Effect of Wind Wave Parameter Fluctuation on the Nonlinear Spectrum Evolution

Igor V. Lavrenov State Research Center of the Russian Federation, Arctic and Antarctic Research Institute, St. Petersburg, Russia

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Abstract

The influence of the wind wave parameter fluctuation on the nonlinear spectrum evolution is estimated by solving numerically the kinetic equation taking into account the nonlinear interaction in the wave spectrum. The nonlinear energy transfer is calculated using an original numerical integrating method of the highest accuracy that is described in the paper. The results of numerical simulation shows that wind wave parameter fluctuation produces a significant increase effect of the nonlinear wave spectrum evolution. The present study results in a parameterization, which is made possible taking into account this effect in spectral wind wave models.

Corresponding author address: Dr. Igor Lavrenov, State Scientific Center of the Russian Federation, Arctic and Antarctic Research Institute, 38 Bering Street, St. Petersburg 199397, Russia.

Abstract

The influence of the wind wave parameter fluctuation on the nonlinear spectrum evolution is estimated by solving numerically the kinetic equation taking into account the nonlinear interaction in the wave spectrum. The nonlinear energy transfer is calculated using an original numerical integrating method of the highest accuracy that is described in the paper. The results of numerical simulation shows that wind wave parameter fluctuation produces a significant increase effect of the nonlinear wave spectrum evolution. The present study results in a parameterization, which is made possible taking into account this effect in spectral wind wave models.

Corresponding author address: Dr. Igor Lavrenov, State Scientific Center of the Russian Federation, Arctic and Antarctic Research Institute, 38 Bering Street, St. Petersburg 199397, Russia.

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  • Andreev, B. M., 1988: Variability of spectral characteristics of wave developing. Theoretical Foundations and Calculation Methods of Wind Waves (in Russian), Gidrometeoizdat, 75–81.

  • AS USSR, 1954: Tables with Bessel function means of an imaginary argument (in Russian). AS USSR, 1–258.

  • Babanin, A. V., and Y. P. Soloviev, 1998: Field investigation of transformation of the wind wave frequency spectrum with fetch and stage of development. J. Phys. Oceanogr.,28, 563–576.

  • Bitner-Gregersen, E., and S. Gran, 1983: Local properties of sea waves derived from a wave record. Appl. Ocean Res.,5, 210–214.

  • Davidan, I. N., L. I. Lopatukhin, and V. A. Rozhkov, 1978: Wind Waves as Probability Hydrodynamic Process (in Russian). Gidrometeoizdat, 285 pp.

  • ——, and Coauthors, 1985: Wind Waves in the World Ocean (in Russian). Gidrometeoizdat, 256 pp.

  • Donelan, M. S., and Coauthors, 1985: Directional spectra of wind-generated waves. Philos. Trans. Roy. Soc. London,A315, 509–562.

  • Efimov, V. V., and Y. P. Soloviev, 1984: Low frequency sea level oscillations and wind waves group structure. Izv. Acad. Sci. USSR. Atmos. Oceanic Phys.,20, 985–994.

  • Hasselmann, K., 1962: On the non-linear energy transfer in a gravity wave spectrum. Part I. J. Fluid Mech.,12, 481–500.

  • ——, 1963: On the non-linear energy transfer in a gravity wave spectrum. Part 2. J. Fluid Mech.,15, 273–281.

  • ——, and Coauthors, 1973: Measurements of wind-waves growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutsch. Hydrogr. Inst., 95 pp.

  • Hasselmann, S., and K. Hasselmann, 1981: A symmetrical method of computing the nonlinear transfer in a gravity wave spectrum. J. Hamburger Geophys. Einzelschrifte,52, 138 pp.

  • ——, and ——, 1985a: Computations and parametrizations of the non-linear energy transfer in gravity-wave spectrum. Part I: A new method of the nonlinear energy transfer integral. J. Phys. Oceanogr.,15, 1369–1377.

  • ——, and ——, 1985b: The model EXACT-NL. Ocean Wave Modeling (The SWAMP Group), Plenum Press, 249–251.

  • Komatsu, K., and A. Masuda, 1996: A new scheme of nonlinear energy transfer among wind waves: RIAM method. Algorithm and performance. J. Oceanogr.,52, 509–537.

  • Komen, G. J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and P. A. E. M. Janssen 1994: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532 pp.

  • Krylov, V. I., and E. T. Shulgina, 1966: Manual on a Numerical Integration (in Russian). Nauka, 371 pp.

  • Lavrenov, I. V., 1991a: Non-linear interaction in rips spectrum. Izv. Acad. Sci. USSR. Atmos. Oceanic Phys.,27, 438–447.

  • ——, 1991b: Non-linear evolution of wave spectrum in shallow water area. Izv. Acad. Sci. USSR. Atmos. Oceanic Phys.,27, 1373–1378.

  • ——, 1998: Mathematical Modelling of Wind Waves at Non-Uniform Ocean (in Russian). Gidrometeoizdat, 500 pp.

  • ——, 1999: The effect of quasi-oscillations in wind wave spectrum on its low-frequency non-linear evolution. Izv. Acad. Sci. USSR. Atmos. Oceanic Phys.,35, 339–405.

  • Mase, H., 1989: Goupiness factor and wave height distribution. J. Wat., Port, Coast Ocean Eng.,115, 105–121.

  • Masuda, A., 1980: Nonlinear energy transfer between wind waves. J. Phys. Oceanogr.,10, 2082–2093.

  • Mitsuyasu, H., F. Tasai, T. Suhara, S. Mizuno, M. Ohkusu, T. Honda, and K. Rikiihi, 1980: Observation of the power spectrum of ocean waves using a clover leaf buoy. J. Phys. Oceanogr.,10, 286–296.

  • Monin, A. S., and A. M. Iaglom, 1996: Statistical Hydrodynamics. Part 2. Gidrometeoizdat, 742 pp.

  • Polnikov, V. G., 1989: Calculation of non-linear energy transfer by surface gravitational waves spectrum. Izv. Acad. Sci. USSR. Atmos. Oceanic Phys.,25, 1214–1225.

  • Resio, D., and W. Perrie, 1991: A numerical study of nonlinear energy flux due to wave-wave interaction. Part 1. Methodology and basic results. J. Fluid Mech.,223, 603–629.

  • Sand, S., 1982: Wave grouping described by bundled long waves. Ocean Eng.,9, 567–579.

  • Snyder, R. L., W. C. Thacker, K. Hasselmann, S. Hasselmann, and G. Barzel, 1993: Implementation of an efficient scheme for calculating nonlinear transfer from wave-wave interaction. J. Geophys. Res.,98, 14 507–14 524.

  • Webb, D. J., 1978: Non-linear transfer between sea waves. Deep-Sea Res.,25, 279–298.

  • Yuen, G., and A. Lake, 1987: Nonlinear Dynamics of Gravitational Waves in Deep Water. Mir, 180 pp.

  • Zakharov, V. Ye., 1968: Stability of periodic waves of final amplitude on a deep liquid surface. PMTF,2, 86–94.

  • Zaslavskii, M. M., and V. P. Krasitskii, 1993: About wave fluctuations of wind waves spectrum parameters. J. Okeanologia,33, 21–26.

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