Comments on ‘numerical simulation of a random sea: a common error and its effect upon wave group statistics by M.J. Tucker, T.G. Challenor and D.J.T. Carter’

L E T T E R S TO T H E E D I T O R Comments on 'Numerical simulation of a random sea: a c o m m o n error and its effect upon wave group statistics by M.J. Tucker, T . G . Challenor and D . J . T . Carter' The above paper was published in Volume 6, No. 2 of Applied Ocean Research and, while there are some interestLug comments on numerical simulation and wave groups, significant references on this topic have been omitted. Seven years ago, Goda ~ published a study on the variability of statistics of surface elevations from simulated wave profiles and field data. The unsatisfactory performance of the deterministic amplitude wave simulation models was pointed out and the random characteristics of the amplitudes noted. From a general numerica! directional simulator a one-dimensional model was developed in which it was shown that the variables Cn/(S(fn) Afn) 1/2 and c~/(S(fn) Afn) had a chi-squared distribution with two degrees of freedom (2 DOF) respectively. In his most recent publications, Goda 1-3 used this directional simulator (a onedimensional nondeterministic amplitude model) with a A f n in which S(fn) Afn was constant. Rye 4 has published an extensive study on wave groups in which numerical random sea simulation techniques were analysed. Rye 4 examined the use of deterministic and nondeterministic amplitude models in order to reproduce the wave groupiness properly. Several groupiness parameters, spectral shapes, peak frequencies, numbers of wave components, etc. were employed in his numerical experiments. The first digital simulation method shown by the authors was used by Rye 4 who had cited S~flrenssen's s report. Borgman, 6'7 analysing the statistical structure of the FFT coefficients computed from random sequences, showed the satisfactory agreement between the measured distributions and the predicted chi-squared probability law. Even though the sea elevations recorded differed from the normality, the distribitions of the finite Fourier transform coefficients were approximately independent and normally distributed (×2 distribution with 2 DOF for spectral line estimates). Tuah and Hudspeth s show linear and nonlinear simulators using a FFT algorithm on Rice's two models for Gaussian signals. The wave superposition method with deterministic amplitudes was referred to as a deterministic spectral amplitude (DSA) model, while the other one was called a nondeterministic spectral amplitude (NSA) model. They developed a technique for initialising complex Fourier coefficients in the frequency domain for generating linear and nonlinear DSA and NSA simulations (via FFT). Medina and Diez 9 have shown an efficient algorithm for computing linear NSA simulations and have noted their relationship to directional simulations. In our opinion, the authors base the main part of their discussion on the comparisons of the three simulation techniques represented in Figs. 1-3, called FFT, Goda and Goda and Rayleigh. Without a doubt, the FFT-NSA is the best of the three, but the authors do not prove 'the common error' with this comparison because Goda, ~-a has not used his old simulator since 1977. 0141-1187/85/020113-02 $2.00 © 1985 CML Publications

In our opinion, the conclusions are far too general to be accepted without a detailed study of the simulation techniques commonly employed. The rec~nt publications of both Goda and Rye have to be considered at the very least, because the technical note in its present form gives a distorted idea of their work, and this, in turn, permits the authors to use the words 'common error', when these 'errors' have already been surpassed (see references).

REFERENCES 1 Goda, Y. Numerical experiments on statistical variability of ocean waves, Report of the Port and Harbour Res. Inst. 1977, 16 (2), 3 2 Goda, Y. Wave simulation for the examination of directional resolution, Proc. Directional Wave Spectra Applications, Berkeley, September 1981, 387 3 Goda, Y. Analysis of wave grouping and spectra of long-travelled swell, Report of the Port and Harbour Res. Inst. 1983, 22 (1), 7 4 Rye, H. Ocean wave groups, Ph.D. thesis, University of Trondheim, Norway, Nov. 1981 5 S~renssen, A. Artificial irregular waves in the Norwegian Hydrodynamic Laboratory, NHL-report, div. VHL, April 1979 6. Borgman, L. E. The statistical anatomy of ocean wave spectra, Research Report 73-1, Univ. of Wyoming, August 1973 7 Borgman, L. E. Statistical properties of fast Fourier transform coefficients computed from real-valued, covariance-stationary, periodic random sequences, Research Paper No. 23, Univ. of Wyoming, September 1973 8 Tuah, H. and Hudspeth, R. T. Comparisons of numerical random sea simulations, 3". Waterway, Port, Coastal and Ocean Division 1982, 108 (4), 569 9 Medina, J. R. and Diez, J. J. Comparisons of numerical random sea simulations (discussion), J. Waterway, Port, Coastal and Ocean Engineering 1984, 110 (1), 114 June, 1984 J o s e p R. Medina and Jos6 Aguilar E.T.S.L Caminos, Univ. Politdcnica de Valencia, Valencia, Spain

Reply to the Comments by J. R. Medina and J. Aguilar o n 'Numerical simulation o f a random sea: a c o m m o n error and its effect u p o n wave group statistics'

We did not intend to imply by the phrase 'a common error' in our paper that the mistake was universal, only that it was widespread. If this was not evident, we are grateful to Medina and Aguilar for enabling us to clarify our position. Many of the papers referred to by Medina and Aguilar are in the 'grey literature' and are not readily available. We have, in fact, copies of most of them, but prefer not to quote such papers unless we consider it to be essential. In most cases, the authors have published later papers in the open literature on the same or closely allied subjects.

Applied Ocean Research, 1985, Vol. 7, No. 2

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