ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
Research article
Exponential distribution of wave-driven near-bed water speeds under short-crested waves: a case study in the eastern Gulf of Riga, the Baltic Sea; pp. 23–42
PDF | https://doi.org/10.3176/proc.2025.1.03

Authors
Maris Eelsalu ORCID Icon, Laura Piho ORCID Icon, Juris Aigars ORCID Icon, Loreta Kelpšaitė-Rimkienė ORCID Icon, Vitalijus Kondrat ORCID Icon, Maarja Kruusmaa ORCID Icon, Kevin E. Parnell ORCID Icon, Asko Ristolainen ORCID Icon, Ilona Šakurova ORCID Icon, Māris Skudra ORCID Icon, Maija Viška ORCID Icon, Tarmo Soomere ORCID Icon
Abstract

Loads exerted to the seabed by short-crested wind-seas with a wide directional spread have extensive spatio-temporal variability. We quantify this variability in terms of near-bed water speed using an array of nine high-resolution hydromast devices for recording pressure and water velocity in the range of 0.12–1 m/s mounted at a distance of 10 m from each other on a rigid rectangular frame of 20 × 20 m in approximately 4 m deep water and 700 m from the eastern shore of the Gulf of Riga near Skulte (Latvia) in August–September 2022. This array is complemented by an acoustic Doppler velocimeter (ADV). The average background current is very weak, approximately 0.003 m/s in the measurement location. The empirical distributions of velocity components are symmetric but greatly deviate from the expected Gaussian distribution. The empirical distributions of water speeds follow an exponential distribution rather than a Rayleigh or Forristall distribution. This shape of the distributions appears in the range of 0.2–0.7 m/s while the maximum speed reaches 1.22 m/s. The rate parameter (inverse scale parameter) varies almost by a factor of two in recordings by different devices. The recordings make it possible to identify wakes of vessels entering to or departing from the Port of Skulte.

References

Aagaard, T., Brinkkemper, J., Christensen, D. F., Hughes, M. G. and Ruessink, G. 2021. Surf zone turbulence and suspended sediment dynamics – a review. J. Mar. Sci. Eng.9(11), 1300. 
https://doi.org/10.3390/jmse9111300  

Battjes, J. A. and Groenendijk, H. W. 2000. Wave height distributions on shallow foreshores. Coast. Eng.40(3), 161–182. 
https://doi.org/10.1016/S0378-3839(00)00007-7  

Bian, C., Liu, X., Zhou, Z., Chen, Z., Wang, T. and Gu, Y. 2020. Calculation of winds induced bottom wave orbital velocity using the empirical mode decomposition method. J. Atmos. Ocean. Technol.37(5), 889–900. 
https://doi.org/10.1175/JTECH-D-19-0185.1  

Björkqvist, J.-V., Lukas, I., Alari, V., Vledder, G. P. V., Hulst, S., Pettersson, H. et al. 2018. Comparing a 41-year model hindcast with decades of wave measurements from the Baltic Sea. Ocean Eng.152, 57–71. 
https://doi.org/10.1016/j.oceaneng.2018.01.048  

Björkqvist, J.-V., Pärt, S., Alari, V., Rikka, S., Lindgren, E. and Tuomi, L. 2021. Swell hindcast statistics for the Baltic Sea. Ocean Sci.17, 1815–1829. https://doi.org/10.5194/os-17-1815-2021 

Bleckmann, H. and Zelick, R. 2009. Lateral line system of fish. Integr. Zool.4(1), 13–25. 
https://doi.org/10.1111/j.1749-4877.2008.00131.x  

Broman, B., Hammarklint, T., Rannat, K., Soomere, T. and Valdmann, A. 2006. Trends and extremes of wave fields in the north-eastern part of the Baltic Proper. Oceanologia48, 165–184.

Bullock, G. N., Obhrai, C., Peregrine, D. H. and Bredmose, H. 2007. Violent breaking wave impacts. Part 1: results from large-scale regular wave tests on vertical and sloping walls. Coast. Eng.54(8), 602–617. 
https://doi.org/10.1016/j.coastaleng.2006.12.002  

Christensen, D. F., Hughes, M. G. and Aagaard, T. 2019. Wave period and grain size controls on short-wave suspended sediment transport under shoaling and breaking waves. J. Geophys. Res. Earth Surf.124(12), 3124–3142. 
https://doi.org/10.1029/2019JF005168  

Coles, S. 2004. An Introduction to Statistical Modeling of Extreme Values. 3rd ed. Springer, London.

Dean, R. G. and Dalrymple, R. A. 1991. Water Wave Mechanics for Engineers and Scientists. World Scientific, Portland.
https://doi.org/10.1142/9789812385512

Diplas, P., Dancey, C. L., Celik, A. O., Valyrakis, M., Greer, K. and Akar, T. 2008. The role of impulse on the initiation of particle movement under turbulent flow conditions. Science322(5902), 717–720. 
https://doi.org/10.1126/science.1158954  

Eelsalu, M., Org, M. and Soomere, T. 2014. Visually observed wave climate in the Gulf of Riga. In 2014 IEEE/OES Baltic International Symposium (BALTIC), Tallinn, Estonia, 27–29 May 2014. IEEE, 1–10. 
https://doi.org/10.1109/BALTIC.2014.6887829

Egerer, M., Ristolainen, A., Piho, L., Vihman, L. and Kruusmaa, M. 2024. Hall effect sensor-based low-cost flow monitoring device: design and validation. IEEE Sens. J.24(5), 5986–5997. 
https://doi.org/10.1109/JSEN.2024.3354194  

Forristall, G. Z. 1978. On the statistical distributions of wave heights in a storm. J. Geophys. Res. Oceans83(C5), 2353–2358. 
https://doi.org/10.1029/JC083iC05p02353  

Foster, D. L., Beach, R. A. and Holman, R. A. 2000. Field observations of the wave bottom boundary layer. J. Geophys. Res. Oceans105(C8), 19631–19647. 
https://doi.org/10.1029/1999JC900018  

Giudici, A., Jankowski, M. Z., Männikus, R., Najafzadeh, F., Suursaar, Ü. and Soomere, T. 2023. A comparison of Baltic Sea wave properties simulated using two modelled wind data sets. Estuar. Coast. Shelf Sci.290, 108401. 
https://doi.org/10.1016/j.ecss.2023.108401  

Huang, N. E., Sheng, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q. et al. 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis. Proc. R. Soc. Lond. A.454(1971), 903–995. 
https://doi.org/10.1098/rspa.1998.0193  

Kvingedal, B., Bruserud, K. and Nygaard, E. 2018. Individual wave height and wave crest distributions based on field measurements from the northern North Sea. Ocean Dyn.68(12), 1727–1738. 
https://doi.org/10.1007/s10236-018-1216-y  

Leppäranta, M. and Myrberg, K. 2009. Physical Oceanography of the Baltic Sea. Springer, Berlin, Heidelberg. 
https://doi.org/10.1007/978-3-540-79703-6  

Lips, U., Zhurbas, V., Skudra, M. and Väli, G. 2016. A numerical study of circulation in the Gulf of Riga, Baltic Sea. Part I: whole-basin gyres and mean currents. Cont. Shelf Res.112, 1–13. 
https://doi.org/10.1016/j.csr.2015.11.008  

Longuet-Higgins, M. S. 1952. On the statistical distribution of heights of sea waves. J. Mar. Res.11(3), 245–266.

Ma, Y., Tai, B., Xie, B., Xu, T., Perlin, M. and Dong, G. 2023. Progress in the research of wave slamming forces on vertical cylinders. J. Mar. Sci. Appl.22(1), 1–13. 
https://doi.org/10.1007/s11804-023-00313-1  

Männikus, R. and Soomere, T. 2023. Directional variation of return periods of water level extremes in Moonsund and in the Gulf of Riga, Baltic Sea. Reg. Stud. Mar. Sci., 57, 102741. 
https://doi.org/10.1016/j.rsma.2022.102741  

Najafzadeh, F., Jankowski, M. Z., Giudici, A., Männikus, R., Suursaar, Ü., Viška, M. et al. 2024. Spatiotemporal variability of wave climate in the Gulf of Riga. Oceanologia66(1), 56–77. 
https://doi.org/10.1016/j.oceano.2023.11.001  

Pähtz, T., Clark, A. H., Valyrakis, M. and Durán, O. 2020. The physics of sediment transport initiation, cessation, and entrainment across aeolian and fluvial environments. Rev. Geophys.58(1), e2019RG000679. 
https://doi.org/10.1029/2019RG000679  

Poncet, P. A., Liquet, B., Larroque, B., D’Amico, D., Sous, D. and Abadie, S. 2022. In-situ measurements of energetic depth-limited wave loading. Appl. Ocean Res.125, 103216. 
https://doi.org/10.1016/j.apor.2022.103216  

Rätsep, M., Parnell, K. E., Soomere, T., Kruusmaa, M., Ristolainen, A. and Tuhtan, J. A. 2020. Using spectrograms from underwater total pressure sensors to detect passing vessels in a coastal environ­ment. J. Atmos. Ocean. Technol.37(8), 1353–1363. 
https://doi.org/10.1175/JTECH-D-19-0192.1  

Rätsep, M., Parnell, K. E., Soomere, T., Kruusmaa, M., Ristolainen, A. and Tuhtan, J. A. 2021. Surface vessel localization from wake measurements using an array of pressure sensors in the littoral zone. Ocean Eng.233, 109156. 
https://doi.org/10.1016/j.ocean eng.2021.109156  

Ristolainen, A., Tuhtan, J. A., Kuusik, A. and Kruusmaa, M. 2016. Hydromast: a bioinspired flow sensor with accelerometer. In  Biomimetic and Biohybrid Systems. Living Machines 2016. Lecture Notes in Computer Science (Lepora, N., Mura, A., Mangan, M., Verschure, P., Desmulliez, M. and Prescott, T., eds). Springer, Cham, 9793, 510–517. 
https://doi.org/10.1007/978-3-319-42417-0_55  

Ristolainen, A., Tuhtan, J. A. and Kruusmaa, M. 2019. Continuous, near-bed current velocity estimation using pressure and inertial sensing. IEEE Sens. J.19(24), 12398–12406. 
https://doi.org/10.1109/JSEN.2019.2937954  

Soomere, T. 2003. Anisotropy of wind and wave regimes in the Baltic Proper. J. Sea Res., 49(4), 305–316. 
https://doi.org/10.1016/S1385-1101(03)00034-0  

Soomere, T. 2005. Wind wave statistics in Tallinn Bay. Boreal Env. Res.10(2), 103–118. 
http://www.borenv.net/BER/archive/pdfs/ber10/ber10-103.pdf   

Soomere, T. and Eelsalu, M. 2014. On the wave energy potential along the eastern Baltic Sea coast. Renew. Energ.71, 221–233. 
https://doi.org/10.1016/j.renene.2014.05.025  

Soomere, T., Männikus, R., Pindsoo, K., Kudryavtseva, N. and Eelsalu, M. 2017. Modification of closure depths by synchronisation of severe seas and high water levels. Geo-Mar. Lett.37(1), 35–46. 
https://doi.org/10.1007/s00367-016-0471-5  

Soosaar, E., Maljutenko, I., Raudsepp, U. and Elken, J. 2014. An investigation of anticyclonic circulation in the southern Gulf of Riga during the spring period. Cont. Shelf Res.78, 75–84. 
https://doi.org/10.1016/j.csr.2014.02.009  

Sultan, N. J. 1992. Irregular wave-induced velocities in shallow water. Technical report CERC-92-9. US Army Corps of Engineers, Washington DC. 

Sultan, N. J. and Hughes, S. A. 1993. Irregular wave-induced velocities in shallow water. J. Waterw. Port Coast. Ocean Eng.119(4), 429–447. 
https://doi.org/10.1061/(ASCE)0733-950X(1993)119:4(429)  

Suursaar, Ü., Kullas, T. and Otsmann, M. 2002. A model study of the sea level variations in the Gulf of Riga and the Väinameri Sea. Cont. Shelf Res.22(14), 2001–2019. 
https://doi.org/10.1016/S0278-4343(02)00046-8   

Torsvik, T., Soomere, T., Didenkulova, I. and Sheremet, A. 2015. Identification of ship wake structures by a time-frequency method. J. Fluid Mech.765, 229–251. 
https://doi.org/10.1017/jfm.2014.734  

Trowbridge, J. H. and Lentz, S. J. 2018. The bottom boundary layer. Ann. Rev. Mar. Sci.10, 397–420. 
https://doi.org/10.1146/annurev-marine-121916-063351  

Vanem, E. and Fazeres-Ferradosa, T. 2022. A truncated, translated Weibull distribution for shallow water sea states. Coast. Eng.172, 104077. 
https://doi.org/10.1016/j.coastaleng.2021.104077  

Viška, M. and Soomere, T. 2013. Simulated and observed reversals of wave-driven alongshore sediment transport at the eastern Baltic Sea coast. Baltica26(2), 145–156. 
https://doi.org/10.5200/baltica. 2013.26.15  

Wiberg, P. L. and Sherwood, C. R. 2008. Calculating wave-generated bottom orbital velocities from surface-wave parameters. Comput. Geosci.34(10), 1243–1262. 
https://doi.org/10.1016/j.cageo.2008.02.010  

Wu, Y., Randell, D., Christou, M., Ewans, K. and Jonathan, P. 2016. On the distribution of wave height in shallow water. Coast. Eng.111, 39–49. 
https://doi.org/10.1016/j.coastaleng.2016.01.015  

Xiong, J., You, Z.-J., Li, J., Gao, S., Wang, Q. and Wang, Y. P. 2020. Variations of wave parameter statistics as influenced by water depth in coastal and inner shelf areas. Coast. Eng.159, 103714. 
https://doi.org/10.1016/j.coastaleng.2020.103714  

You, Z.-J. 2009. The statistical distribution of nearbed wave orbital velocity in intermediate coastal water depth. Coast. Eng.56(8), 844–852. 
https://doi.org/10.1016/j.coastaleng.2009.04.005  

Zhai, Z., Li, X. and Yang, L. 2022. Analytical approach to the solution of short-crested wave interaction with V-shaped and arc-shaped breakwaters. Phys. Fluids34(2), 022112. 
https://doi.org/10.1063/5.0078604  

Zheng, J. H., Qian, J., Zhong, H. S. and Guo, D. 2006. Three-dimensional physical study on wave characteristics in front of concave breakwaters. In Proceedings of the Second Sino-German Joint Symposium on Coastal and Ocean Engineering (Yixin, Y., ed.), Nanjing, China, 11–20 October 2004. China Ocean Press, 100–106.

Zou, Q. and Hay, A. E. 2003. The vertical structure of the wave bottom boundary layer over a sloping bed: theory and field measurements. J. Phys. Oceanogr.33(7), 1380–1400. 
https://doi.org/10.1175/1520-0485(2003)033<1380:TVSOTW>2.0.CO;2

Back to Issue