Interpretations and observations of ocean wave spectra |
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| Authors: | Harald Elias Krogstad Karsten Trulsen |
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| Institution: | (1) Dept. of Mathematical Sciences, NTNU, 7491 Trondheim, Norway;(2) Dept. of Mathematics, University of Oslo, 0316 Oslo, Norway |
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| Abstract: | The paper starts with a discussion of the linear stochastic theory of ocean waves and its various nonlinear extensions. The directional spectrum, with its unique dispersion relation connecting frequency (ω) and wavenumber (k), is no longer valid for nonlinear waves, and examples of $\left( \mathbf{k},\omega\right) The paper starts with a discussion of the linear stochastic theory of ocean waves and its various nonlinear extensions. The
directional spectrum, with its unique dispersion relation connecting frequency (ω) and wavenumber (k), is no longer valid for nonlinear waves, and examples of ( k,w)\left( \mathbf{k},\omega\right) -spectra based on analytical expressions and computer simulations of nonlinear waves are presented. Simulations of the dynamic
nonlinear evolution of unidirectional free waves using the nonlinear Schr?dinger equation and its generalizations show that
components above the spectral peak have larger phase and group velocities than anticipated by linear theory. Moreover, the
spectrum does not maintain a thin well-defined dispersion surface, but rather develops into a continuous distribution in ( k,w)\left( \mathbf{k,}\omega\right) -space. The majority of existing measurement systems rely on linear theory for the interpretation of their data, and no measurement
systems are currently able to measure the full spectrum in the open ocean with high accuracy. Nevertheless, there exist a
few low-resolution systems where data may be interpreted within a minimal assumption of a non-restricted ( k,w)\left( \mathbf{k,}\omega\right) -spectrum. The theory is reviewed, and analyses based on conventional spectral analysis as well as a directional wavelet analysis
are carried out on data from a compact laser array at the Ekofisk field in the North Sea. The investigation confirms the strong
impact of the second order spectrum below the spectral peak, but is non-conclusive about the off-set in the support of the
first order spectrum seen in the dynamical simulations. |
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