Directional Analysis of Nonlinear Waves: Nonlinear Effects in Relation to Estimation of Directional Parameters

Vixø, Louise ; Iversen, Sarah Krogh

4. term

Structural and Civil Engineering, Master

2022

2022-06-08

701 pages

The purpose of this master thesis is to study if nonlinearity will have an influence on the directional wave analysis, when the analysis is based on linear wave theory. Two methods are considered; a simple method containing a geometrical solution of the wave propagation direction using the phase difference of the waves, in which only long-crested waves are possible to analyse. A statistical method with the directional parameters including the mean wave direction and the spreading when analysing the spectral density using the method containing cross-spectral analysis and the fitting method of maximum likelihood estimation of directional spectrum in standard form, which is determined as the Mitsuyasu-type directional spreading function. This analysis manages both long-crested and short-crested waves. The analyses are performed for different cases placed in different water depths related to the Diagram of Le Mehaute, which contain different amount of second order energy when including this, and the cases similarly have different amount of amplitude dispersion. Furthermore, different generation methods produce different accuracy of the directional parameters. In this master thesis both long-crested and short-crested waves are considered. From the analyses of the waves fields, an impact of the nonlinearity is discovered for the cases including most second order energy or containing a faster wave celerity than predicted by linear wave theory. The directional analyses of the wave fields show a correlation between the amount of second order energy and the errors on the estimated directions. For further investigation of the sensibility of the directional analysis of the waves, other effects are added including noise, calibration error and missing gauges. These analyses show random errors related when including noise, more organised errors related to calibration errors depending on the affected gauge, even larger than if a gauge is missing. This is also placed in context with both the second order waves and the waves with amplitude dispersion. The worst error is discovered for Method 1 including second order energy. Overall, Method 1 has a high accuracy from only three gauges and seems to be a fine estimation of long-crested waves, but is quiet sensible to second order waves, especially, for cases which do not fulfill the requirement of linear theory or Stokes second order wave theory. This method is however not implemented in practice. Method 2 seems more robust but must contain more wave gauges measurements. When using Method 2, all results show an accuracy within ±5°, except for cases for which the combination of a relative high wave steepness, shallow water depth and more than 12% of second order energy compared to first order energy, which results in an inaccurate estimation of the directional parameters from a directional analysis.

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