Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-17T15:13:02.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Field observations of orbital velocities and pressure in weakly nonlinear surface gravity waves

Published online by Cambridge University Press:  26 April 2006

T. H. C. Herbers ,
R. L. Lowe  and
R. T. Guza
T. H. C. Herbers
Affiliation:
Center for Coastal Studies. 0209, Scripps Institution of Oceanography, La Jolla. CA 92093, USA
R. L. Lowe
Affiliation:
Center for Coastal Studies. 0209, Scripps Institution of Oceanography, La Jolla. CA 92093, USA
R. T. Guza
Affiliation:
Center for Coastal Studies. 0209, Scripps Institution of Oceanography, La Jolla. CA 92093, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Field measurements of wave orbital velocities and pressure, collected in the lower part of the water column in 7 m depth with a three-component acoustic Doppler current meter and a co-located pressure transducer, are compared to the second-order theory for weakly nonlinear surface gravity waves in arbitrary water depth (Hasselmann 1962). Pressure and velocity spectra and cross-spectra are in excellent agreement with (linear) free wave transfer functions, even at (and higher than) twice the spectral peak frequency where nonlinearities (forced secondary waves) are expected to be important. Theoretical predictions show that although secondary waves sometimes contribute a significant fraction of the energy observed at double swell and sea frequencies, their effect on velocity-pressure transfer functions is small. However, forced waves are more apparent in deviations from Gaussian statistics. Good agreement between observed and predicted third-order statistics shows that Hasselmann's weakly nonlinear theory accurately describes the secondary pressure and orbital velocity (both horizontal and vertical components) field at double swell and sea frequencies, even for moderately large (0(0.1–0.2)) values of the nonlinear perturbation parameter. Only with near-breaking swell and relatively strong nonlinearities (perturbation parameter ≈ 0.22), do the observed third-order statistics diverge significantly from Hasselmann's theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 413 - 435
Copyright
© 1992 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Battjes, J. A. & Heteren J. van 1984 Verification of linear theory for particle velocities in wind waves based on field measurements. Appl. Ocean Res. 6, 187–196.Google Scholar
Bowden, K. F. & White R. A. 1966 Measurements of the orbital velocities of sea waves and their use in determining the directional spectrum. Geophys. J. R. Astron. Soc. 12, 33–54.Google Scholar
Cavaleri L. 1980 Wave measurement using pressure transducer. Oceanol. Acta 3, 339–346.Google Scholar
Cox, C. S. & Jacobs D. C. 1989 Cartesian diver observations of double frequency pressure fluctuations in the upper levels of the ocean Geophys. Res. Lett., 16, 807–810.Google Scholar
Donelan M. A., Hamilton, J. & Hui W. H. 1985 Directional spectra of wind-generated waves Phil. Trans. R. Soc. Lond. A 315, 509–562.Google Scholar
Elgar S., Freilich, M. H. & Guza. R. T. 1990 Model-data comparisons of moments of non-breaking shoaling surface gravity waves. J. Geophys. Res. 95, 16055–16063.Google Scholar
Elgar, S. & Guza R. T. 1985 Observations of bispectra of shoaling surface gravity waves. J. Fluid Mech. 161, 425–448.Google Scholar
Elgar S., Herbers T. H. C., Okihiro M., Oltman-Shay, J. & Guza R. T. 1992 Observations of infragravity waves. J. Geophys. Res. (in press).Google Scholar
Freilich, M. H. & Guza R. T. 1984 Nonlinear effects on shoaling surface gravity waves Phil. Trans. R. Soc. Lond. A 311, 1–41.Google Scholar
Freilich M. H., Guza, R. T. & Elgar S. L. 1990 Observations of nonlinear effects in directional spectra of shoaling gravity waves. J. Geophys. Res. 95, 9645–9656.Google Scholar
Grimshaw R. 1970 The solitary wave in water of variable depth. J. Fluid Mech. 42, 639–656.Google Scholar
Guza R. T., Clifton, M. C. & Rezvani F. 1988 Field intercomparisons of electromagnetic current meters. J. Geophys. Res. 93, 9302–9314.Google Scholar
Guza, R. T. & Thornton E. B. 1980 Local and shoaled comparisons of sea surface elevations, pressures, and velocities. J. Geophys. Res. 85, 1524–1530.Google Scholar
Guza, R. T. & Thornton E. B. 1985 Velocity moments in nearshore. J. Waterways, Port, Coastal Ocean Engng 111, 235–256.Google Scholar
Hasselmann K. 1962 On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech. 12, 481–500.Google Scholar
Hasselmann K, Munk, W. & MacDonald G. 1963 Bispectra of ocean waves. In Times Series Analysis (ed M. Rosenblatt), pp. 125–139. John Wiley.
Herbers, T. H. C. & Guza R. T. 1990 Estimation of directional wave spectra from multicomponent observations. J. Phys. Oceanogr. 20, 1703–1724.Google Scholar
Herbers, T. H. C. & Guza R. T. 1991 Wind-wave nonlinearity observed at the sea floor. Part I Forced wave energy. J. Phys. Oceanogr. 21, 1740–1761.Google Scholar
Herbers, T. H. C. & Guza R. T. 1992 Wind-wave nonlinearity observed at the sea floor. Part II. Wavenumbers and third order statistics. J. Phys. Oceanogr. 22, 489–504.Google Scholar
Herbers T. H. C., Lowe, R. L. & Guza R. T. 1991 Field verification of acoustic Doppler surface gravity wave measurements. J. Geophys. Res. 96, 17023–17035.Google Scholar
Komen G. J. 1980 Nonlinear contributions to the frequency spectrum of wind-generated water waves J. Phys. Oceanogr, 10, 779–790.Google Scholar
Kuik A. J., Vledder, G. Ph. van & Holthuijsen L. H. 1988 A method for the routine analysis of pitch-and-roll buoy data. J. Phys. Oceanogr. 18, 1020–1034.Google Scholar
Laing A. K. 1986 Nonlinear properties of random gravity waves in water of finite depth. J. Phys. Oceanogr. 16, 2013–2030.Google Scholar
Lhermitte R. 1985 Water velocity and turbulence measurements by coherent Doppler sonar. Oceans 85, pp. 1159–1164. IEEE.
Liu P. L.-F., Yoon, S. B. & Kirby J. T. 1985 Nonlinear refraction-diffraction of waves in shallow water. J. Fluid Mech. 153, 185–201.Google Scholar
Longuet-Higgins M. S. 1963 The effect of non-linearities on statistical distributions in the theory of sea waves. J. Fluid Mech. 17, 459–480.Google Scholar
Longuet-Higgins M. S., Cartwright, D. E. & Smith N. D. 1963 Observations of the directional spectrum of sea waves using the motions of a floating buoy. In Ocean Wave Spectra, pp. 111–136. Prentice-Hall.
Longuet-Higgins, M. S. & Stewart R. W. 1962 Radiation stress and mass transport in surface gravity waves with application to ‘surf beats.’ J. Fluid Mech. 13, 481–504.Google Scholar
Okihiro M., Guza, R. T. & Seymour R. J. 1992 Bound infragravity waves J. Geophys. Res. 97, 11453–11469.Google Scholar
Peregrine D. H. 1967 Long waves on a beach. J. Fluid Mech. 27, 815–827.Google Scholar
Phillips O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions. J. Fluid Mech. 9, 193–217.Google Scholar
Simpson J. H. 1969 Observations of the directional characteristics of sea waves. Geophys. J. R. Astron. Soc. 17, 93–120.Google Scholar
Thornton, E. B. & Guza R. T. 1983 Transformation of wave height distribution. J. Geophys. Res. 88, 5925–5938.Google Scholar
Thornton, E. B. & Krapohl R. F. 1974 Water particle velocities measured under ocean waves. J. Geophys. Res. 79, 847–852.Google Scholar
Webb, S. C. & Cox C. S. 1986 Observations and modeling of seafloor microseisms. J. Geophys. Res. 91, 7343–7358.Google Scholar