoral studies explored the trajectories of floating macroalgae, utilizing Lagrangian-based numerical experiments, and integrating geophysical fluid dynamics, oceanography, and ecology. His work sheds light on the influences of hydrodynamics and wind drag on floating macroalgae. His career spans varied roles, including serving as a Freelance Researcher for institutions, such as the University of Cape Town and the City of Cape Town, and the fisheries sector in South Africa. His freelance endeavours encompassed research, data analysis, sustainability reports, environmental impact assessments, and public participation processes; mainly in the fisheries sector.

Christo Rautenbach

Dr Christo Rautenbach is a distinguished double PhD holder, excelling in Applied Mathematics and Physical Oceanography. With an extensive background in numerical modelling spanning over a decade, he is an expert in coastal and ocean hydro- and wave dynamics. His expertise encompasses operational physical oceanography, coastal engineering, and coastal dynamics research. As a seasoned project manager and team leader, he spearheads applied research initiatives, integrating data science and artificial intelligence methodologies.

Albertus J. Smit

Professor Albertus J. Smit, a marine scientist, applies innovative statistical methods to vast environmental and biological datasets. His critical perspective drives research into pressing ecological and environmental issues crucial for human well-being. Aligned with national strategies, his work spans global change, marine research, and biodiversity, supporting Sustainable Development Goals. Proficient in diverse hardware, computing, and software tools, his expertise focuses on oceanic climate change. With a string of impactful publications and successful grant acquisitions, Smit’s leadership ensures program completion and fosters inclusive, transdisciplinary collaborations for actionable research outcomes.

Acknowledgements

This paper would not have been possible without the OceanParcels open-source software (available from: https://oceanparcels.org/). This study also uses ocean and wind model data from Copernicus Marine Data Store. The products used in this study have been updated/changed and therefore do no longer exist. However, the data sets used in this study can be provided upon request from the author.

Research ethics: The processes and procedures are undertaken over the duration of this study abided by national laws and permit conditions.
Author contributions: Ross Coppin conceptualised the scope of the research reported in this manuscript, designed the model, conducted the simulations, undertook the numerical and statistical analyses, made the first round of interpretation, and did the writing. AJ Smit and Christo Rautenbach provided guidance in writing, statistical analyses, and overall presentation of the manuscript. The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Competing interests: The authors declare that the research was conducted without any commercial or financial relationships that could be construed as a potential conflict of interest.
Research funding: This research was funded by the South African National Research Foundation (http://www.nrf.ac.za). The funding number is CSRP170430229220. Aside from the funding provided, the funders had no role in the study design, data collection and analysis, publication decision, or manuscript preparation.
Data availability: The raw data can be obtained on request from the corresponding author.

References

Allen, A.A. and Plourde, J.V. (1999). Review of leeway: field experiments and implementation. US Coast Guard, Alexandria, United States.Search in Google Scholar

Bäck, S., Lehvo, A., and Blomster, J. (2000). Mass occurrence of unattached Enteromorpha intestinalis on the Finnish Baltic Sea coast. Annales Botanici Fennici: 155–161.Search in Google Scholar

Beal, L.M., Elipot, S., Houk, A., and Leber, G.M. (2015). Capturing the transport variability of a western boundary jet: results from the Agulhas Current Time-Series Experiment (ACT). J. Phys. Oceanogr. 45: 1302–1324, https://doi.org/10.1175/jpo-d-14-0119.1.Search in Google Scholar

Bernardes Batista, M., Batista Anderson, A., Franzan Sanches, P., Simionatto Polito, P., Cesar Lima Silveira, T., Velez-Rubio, G.M., Scarabino, F., Camacho, O., Schmitz, C., Martinez, A., et al.. (2018). Kelps’ long-distance dispersal: role of ecological/oceanographic processes and implications to marine forest conservation. Diversity 10: 12228–12233, https://doi.org/10.3390/d10010011.Search in Google Scholar

Beron-Vera, F.J., Olascoaga, M.J., and Lumpkin, R. (2016). Inertia-induced accumulation of flotsam in the subtropical gyres. Geophys. Res. Lett. 43, https://doi.org/10.1002/2016gl071443.Search in Google Scholar

Blanke, B., Roy, C., Penven, P., Speich, S., McWilliams, J., and Nelson, G. (2002). Linking wind and interannual upwelling variability in a regional model of the southern Benguela. Geophys. Res. Lett. 29, https://doi.org/10.1029/2002GL015718.Search in Google Scholar

Blanke, B., Speich, S., Bentamy, A., Roy, C., and Sow, B. (2005). Modeling the structure and variability of the southern Benguela upwelling using QuikSCAT wind forcing. J. Geophys. Res. C Oceans 110: 2004JC002529, https://doi.org/10.1029/2004JC002529.Search in Google Scholar

Breivik, Ø., Allen, A.A., Maisondieu, C., and Roth, J.C. (2011). Wind-induced drift of objects at sea: the leeway field method. Appl. Ocean Res. 33: 100–109, https://doi.org/10.1016/j.apor.2011.01.005.Search in Google Scholar

Brooks, M.T., Coles, V.J., and Coles, W.C. (2019). Inertia influences pelagic Sargassum advection and distribution. Geophys. Res. Lett. 46: 2610–2618, https://doi.org/10.1029/2018gl081489.Search in Google Scholar

Brooks, M.T., Coles, V.J., Hood, R.R., and Gower, J.F. (2018). Factors controlling the seasonal distribution of pelagic Sargassum. Mar. Ecol. Prog. Ser. 599: 1–18, https://doi.org/10.3354/meps12646.Search in Google Scholar

Christiansen, F., Putman, N.F., Farman, R., Parker, D.M., Rice, M.R., Polovina, J.J., Balazs, G.H., and Hays, G.C. (2016). Spatial variation in directional swimming enables juvenile sea turtles to reach and remain in productive waters. Mar. Ecol. Prog. Ser. 557: 247–259, https://doi.org/10.3354/meps11874.Search in Google Scholar

Coppin, R., Rautenbach, C., Ponton, T.J., and Smit, A.J. (2020). Investigating waves and temperature as drivers of kelp morphology. Front. Mar. Sci. 7: 567, https://doi.org/10.3389/fmars.2020.00567.Search in Google Scholar

D’Asaro, E.A., Shcherbina, A.Y., Klymak, J.M., Molemaker, J., Novelli, G., Guigand, C.M., Haza, A.C., Haus, B.K., Ryan, E.H., Jacobs, G.A., et al.. (2018). Ocean convergence and the dispersion of flotsam. Proc. Natl. Acad. Sci. U. S. A. 115: 1162–1167, https://doi.org/10.1073/pnas.1718453115.Search in Google Scholar PubMed PubMed Central

Davis, R.E. (1991). Observing the general circulation with floats. Deep-Sea Res. Part A Oceanogr. Res. Pap. 38: S531–S571, https://doi.org/10.1016/s0198-0149(12)80023-9.Search in Google Scholar

Dayton, P.K. (1985). Ecology of kelp communities. Annu. Rev. Ecol. Systemat. 16: 215–245, https://doi.org/10.1146/annurev.ecolsys.16.1.215.Search in Google Scholar

Delandmeter, P. and Van Sebille, E. (2019). The Parcels v2. 0 Lagrangian framework: new field interpolation schemes. Geosci. Model Dev. 12: 3571–3584, https://doi.org/10.5194/gmd-12-3571-2019.Search in Google Scholar

Denny, M. and Gaylord, B. (2002). The mechanics of wave-swept algae. J. Exp. Biol. 205: 1355–1362, https://doi.org/10.1242/jeb.205.10.1355.Search in Google Scholar PubMed

Denny, M.W., Gaylord, B.P., and Cowen, E.A. (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: 3165–3183, https://doi.org/10.1242/jeb.200.24.3165.Search in Google Scholar PubMed

Dromgoole, F.I. (1982). The buoyant properties of Codium. Bot. Mar. 25: 391–397, https://doi.org/10.1515/botm.1982.25.8.391.Search in Google Scholar

Dyer, D.C. (2018). Stable isotope ecology of South African kelp forests, Available at: https://open.uct.ac.za/handle/11427/29601.Search in Google Scholar

Fossette, S., Putman, N.F., Lohmann, K.J., Marsh, R., and Hays, G.C. (2012). A biologist’s guide to assessing ocean currents: a review. Mar. Ecol. Prog. Ser. 457: 285–301, https://doi.org/10.3354/meps09581.Search in Google Scholar

Fraser, C.I., Morrison, A.K., Hogg, A.M., Macaya, E.C., van Sebille, E., Ryan, P.G., Padovan, A., Jack, C., Valdivia, N., and Waters, J.M. (2018). Antarctica’s ecological isolation will be broken by storm-driven dispersal and warming. Nat. Clim. Change 8: 704–708, https://doi.org/10.1038/s41558-018-0209-7.Search in Google Scholar

Fraser, C.I., Nikula, R., and Waters, J.M. (2011). Oceanic rafting by a coastal community. Proc. R. Soc. B 278: 649–655, https://doi.org/10.1098/rspb.2010.1117.Search in Google Scholar PubMed PubMed Central

Furnans, J., Imberger, J., and Hodges, B.R. (2008). Including drag and inertia in drifter modelling. Environ. Model. Software 23: 714–728, https://doi.org/10.1016/j.envsoft.2007.09.010.Search in Google Scholar

Garzoli, S.L., Gordon, A.L., Kamenkovich, V., Pillsbury, D., and Duncombe-Rae, C. (1996). Variability and sources of the southeastern Atlantic circulation. J. Mar. Res. 54: 1039–1071, https://doi.org/10.1357/0022240963213763.Search in Google Scholar

Gaylord, B. and Denny, M.W. (1997). Flow and flexibility I. Effects of size, shape and stiffness in determining wave forces on the stipitate kelps Eisenia arborea and Pterygophora californica. J. Exp. Biol. 200: 3141–3164, https://doi.org/10.1242/jeb.200.24.3141.Search in Google Scholar PubMed

Gilson, A.R., Smale, D.A., Burrows, M.T., and O’Connor, N.E. (2021). Spatio-temporal variability in the deposition of beach-cast kelp (wrack) and inter-specific differences in degradation rates. Mar. Ecol. Prog. Ser. 674: 89–102, https://doi.org/10.3354/meps13825.Search in Google Scholar

Graiff, A., Pantoja, J.F., Tala, F., and Thiel, M. (2016). Epibiont load causes sinking of viable kelp rafts: seasonal variation in floating persistence of giant kelp Macrocystis pyrifera. Mar. Biol. 163: 191, https://doi.org/10.1007/s00227-016-2962-3.Search in Google Scholar

Griffin, D.A., Oke, P.R., and Jones, E.M. (2017). The search for MH370 and ocean surface drift. Commonwealth Scientific and Industrial Research Organisation, Available at: https://www.atsb.gov.au/sites/default/files/media/5772119/mh370_ocean_driftv29.pdf.Search in Google Scholar

Grue, J. and Biberg, D. (1993). Wave forces on marine structures with small speed in water of restricted depth. Appl. Ocean Res. 15: 121–135, https://doi.org/10.1016/0141-1187(93)90036-w.Search in Google Scholar

Harrold, C. and Lisin, S. (1989). Radio-tracking rafts of giant kelp: local production and regional transport. J. Exp. Mar. Biol. Ecol. 130: 237–251, https://doi.org/10.1016/0022-0981(89)90166-4.Search in Google Scholar

Hart-Davis, M., Backeberg, B., and Bakhoday-Paskyabi, M. (2018). An assessment of the importance of combining wind, ocean currents and stochastic motions in a particle trajectory model for search and rescue applications. South Afr. Soc. Atmos. Sci. 34: 157–160.Search in Google Scholar

Hobday, A.J. (2000a). Abundance and dispersal of drifting kelp Macrocystis pyrifera rafts in the Southern California Bight. Mar. Ecol. Prog. Ser. 195: 101–116, https://doi.org/10.3354/meps195101.Search in Google Scholar

Hobday, A.J. (2000b). Age of drifting Macrocystis pyrifera (L.) C. Agardh rafts in the southern California bight. J. Exp. Mar. Biol. Ecol. 253: 97–114, https://doi.org/10.1016/s0022-0981(00)00255-0.Search in Google Scholar PubMed

Holden, J.J., Kingzett, B.C., MacNeill, S., Smith, W., Juanes, F., and Dudas, S.E. (2018). Beach-cast biomass and commercial harvesting of a non-indigenous seaweed, Mazzaella japonica, on the east coast of Vancouver Island, British Columbia. J. Appl. Phycol. 30: 1175–1184, https://doi.org/10.1007/s10811-017-1321-1.Search in Google Scholar

Holmquist, J.G. (1994). Benthic macroalgae as a dispersal mechanism for fauna: influence of a marine tumbleweed. J. Exp. Mar. Biol. Ecol. 180: 235–251, https://doi.org/10.1016/0022-0981(94)90069-8.Search in Google Scholar

Hutchings, L., Van der Lingen, C.D., Shannon, L.J., Crawford, R.J.M., Verheye, H.M.S., Bartholomae, C.H., Van der Plas, A.K., Louw, D., Kreiner, A., Ostrowski, M., et al.. (2009). The Benguela Current: an ecosystem of four components. Prog. Oceanogr. 83: 15–32, https://doi.org/10.1016/j.pocean.2009.07.046.Search in Google Scholar

Jutzeler, M., Marsh, R., Van Sebille, E., Mittal, T., Carey, R.J., Fauria, K.E., Manga, M., and McPhie, J. (2020). Ongoing dispersal of the 7 August 2019 pumice raft from the Tonga arc in the Southwestern Pacific ocean. Geophys. Res. Lett. 47: e1701121, https://doi.org/10.1029/2019gl086768.Search in Google Scholar

Kirkman, H. and Kendrick, G.A. (1997). Ecological significance and commercial harvesting of drifting and beach-cast macro-algae and seagrasses in Australia: a review. J. Appl. Phycol. 9: 311–326, https://doi.org/10.1023/A:1007965506873.10.1023/A:1007965506873Search in Google Scholar

Le Gouvello, D.Z.M., Hart-Davis, M.G., Backeberg, B.C., and Nel, R. (2020). Effects of swimming behaviour and oceanography on sea turtle hatchling dispersal at the intersection of two ocean current systems. Ecol. Modell. 431, https://doi.org/10.1016/j.ecolmodel.2020.109130.Search in Google Scholar

Lutjeharms, J.R.E. (2007). Three decades of research on the greater Agulhas Current. Ocean Sci. 3: 129–147, https://doi.org/10.5194/os-3-129-2007.Search in Google Scholar

Lutjeharms, J.R.E., Cooper, J., and Roberts, M. (2000). Upwelling at the inshore edge of the Agulhas current. Continent. Shelf Res. 20: 737–761, https://doi.org/10.1016/s0278-4343(99)00092-8.Search in Google Scholar

Lutjeharms, J.R.E. and Van Ballegooyen, R.C. (1988). The retroflection of the Agulhas current. J. Phys. Oceanogr. 18: 1570–1583, https://doi.org/10.1175/1520-0485(1988)018<1570:trotac>2.0.co;2.10.1175/1520-0485(1988)018<1570:TROTAC>2.0.CO;2Search in Google Scholar

McCormick, T.B., Buckley, L.M., Brogan, J., and Perry, L.M. (2008). Drift macroalgae as a potential dispersal mechanism for the white abalone Haliotis sorenseni. Mar. Ecol. Prog. Ser. 362: 225–232, https://doi.org/10.3354/meps07419.Search in Google Scholar

Miron, P., Olascoaga, M.J., Beron-Vera, F.J., Putman, N.F., Triñanes, J., Lumpkin, R., and Goni, G.J. (2020). Clustering of marine-debris- and Sargassum-like drifters explained by inertial particle dynamics. Geophys. Res. Lett. 47: e2020GL089874, https://doi.org/10.1029/2020gl089874.Search in Google Scholar

Nikula, R., Spencer, H.G., and Waters, J.M. (2013). Passive rafting is a powerful driver of transoceanic gene flow. Biol. Lett. 9: 20120821, https://doi.org/10.1098/rsbl.2012.0821.Search in Google Scholar PubMed PubMed Central

North, E.W., Gallego, A., and Petitgas, P. (2009). Manual of recommended practices for modelling physical–biological interactions during fish early life. ICES Coop. Res. Rep. 295.Search in Google Scholar

Norton, T.A. (1992). Dispersal by macroalgae. Br. Phycol. J. 27: 293–301, https://doi.org/10.1080/00071619200650271.Search in Google Scholar

Olascoaga, M.J., Beron-Vera, F.J., Miron, P., Triñanes, J., Putman, N.F., Lumpkin, R., and Goni, G.J. (2020). Observation and quantification of inertial effects on the drift of floating objects at the ocean surface. Phys. Fluids 32: 026601, https://doi.org/10.1063/1.5139045.Search in Google Scholar

Putman, N.F., Goni, G.J., Gramer, L.J., Hu, C., Johns, E.M., Trinanes, J., and Wang, M. (2018). Simulating transport pathways of pelagic Sargassum from the Equatorial Atlantic into the Caribbean sea. Prog. Oceanogr. 165: 205–214, https://doi.org/10.1016/j.pocean.2018.06.009.Search in Google Scholar

Putman, N.F., Lumpkin, R., Olascoaga, M.J., Trinanes, J., and Goni, G.J. (2020). Improving transport predictions of pelagic Sargassum. J. Exp. Mar. Biol. Ecol. 529: 151398, https://doi.org/10.1016/j.jembe.2020.151398.Search in Google Scholar

Putman, N.F., Scott, R., Verley, P., Marsh, R., and Hays, G.C. (2012a). Natal site and offshore swimming influence fitness and long-distance ocean transport in young sea turtles. Mar. Biol. 159: 2117–2126, https://doi.org/10.1007/s00227-012-1995-5.Search in Google Scholar

Putman, N.F., Verley, P., Shay, T.J., and Lohmann, K.J. (2012b). Simulating transoceanic migrations of young loggerhead sea turtles: merging magnetic navigation behavior with an ocean circulation model. J. Exp. Biol. 215: 1863–1870, https://doi.org/10.1242/jeb.067587.Search in Google Scholar PubMed

Ragoasha, N., Herbette, S., Cambon, G., Veitch, J., Reason, C., and Roy, C. (2019). Lagrangian pathways in the southern Benguela upwelling system. J. Mar. Syst. 195: 50–66, https://doi.org/10.1016/j.jmarsys.2019.03.008.Search in Google Scholar

Rothäusler, E., Gómez, I., Hinojosa, I.A., Karsten, U., Miranda, L., Tala, F., and Thiel, M. (2011). Kelp rafts in the Humboldt current: interplay of abiotic and biotic factors limit their floating persistence and dispersal potential. Limnol. Oceanogr. 56: 1751–1763, https://doi.org/10.4319/lo.2011.56.5.1751.Search in Google Scholar

Rubio, A., Blanke, B., Speich, S., Grima, N., and Roy, C. (2009). Mesoscale eddy activity in the southern Benguela upwelling system from satellite altimetry and model data. Prog. Oceanogr. 83: 288–295, https://doi.org/10.1016/j.pocean.2009.07.029.Search in Google Scholar

Shannon, L.V. and Nelson, G. (1996). The Benguela: large scale features and processes and system variability. In: Wefer, G., Berger, W.H., Siedler, G., and Webb, D.J. (Eds.), The south Atlantic. Springer, Berlin Heidelberg, pp. 163–210.10.1007/978-3-642-80353-6_9Search in Google Scholar

Smith, S.D.A. (2002). Kelp rafts in the southern ocean. Global Ecol. Biogeogr. 11: 67–69, https://doi.org/10.1046/j.1466-822x.2001.00259.x.Search in Google Scholar

Tala, F., Gómez, I., Luna-Jorquera, G., and Thiel, M. (2013). Morphological, physiological and reproductive conditions of rafting bull kelp (Durvillaea antarctica) in northern-central Chile (30°S). Mar. Biol. 160: 1339–1351, https://doi.org/10.1007/s00227-013-2186-8.Search in Google Scholar

Tala, F., Penna-Díaz, M.A., Luna-Jorquera, G., Rothäusler, E., and Thiel, M. (2017). Daily and seasonal changes of photobiological responses in floating bull kelp Durvillaea antarctica (Chamisso) Hariot (Fucales: Phaeophyceae). Phycologia 56: 271–283, https://doi.org/10.2216/16-93.1.Search in Google Scholar

Troell, M., Robertson-Andersson, D., Anderson, R.J., Bolton, J.J., Maneveldt, G., Halling, C., and Probyn, T. (2006). Abalone farming in South Africa: an overview with perspectives on kelp resources, abalone feed, potential for on-farm seaweed production and socio-economic importance. Aquaculture 257: 266–281, https://doi.org/10.1016/j.aquaculture.2006.02.066.Search in Google Scholar

van den Bremer, T.S. and Breivik, Ø. (2018). Stokes drift. Phil. Trans. Math. Phys. Eng. Sci. 376: 20170104, https://doi.org/10.1098/rsta.2017.0104.Search in Google Scholar PubMed PubMed Central

Van Sebille, E., Griffies, S.M., Abernathey, R., Adams, T.P., Berloff, P., Biastoch, A., Blanke, B., Chassignet, E.P., Cheng, Y., Cotter, C.J., et al.. (2018). Lagrangian ocean analysis: fundamentals and practices. Ocean Model. 121: 49–75, https://doi.org/10.1016/j.ocemod.2017.11.008.Search in Google Scholar

Veitch, J., Hermes, J., Lamont, T., Penven, P., and Dufois, F. (2018). Shelf-edge jet currents in the southern Benguela: a modelling approach. J. Mar. Syst. 188: 27–38, https://doi.org/10.1016/j.jmarsys.2017.09.003.Search in Google Scholar

Veitch, J., Penven, P., and Shillington, F. (2010). Modeling equilibrium dynamics of the Benguela Current system. J. Phys. Oceanogr. 40: 1942–1964, https://doi.org/10.1175/2010jpo4382.1.Search in Google Scholar

Veitch, J.A. and Penven, P. (2017). The role of the Agulhas in the Benguela current system: a numerical modeling approach. J. Geophys. Res. C Oceans 122: 3375–3393, https://doi.org/10.1002/2016jc012247.Search in Google Scholar

Vogel, S. (2020). Life in moving fluids: the physical biology of flow, Revised and expanded 2nd ed Princeton University press, Princeton, New Jersey, USA.10.2307/j.ctvzsmfc6Search in Google Scholar

Wang, M., Hu, C., Barnes, B.B., Mitchum, G., Lapointe, B., and Montoya, J.P. (2019). The great Atlantic Sargassum belt. Science 365: 83–87, https://doi.org/10.1126/science.aaw7912.Search in Google Scholar PubMed

Woodborne, M.W., Rogers, J., and Jarman, N. (1989). The geological significance of kelp-rafted rock along the west coast of South Africa. Geo Mar. Lett. 9: 109–118, https://doi.org/10.1007/bf02430432.Search in Google Scholar

Zhong, Y., Bracco, A., and Villareal, T.A. (2012). Pattern formation at the ocean surface: Sargassum distribution and the role of the eddy field. Limnol. Oceanogr. Fluid. Environ. 2: 12–27, https://doi.org/10.1215/21573689-1573372.Search in Google Scholar