Editorial Type:
Article
Article Type:
Research Article

Evolution of the Bimodal Directional Distribution of Ocean Waves

David W. Wang Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi

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Paul A. Hwang Oceanography Division, Naval Research Laboratory, Stennis Space Center, Mississippi

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Print Publication:
01 May 2001
DOI:
https://doi.org/10.1175/1520-0485(2001)031<1200:EOTBDD>2.0.CO;2
Page(s):
1200–1221
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Abstract

Recent results of numerical wave models have shown that the presence of a bimodal directional spreading is a robust feature at wavenumbers above the spectral peak. This directional bimodality is controlled mainly by directional transfer of energy through nonlinear wave–wave interactions. The bimodal feature has also been observed in the directional spectra derived from the spatial topography of ocean surface waves acquired by stereo-photography, image radars, and an airborne scanning lidar system. In this study, a comprehensive data analysis of the evolution of the wave directional distribution during two active wave growth periods in Lake Michigan is conducted. The wind and wave measurements are acquired by two heave–pitch–roll buoys moored at a nearshore and an offshore station. An empirical method averaging the results of the maximum likelihood method and maximum entropy method is used to estimate the directional distribution from buoy measurements. The study shows that the bimodal distribution is a distinctive and persistent feature over a broad frequency range throughout the wave growth process. The characteristics of directional bimodality are quantified by parameters related to the separation angles and the amplitudes of the sidelobes. In general, the values of the parameters are smallest near the peak frequency and increase toward both lower and higher frequencies. This frequency-dependent pattern appears to be invariant to the change of wave age throughout the wave growth process. The persistent nature of the directional bimodality indicates that the nonlinear wave–wave interaction mechanism not only actively moves wave energy away from the peak frequency into both higher and lower frequency components but also constantly redistributes wave energy into directions oblique to the wind direction. At the offshore buoy site when the wind and peak wave directions align closely, the bimodal distribution is symmetric about the wind direction. At the nearshore buoy site when the local wind and the peak wave are not moving in the same direction or the wind field is less homogeneous, the bimodal distribution is asymmetric.

Corresponding author address: David Wang, Oceanography Division, Naval Research Laboratory, Stennis Space Center, MS 39529-5004.

Email: dwang@nrlssc.navy.mil

Abstract

Recent results of numerical wave models have shown that the presence of a bimodal directional spreading is a robust feature at wavenumbers above the spectral peak. This directional bimodality is controlled mainly by directional transfer of energy through nonlinear wave–wave interactions. The bimodal feature has also been observed in the directional spectra derived from the spatial topography of ocean surface waves acquired by stereo-photography, image radars, and an airborne scanning lidar system. In this study, a comprehensive data analysis of the evolution of the wave directional distribution during two active wave growth periods in Lake Michigan is conducted. The wind and wave measurements are acquired by two heave–pitch–roll buoys moored at a nearshore and an offshore station. An empirical method averaging the results of the maximum likelihood method and maximum entropy method is used to estimate the directional distribution from buoy measurements. The study shows that the bimodal distribution is a distinctive and persistent feature over a broad frequency range throughout the wave growth process. The characteristics of directional bimodality are quantified by parameters related to the separation angles and the amplitudes of the sidelobes. In general, the values of the parameters are smallest near the peak frequency and increase toward both lower and higher frequencies. This frequency-dependent pattern appears to be invariant to the change of wave age throughout the wave growth process. The persistent nature of the directional bimodality indicates that the nonlinear wave–wave interaction mechanism not only actively moves wave energy away from the peak frequency into both higher and lower frequency components but also constantly redistributes wave energy into directions oblique to the wind direction. At the offshore buoy site when the wind and peak wave directions align closely, the bimodal distribution is symmetric about the wind direction. At the nearshore buoy site when the local wind and the peak wave are not moving in the same direction or the wind field is less homogeneous, the bimodal distribution is asymmetric.

Corresponding author address: David Wang, Oceanography Division, Naval Research Laboratory, Stennis Space Center, MS 39529-5004.

Email: dwang@nrlssc.navy.mil

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  • Banner, M. L., and I. R. Young, 1994: Modeling spectral dissipation in the evolution of wind waves. Part I: Assessment of existing model performance. J. Phys. Oceanogr.,24, 1550–1571.

  • Benoit, M., 1992: Practical comparative performance survey of methods used for estimating directional wave spectra form heave–pitch–roll data. Proc. 23d Int. Conf. on Coastal Engineering, Vol. 2, Venice, Italy, American Society of Civil Engineers, 162–75.

  • ——, P. Frigaard, and H. A. Schaffer, 1997: Analyzing multidirectional wave spectra: A tentative classification of available methods. Proc. IAHR Seminar on Multidirectional Waves and Their Interaction with Structures, San Francisco, CA, International Assembly of Hydraulic Research, 131–158.

  • Brissette, F. P., and J. Wu, 1992: Wave directional spectra and current interaction in Lake St. Clair. Proc. Third Int. Workshop on Wave Hindcasting and Forecasting, Montreal, PQ, Canada, Environment Canada, 24–31.

  • ——, and I. K. Tsanis, 1994: Estimation of wave directional spectra from pitch-roll buoy data. J. Waterway, Port, Coastal Ocean Eng.,120, 93–115.

  • Cote, L. J., and Coauthors, 1960: The directional spectrum of a wind generated sea as determined from data obtained by the Stereo Wave Observation Project. Meteor. Papers, Vol. 2, New York University, 88 pp.

  • Donelan, M. A., J. Hamilton, and W. H. Hui, 1985: Directional spectra of wind-generated waves. Philos. Trans. Roy. Soc. London,A315, 509–562.

  • Earle, M. D., 1996: Nondirectional and directional wave data analysis procedures. NDBC Tech. Doc. 96-01, National Data Buoy Center, 35 pp.

  • Ewans, K. C., 1998: Observations of the directional spectrum of fetch-limited waves. J. Phys. Oceanogr.,28, 495–512.

  • ——, and T. Van der Vlugt, 1999: Estimating bimodal frequency-direction spectra from surface buoy data recorded during tropical cyclones. J. Offshore Mech. Arctic Eng.,121, 172–180.

  • Gilhousen, D. B., 1987: A field evaluation of NDBC moored buoy winds. J. Atmos. Oceanic Technol.,4, 94–104.

  • ——, 1989: Field evaluation of NDBC directional wave data. Proc. Second Int. Workshop on Wave Hindcasting and Forecasting, Vancouver, BC, Canada, Environment Canada, 1–10.

  • Hasselmann, D. E., M. Dunckel, and J. A. Ewing, 1980: Directional wave spectra observed during JONSWAP 1973. J. Phys. Oceanogr.,10, 1264–1280.

  • Hasselmann, K., 1962: On the non-linear energy transfer in a gravity-wave spectrum. 1: General theory. J. Fluid Mech.,15, 273–281.

  • Holthuijsen, L. H., 1983: Observations of the directional distribution of ocean-wave energy in fetch-limited conditions. J. Phys. Oceanogr.,13, 191–207.

  • Hwang, P. A., S. Atakturk, M. A. Sletten, and D. B. Trizna, 1996: A study of the wavenumber spectra of short water waves in the ocean. J. Phys. Oceanogr.,26, 1266–1285.

  • ——, D. W. Wang, E. J. Walsh, W. B. Krabill, and R. N. Swift, 2000:Airborne measurements of the wavenumber spectra of ocean surface waves. Part 2. Directional distribution. J. Phys. Oceanogr.,30, 2768–2787.

  • Jackson, F. C., W. T. Walton, and C. Y. Peng, 1985: A comparison of in situ and airborne radar observations of ocean wave directionality. J. Geophys. Res.,90, 1005–1018.

  • Krogstad, H. E., 1990: Reliability and resolution of directional wave spectra from heave, pitch, and roll data buoys. Directional Ocean Wave Spectra, R. C. Beal, Ed., Johns Hopkins University Press, 66–71.

  • Kuik, A. J., G. Ph. Van Vledder, and L. H. Holthuisen, 1988: A method for the routine analysis of pitch-and-roll buoy wave data. J. Phys. Oceanogr.,18, 1020–1034.

  • Liu, P., 1997: Nearshore hydrodynamics studies in western Lake Michigan, 1993–1995. NOAA Tech. Memo. ERL GLERL-103, NOAA/ERL, 40 pp.

  • Longuet-Higgins, M. S., D. E. Cartwright, and N. D. Smith, 1963: Observations of the directional spectrum of sea waves using the motions of a floating buoy. Ocean Wave Spectra, Prentice Hall, 111–136.

  • Lygre, A., and H. E. Krogstad, 1986: Maximum entropy estimation of the directional distribution in ocean wave spectra. J. Phys. Oceanogr.,16, 2052–2060.

  • Mitsuyasu, H., and Coauthors, 1975: Observations of the directional spectrum of ocean waves using a cloverleaf buoy. J. Phys. Oceanogr.,5, 750–760.

  • Oltman-Shay, J., and R. T. Guza, 1984: A data-adaptive ocean wave directional spectrum estimator for pitch-roll type measurements. J. Phys. Oceanogr.,14, 1800–1810.

  • Phillips, O. M., 1958: On some properties of the spectrum of wind-generated ocean waves. J. Mar. Res.,16, 231–240.

  • ——, 1985: Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech.,156, 505–531.

  • Steele, K. E., and M. D. Earle, 1991: Directional ocean wave spectra using buoy azimuth, pitch and roll derived from magnetic field components. J. Oceanic Eng.,16, 427–433.

  • ——, C. C. Teng, and D. W. Wang, 1992: Wave direction measurements using pitch-roll buoys. Ocean Eng.,19, 349–375.

  • Walsh, E. J., D. W. Hancock, D. E. Hines, R. N. Swift, and J. F. Scott, 1989: An observation of the directional wave spectrum evolution from shoreline to fully developed. J. Phys. Oceanogr.,19, 670–690.

  • Wyatt, L. R., 1995: The effect of fetch on the directional spectrum of Celtic Sea storm waves. J. Phys. Oceanogr.,25, 1550–1559.

  • Young, I. R., 1994: On the measurement of directional wave spectra. Appl. Ocean Res.,16, 283–294.

  • ——, and G. Ph. Van Vledder, 1993: A review of the central role of nonlinear interactions in wind-wave evolution. Philos. Trans. Roy. Soc. London,A342, 505–524.

  • ——, L. A. Verhagen, and M. L. Banner, 1995: A note on the bimodal directional spreading of fetch-limited wind waves. J. Geophys. Res.,100, 773–778.

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