Synthesizing Nonlinear Transient Gravity Waves in Random Seas

The oceans cover more than two thirds of the earth’s surface and present a unique set of environmental conditions which govern the design, installation, and operation of marine systems. In general, structural loads are dominated by the wave field. Depending on the operating site, the effects of wind, currents, earthquakes or ice may be of great importance as well. The profound knowledge of the hydrodynamics of gravity waves and their complex interaction with marine systems is a necessary prerequisite for safe and efficient system operation. Attention is increasingly being paid to extreme environmental conditions with unexpected large waves developing in the random wave field. In this dissertation, a new procedure is presented for computer-aided synthesizing of nonlinear transient gravity waves in random seas. The aim of the study is to provide a multi-purpose analysis and development tool for performing detailed experimental and numerical investigations of extreme wave events. Large deterministic single waves and wave groups are synthesized into random seas with the two-dimensional nonlinear free surface flow problem described by potential theory. This is achieved by a two-stage procedure applying modern optimization algorithms used in nonlinear programming. To obtain a first approximation of the solution, the free surface boundary conditions of the potential flow problem are linearized. This allows a description of the wave train as the superposition of independent harmonic component waves. In particular, the temporal and spatial evolution can be calculated efficiently in the frequency domain by introducing the fast Fourier transformation. For a given Fourier spectrum, the desired characteristics of the linear wave train are generated by applying sequential quadratic programming which modifies an initially random phase spectrum. A computer program is developed to simulate the nonlinear wave evolution in the numerical wave tank. The simulation procedure is based on the mixed Eulerian-Lagrangian formulation of the nonlinear initial boundary value problem. The Laplace equation is solved for Neumann and Dirichlet

[1]  T. Rowan Functional stability analysis of numerical algorithms , 1990 .

[2]  M. J. Box A Comparison of Several Current Optimization Methods, and the use of Transformations in Constrained Problems , 1966, Comput. J..

[3]  G. X. Wu,et al.  Time stepping solutions of the two-dimensional nonlinear wave radiation problem , 1995 .

[4]  Michael Selwyn Longuet-Higgins,et al.  The deformation of steep surface waves on water - I. A numerical method of computation , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Samuel D. Conte,et al.  Elementary Numerical Analysis , 1980 .

[6]  Philip Jonathan,et al.  TIME DOMAIN SIMULATION OF JACK-UP DYNAMICS WITH THE EXTREMES OF A GAUSSIAN PROCESS , 1997 .

[7]  Günther Clauss,et al.  Gaussian wave packets — a new approach to seakeeping testsof ocean structures* , 1986 .

[9]  Shih-Ping Han,et al.  Superlinearly convergent variable metric algorithms for general nonlinear programming problems , 1976, Math. Program..

[10]  A. Grossmann,et al.  Cycle-octave and related transforms in seismic signal analysis , 1984 .

[11]  Günter F. Clauss,et al.  Simulation of Design Storm Wave Conditions With Tailored Wave Groups , 1997 .

[12]  R. Fletcher Practical Methods of Optimization , 1988 .

[13]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[14]  Günther Clauss,et al.  A NEW APPROACH TO SEAKEEPING TESTS OF SELF-PROPELLED MODELS IN OBLIQUE WAVES WITH TRANSIENT WAVE PACKETS , 1995 .

[15]  L. A. G. Dresel,et al.  Elementary Numerical Analysis , 1966 .

[16]  R Cointe,et al.  NONLINEAR AND LINEAR MOTIONS OF A RECTANGULAR BARGE IN A PERFECT FLUID , 1991 .

[17]  W. Rosenthal,et al.  Similarity of the wind wave spectrum in finite depth water: 1. Spectral form , 1985 .

[18]  O. Andersen,et al.  Freak Waves: Rare Realizations of a Typical Population Or Typical Realizations of a Rare Population? , 2000 .

[19]  Dick K. P. Yue,et al.  Numerical simulations of nonlinear axisymmetric flows with a free surface , 1987, Journal of Fluid Mechanics.

[20]  R. Eatock Taylor,et al.  Finite element analysis of two-dimensional non-linear transient water waves , 1994 .

[21]  M. C. Davis,et al.  Testing Ship models in Transient Waves , 1966 .

[22]  T. Baldock,et al.  NUMERICAL CALCULATIONS OF LARGE TRANSIENT WATER WAVES , 1994 .

[23]  Shih-Ping Han,et al.  Penalty Lagrangian Methods Via a Quasi-Newton Approach , 1979, Math. Oper. Res..

[24]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[25]  Y. Meyer Wavelets and Operators , 1993 .

[26]  Michael Isaacson,et al.  On the Selection of Design Wave Conditions , 2000 .

[27]  David L. Kriebel,et al.  Simulation of Extreme Waves In a Background Random Sea , 2000 .

[28]  S. Mallat Multiresolution approximations and wavelet orthonormal bases of L^2(R) , 1989 .

[29]  I. Daubechies Orthonormal bases of compactly supported wavelets , 1988 .

[30]  H. L. Resnikoff,et al.  Wavelet analysis: the scalable structure of information , 1998 .

[31]  Günther Clauss,et al.  Optimization of Transient Design Waves In Random Sea , 2000 .

[32]  Paul M. Hagemeijer,et al.  A New Model For The Kinematics Of Large Ocean Waves-Application As a Design Wave , 1991 .

[33]  Rodney J. Sobey,et al.  Phase Spectrum of Surface Gravity Waves , 1987 .

[34]  C. Burrus,et al.  Introduction to Wavelets and Wavelet Transforms: A Primer , 1997 .

[35]  Katsuji Tanizawa Long Time Fully Nonlinear Simulation of Floating Body Motions with Artificial Damping Zone , 1996 .

[36]  J. Crease The Dynamics of the Upper Ocean , 1967 .

[37]  J Wolfram,et al.  A NEW APPROACH TO ESTIMATING EXTREME ENVIRONMENTAL LOADING USING JOINT PROBABILITIES , 1994 .

[38]  Michael Selwyn Longuet-Higgins,et al.  The deformation of steep surface waves on water ll. Growth of normal-mode instabilities , 1978, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[39]  T. Barnett,et al.  Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP) , 1973 .

[40]  Günther Clauss,et al.  Numerical simulation of nonlinear transient waves and its validation by laboratory data , 1999 .

[41]  Subrata K. Chakrabarti,et al.  Further verification of Gaussian wave packets , 1988 .

[42]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[43]  I. Daubechies Orthonormal bases of compactly supported wavelets II: variations on a theme , 1993 .

[44]  Peter Deuflhard,et al.  Numerische Mathematik. I , 2002 .

[45]  P H Taylor ON THE KINEMATICS OF LARGE OCEAN WAVES , 1992 .

[46]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[47]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[48]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[49]  Alan R. Jones,et al.  Fast Fourier Transform , 1970, SIGP.

[50]  C. T. Stansberg,et al.  Extreme Waves in laboratory Generated Irregular Wave Trains , 1990 .

[51]  O. Phillips The dynamics of the upper ocean , 1966 .

[52]  Andreas Rieder,et al.  Wavelets - Theorie und Anwendungen , 1994, Teubner Studienbücher Mathematik.

[53]  J. Francis Tides and Waves , 1969, Nature.

[54]  R. J. Sobey,et al.  Hurricane Wind Waves—A Discrete Spectral Model , 1986 .