Development of frequency-dependent ocean wave directional distributions

Abstract The paper discusses the development of a frequency dependent directional spread from an initial condition of frequency-independence. The study applies basin directional measurements from the Maritime Research Institute Netherlands (MARIN), simulated data from a nonlinear wave equation, and field measurements from the Ekofisk field. The basin experiments and numerical simulations are initialized with a JONSWAP spectrum with frequency-independent directional distributions. In both cases we observe the development of a strong frequency-dependence of the directional spread. The numerical simulations suggest that static nonlinear contributions to the surface elevation partially explain the behavior below the spectral peak in accordance with [1] . There are also dynamic nonlinear contributions on both sides of the spectral peak.

[1]  Kanti V. Mardia,et al.  Statistics of Directional Data , 1972 .

[2]  Yoshimi Goda,et al.  Random Seas and Design of Maritime Structures , 1985 .

[3]  Peter Sutherland,et al.  Field measurements and scaling of ocean surface wave‐breaking statistics , 2013 .

[4]  Mark A. Donelan,et al.  Wavelet And Local Directional Analysis of Ocean Waves , 2006 .

[5]  S. Pawka.  Island shadows in wave directional spectra , 1983 .

[6]  Paul A. Hwang,et al.  Evolution of the Bimodal Directional Distribution of Ocean Waves , 2001 .

[7]  H. Krogstad.  Second Order Wave Spectra and Heave/Slope Wave Measurements , 2002 .

[8]  K. Dysthe,et al.  Note on a modification to the nonlinear Schrödinger equation for application to deep water waves , 1979, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[9]  Harald E. Krogstad.  Maximum likelihood estimation of ocean wave spectra from general arrays of wave gauges , 1988 .

[10]  Fukuzo Tasai,et al.  Observations of the Directional Spectrum of Ocean WavesUsing a Cloverleaf Buoy , 1975 .

[11]  Jaak Monbaliu,et al.  Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations , 2010, Journal of Fluid Mechanics.

[12]  A. Benetazzo.  Measurements of short water waves using stereo matched image sequences , 2006 .

[13]  Karsten Trulsen.  Weakly Nonlinear Sea Surface Waves - Freak Waves and Deterministic Forecasting , 2007, Geometric Modelling, Numerical Simulation, and Optimization.

[14]  Kevin Ewans,et al.  Observations of the Directional Spectrum of Fetch-Limited Waves , 1998 .

[15]  Karsten Trulsen,et al.  Weakly nonlinear and stochastic properties of ocean wave fields. Application to an extreme wave event , 2006 .

[16]  K. Dysthe,et al.  Frequency downshift in three-dimensional wave trains in a deep basin , 1997, Journal of Fluid Mechanics.

[17]  Stephen F. Barstow,et al.  Directional Distributions In Ocean Wave Spectra , 1999 .

[18]  Ola Haug,et al.  Directional Distributions in Wave Spectra , 1998 .

[19]  Karsten Trulsen,et al.  Spatial Evolution of Water Surface Waves: Numerical Simulation and Experiment of Bichromatic Waves , 2001 .

[20]  Kevin Ewans,et al.  Worldwide Measurements of Directional Wave Spreading , 1998 .

[21]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[22]  J. A. Ewing,et al.  Directional Spectra of Seas near Full Development , 1987 .

[23]  Janou Hennig,et al.  New Methods and Insights in Advanced and Realistic Basin Wave Modelling , 2013 .

[24]  Karsten Trulsen,et al.  Interpretations and observations of ocean wave spectra , 2010 .

[25]  Chiang C. Mei,et al.  A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation , 1985, Journal of Fluid Mechanics.

[26]  I. G. Jonsson,et al.  Fourth order evolution equations and stability analysis for Stokes waves on arbitrary water depth , 1986 .

[27]  M. Ochi.  Ocean Waves: The Stochastic Approach , 1998 .

[28]  J. Ewing,et al.  Directional Wave Spectra Observed during JONSWAP 1973 , 1980 .

[29]  Jaak Monbaliu,et al.  Development of a bimodal structure in ocean wave spectra , 2010 .

[30]  P. Naaijen,et al.  Real Time Estimation of Ship Motions in Short Crested Seas , 2009 .

[31]  M. Banner,et al.  A note on the bimodal directional spreading of fetch‐limited wind waves , 1995 .

[32]  Martin C. Miller,et al.  High-Resolution Directional Wave Spectra from Horizontally Mounted Acoustic Doppler Current Meters , 1988 .

[33]  C. Mei,et al.  Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study , 1987 .

[34]  M. Donelan,et al.  Directional spectra of wind-generated ocean waves , 1985, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[35]  Harald E. Krogstad,et al.  Maximum Entropy Estimation of the Directional Distribution in Ocean Wave Spectra , 1986 .

[36]  A. Yezzi,et al.  Offshore stereo measurements of gravity waves , 2012 .

[37]  Tommy D. Dickey,et al.  An overview of sea state conditions and air-sea fluxes during RaDyO , 2012 .

[38]  Karsten Trulsen,et al.  Evolution of a narrow-band spectrum of random surface gravity waves , 2003, Journal of Fluid Mechanics.

[39]  N. Hashimoto,et al.  ESTIMATION OF DIRECTIONAL SPECTRA FROM THE MAXIMUM ENTROPY PRINCIPLE , 1986 .