Skip to main content
SpringerLink
Log in

On the Dispersion Relation of Sea Waves

  • Chapter
  • First Online:
Simulation of the Sea Surface for Remote Sensing

Part of the book series: Springer Oceanography ((SPRINGEROCEAN))

  • 291 Accesses

Abstract

With the advent of remote sensing tools making it possible to obtain images of the sea surface with high spatial resolution, research into the spatial and temporal structure of the surface wave field has become very important. When interpreting remote sensing data it is necessary to take into account the nonlinearity of sea waves, especially the function of angular distribution, describing the distribution of wave energy in the directions. In this chapter, on the basis of measurements made on the oceanographic platform, the stability of phase relations in sea waves is analyzed. The models describing the phase relations and the quadratic coherence function in a multicomponent wave field are constructed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 109.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Arena F (2005) On non-linear very large sea wave groups. Ocean Eng 32(11–12):1311–1331

    Article  Google Scholar 

  2. Babanin AV, Soloviev YP (1998) Variability of directional spectra of wind-generated waves, studied by means of wave staff arrays. Mar Freshw Res 49:89–101

    Google Scholar 

  3. Bakhanov VV, Demakova AA, Korinenko AE, Ryabkova MS, Titov VI (2018) Estimation of the wind wave spectra with centimeters-to-meter lengths by the sea surface images. Phys Oceanogr 3:177–190

    Google Scholar 

  4. Chung-Chu T, Bouchard R, Taft B (2004) Determination of pitch and roll angles from data buoys. Oceans ’04 MTS/IEEE Techno-Ocean ’04 (IEEE Cat. No. 04CH37600). https://doi.org/10.1109/oceans.2004.1405777

  5. Danilyichev MV, Nikolaev AN, Kutuza BG (2009) The use of Kirchhoff method for practical calculations in microwave radiometry of the rough sea surface. Radiotehnika i elektronika 54(8):915–925

    Google Scholar 

  6. Donelan MA, Hamilton J, Hui WH (1985) Directional spectra of wind-generated waves. Philos Trans Roy Soc A315:509–562

    Google Scholar 

  7. Dugan JJ, Piotrowski CC (2003) Surface currents measured from a sequence of airborne camera images. In: Proceedings of the IEEE/OES seventh working conference on current measurement technology. https://doi.org/10.1109/ccm.2003.1194284

  8. Fedele F, Tayfun MA (2009) On nonlinear wave groups and crest statistics. J Fluid Mech 620:221–239. https://doi.org/10.1017/S0022112008004424

    Article  Google Scholar 

  9. Fujii S, Heron ML, Kim K, Lai J-W, Lee S-H, Wu X, Wu X, Wyatt LR, Yang W-C (2013) An overview of developments and applications of oceanographic radar networks in Asia and Oceania countries. Ocean Sci J 48(1):69–97

    Article  Google Scholar 

  10. Graber HC, Terray EA, Donelan MA, Drennan WM, Van Leer JC, Peters DB (2000) ASIS—A New Air–Sea interaction spar buoy: design and performance at sea. J Atmos Oceanic Technol 17(5):708–720. https://doi.org/10.1175/1520-0426(2000)017%3c0708:aanasi%3e2.0

  11. Hara T, Karachintsev AV (2003) Observation of Nonlinear Effects in Ocean Surface Wave Frequency Spectra. J Phys Oceanogr 33(2):422–430. https://doi.org/10.1175/1520-0485(2003)033%3c0422:ooneio%3e2.0.co;2

  12. Hasselman DE, Dunckel M, Ewing JA (1980) Directional wave spectra observed during JONSWAP1973. J Phys Oceanogr 10:56–64

    Google Scholar 

  13. Ivonin DV, Telegin VA, Azarov AI, Ermoshkin AV, Bakhanov VV (2011) Possibility to measure velocity vector of surface currents by means of nautical radar with wide beamwidth antenna. Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa 8(4):219–227. (In Russian)

    Google Scholar 

  14. Ivonin DV, Chernyshov PV, Kuklev SB, Myslenkov SA (2016) Preliminary comparisons of sea current velocity vector measurements by a nautical X-band radar and moored ADCP. Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa 13(2):53–66

    Article  Google Scholar 

  15. Khristoforov GN, Zapevalov AS, Smolov VE (1991) Longitudinal and transversal coherence in energy-carrier marine wind-waves. Izvestiya Akademii Nauk SSSR Fizika Atmosfery i Okeana 27(8):887–889

    Google Scholar 

  16. Khristoforov GN, Zapevalov AS, Smolov VE (1989) Measurements of collinear coherence in short-period sea wind-waves. Izvestiya Akademii Nauk SSSR Fizika Atmosfery i Okeana 25(6):636–643

    Google Scholar 

  17. Khristoforov GN, Zapevalov AS, Smolov VE (1995) Anisotropy of spatiotemporal correlations of sea wind-wave field Izvestiya Akademii Nauk Fizika Atmosfery i Okeana. 31(5):692–700

    Google Scholar 

  18. Krogstad HE, Trulsen K (2010) Interpretations and observations of ocean wave spectra. Ocean Dyn 60:973–991

    Article  Google Scholar 

  19. Kudryavtsev V, Yurovskaya M, Chapron B, Collard F, Donlon C (2017) Sun glitter imagery of ocean surface waves: Part 1. Directional spectrum retrieval and validation, J Geophys Res Oceans 122(2):1369–1383

    Google Scholar 

  20. Kudryavtsev V, Yurovskaya M, Chapron B, Collard F, Donlon C (2017) Sun glitter imagery of surface waves. Part 2: waves transformation on ocean currents. J Geophys Res Oceans 122(2):1384–1399

    Google Scholar 

  21. Kuzmin AV, Goryachkin YA, Ermakov DM, Ermakov SA, Komarova NY, Kuznetsov AS, Repina IA, Sadovskii IN, Smirnov MT, Sharkov EA, Chuharev AM (2009) Marine hydrographic platform “Katsiveli” as a subsatellite test site in the Black sea. Earth Observation and Remote Sensing 1:31–44

    Google Scholar 

  22. Lake BM, Yuen HC (1978) A new model for nonlinear gravity waves. Part 1. J Fluid Mech 88:33–62

    Google Scholar 

  23. Lamont-Smith T, Fuchs J, Tulin MP (2003) Radar investigation of the structure of wind waves. J Oceanogr 59:49–63

    Article  Google Scholar 

  24. Longuett-Higgins MS, Cartwrighte DE, Smith ND (1963) Observation of the directional spectrum of sea waves using the motions of the floating buoy. In: Proceeding of conference ocean wave spectra. Englewood Cliffs. NY Prentice Hall, pp 111–132

    Google Scholar 

  25. Mettlach T, Teng CC (2010) Concepts for an ideal ocean wave-measuring buoy. OCEANS 2010 MTS/IEEE SEATTLE. https://doi.org/10.1109/oceans.2010.5664525

  26. Mitsuyasu H, Kuo YY, Musuda A (1979) On the dispersion relation of random gravity waves. Pt. 2. An experiment. J Fluid Mach 92:731–749

    Google Scholar 

  27. Mitsuyasu H, Kuo YY, Musuda A(1979) On the dispersion relation of random gravity waves. Pt. 2. An experiment. J Fluid Mach 92:731–749

    Google Scholar 

  28. Mitsuyasu H, Tasai F, Suhara T, Mizuno S, Ohkuso M, Honda I, Rikiishi K (1975) Observations of the directional spectrum of ocean waves using a cloverleaf buoy. J Phys Octanogr 5(4):750–758

    Article  Google Scholar 

  29. Mollo-Christensen E, Ramamonjiarisoa A (1978) Modeling the presence of waves groups in a random wave field. J Geophys Res 83(C8):4117–4122

    Article  Google Scholar 

  30. Panfilova M, Ryabkova M, Karaev V, Skiba E (2019) Retrieval of the statistical characteristics of wind waves from the width and shift of the doppler spectrum of the backscattered microwave signal at low incidence angles. IEEE Trans Geosci Remote Sensing. 1–7. https://doi.org/10.1109/tgrs.2019.2955546

  31. Pelinovsky EN, Shurgalina EG (2016) Formation of freak waves in a soliton gas described by the modified Korteweg–de Vries equation. Doklady Phys 61(9):423–426

    Google Scholar 

  32. Pereira HPP, Violante-Carvalho N, Nogueira ICM, Babanin A, Liu Q, Ferreira de Pinho U, Nascimento F, Parente CE (2017) Wave observations from an array of directional buoys over the southern Brazilian coast. Ocean Dyn 67:1577–1591

    Google Scholar 

  33. Peureux C, Benetazzo A, Ardhuin F (2018) Note on the directional properties of meter-scale gravity waves. Ocean Sci 14(1):41–52. https://doi.org/10.5194/os-14-41-2018

    Article  Google Scholar 

  34. Phillips OM (1981) The dispersion of short wavelets in the presence of a dominant long wave. J Fluid Mech 107:466–485

    Google Scholar 

  35. Plant WJ (2002) A stochastic, multiscale model of microwave backscatter from the ocean. J Geophys Res 107(C9):3120. https://doi.org/10.1029/2001JC000909

    Article  Google Scholar 

  36. Pokazeev KV, Zapevalov AS, Pustovoytenko VV (2015) A nonlinear model of sea surface waves. Mosc Univ Phys Bull 70(3):213–215

    Article  Google Scholar 

  37. Pokazeev КV, Zapevalov AS (2019) Calculation of phase velocities in the field of sea surface waves. Mosc Univ Phys Bull 74(4):413–418. https://doi.org/10.3103/S0027134919040143

    Article  Google Scholar 

  38. Ramamonjiarisoa A, Coantic M (1976) Loi experimentale de dispersion de vagues produites par le vent sur une faible longueur d’action. C.R. Hehd Seances Acad Sci Ser. B. 282:111–113

    Google Scholar 

  39. Ramamonjiarisoa A, Giovanangeli JP (1978) Observations de la propagation des vagues engendrees par le vent au large. C.R. Hehd Seances Acad Sci Ser B 287:133–136

    Google Scholar 

  40. Rapizo H, Babanin AV, Schulz E, Hemer MA, Durrant TH (2015) Observation of wind-waves from a moored buoy in the Southern Ocean. Ocean Dyn 65(9):1275–1288

    Article  Google Scholar 

  41. Simanesew AW, Krogstad HE, Trulsen K, Nieto Borge JC (2018) Bimodality of directional distributions in ocean wave spectra: a comparison of data-adaptive estimation techniques. J Atmos Oceanic Technol 35(2):365–384. https://doi.org/10.1175/jtech-d-17-0007.1

    Article  Google Scholar 

  42. Wang DW, Hwang PA (2003) Higher fourier harmonics of the directional distribution of an equilibrium wave field under steady wind forcing. J Atmos Ocean Technol 20:217–227

    Article  Google Scholar 

  43. Wyatt LR (2018) Measuring the ocean wave directional spectrum “First Five” with HF radar. Ocean Dyn 69(1):123–144. https://doi.org/10.1007/s10236-018-1235-8

    Article  Google Scholar 

  44. Yefimov VV, Solov’yev P Yu, Khristoforov GN (1972) Observational determination of the phase velocities of spectral components of wind waves, Izv Atmos Oceanic Phys 8(4):435–446

    Google Scholar 

  45. Young IR (2006) Directional spectra of hurricane wind waves. J Geophys Res 111:C08020. https://doi.org/10.1029/2006JC003540

    Article  Google Scholar 

  46. Yuen HC, Lake BM (1982) Nonlinear dynamics of deep-water gravity waves. Adv Appl Mech 22:67–229. https://doi.org/10.1016/s0065-2156(08)70066-8

    Article  Google Scholar 

  47. Yurovskaya MV, Kudryavtsev VN, Stanichny SV (2019) Reconstruction of surface wave kinematic characteristics and bathymetry from Geoton-L1 multichannel optical images from “Resurs-P” satellite. Sovremennye problemy distantsionnogo zondirovaniya Zemli iz kosmosa. 16(2):218–226. (In Russian)

    Google Scholar 

  48. Zapevalov AS (1995) Estimation of the angular energy distribution function of the dominant sea waves. Izvestiya Akademii Nauk Fizika Atmosfery i Okeana 31(6):835–841

    Google Scholar 

  49. Zapevalov AS (2008) Statistical models of the sea surface in problems of acoustic and electromagnetic radiation scattering. Manuscript to claim the academic degree of doctor of physico-mathematical sciences on the speciality 04.00.22—geophysics. Marine Hydrophysical Institute of the National Academy of Sciences of Ukraine, Sebastopol, 2008

    Google Scholar 

  50. Zapevalov AS, Bol’shakov AN, Smolov VE (2004) Studies of the coherence level of sea surface waves. Izvestiya, Atmos Oceanic Phys 40(4):483–487

    Google Scholar 

  51. Zapevalov AS (2009) Bragg scattering of centimeter electromagnetic radiation from the sea surface: the effect of waves longer than Bragg components. Izvestiya Atmos Ocean Phys 45(2):253–261

    Article  Google Scholar 

  52. Zapevalov AS, Bol’shakov AN, Smolov VE (2009) Studying the sea surface slopes using an array of wave gauge sensors. Oceanology 49(1):31–38

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Marine Hydrophysical Institute, Russian Academy of Sciences, Sevastopol, Russia

    Alexander Zapevalov

  2. Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, Russia

    Konstantin Pokazeev

  3. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    Tatiana Chaplina

Authors
  1. Alexander Zapevalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Konstantin Pokazeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tatiana Chaplina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Zapevalov .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zapevalov, A., Pokazeev, K., Chaplina, T. (2021). On the Dispersion Relation of Sea Waves. In: Simulation of the Sea Surface for Remote Sensing. Springer Oceanography. Springer, Cham. https://doi.org/10.1007/978-3-030-58752-9_3

Download citation

Publish with us

Policies and ethics

Search

Navigation