The study presented is deterministic and considers both wave directionality and the nonlinearity. In several respects, this study is innovative and unique. First, based on as few as three independent measurements recorded at fixed-points, the DHWM is able to decompose a directional irregular wave field into free-wave components without the assumptions of random initial phases of free-wave components and a prior directional spreading function. Secondly, the nonlinear effects are decoupled from the measured wave characteristics by using two different perturbation approaches: a conventional and a phrase modulation methods. It was found that truncated solutions for bound-wave components given by a conventional perturbation method may not converge if the wavelengths of two interacting wave components are quite different while the convergent solutions can be derived using the phase modulation method (Zhang et al. 1993). For a wave field of energy distributed in a relatively broad frequency band, use of both conventional and phase modulation methods to describe the wave-wave interaction can provide convergent solutions for unidirectional irregular waves (Zhang et al. 1996a), which is also numerically demonstrated for multi-directional waves. In our earlier study, only conventional method was used for the solution of bound-wave components, which limits the application to a wave field of relatively narrow-band spectrum (Prisling et al. 1997). Thirdly, this study renders deterministic predictions of wave characteristics of a measured directional field. It is demonstrated that a variety of wave measurements (pressure transducers, surface piercing wave gauges and velocimetry) can be used as input for the wave decomposition. Since all wave characteristics can be straightforwardly extended to allow for other measurements, such as wave slopes and accelerations as well. Finally, because of above capabilities, extensive and rigorous examinations about the validity and accuracy of this model and numerical scheme can be made through the comparisons in the time-domain between the predicted wave characteristics and the corresponding laboratory and field measurements.
In addition to the neglect of viscous and wind effects, and wave breaking due to the use of potential theory, the proposed directional hybrid wave model (DHWM) developed in this study is truncated at the second order in wave steepness. The ‘weak’ or resonant wave interactions in deep or intermediate-depth water are of third order and hence are not considered. The weak wave interactions can become substantial after hundreds of dominant wave periods (Su & Green 1981; Phillips 1979). Hence, for accurate prediction, the computation of wave characteristics based on this study should be limited within a short distance fro the measurements (typically a few wavelengths of the dominant wave components) and the proposed model is not valid for the study of long-term or long-distance wave evolution, such as wave energy transfer among wave components with different frequencies (Hasselman 1962).
Related Publications: Zhang, J. and Prislin, I., “Decomposition and Prediction of Short-Crested Irregular Waves,” Proceedings 2nd International Conference on Hydrodynamics, Vol. 1, pp. 495-500, 1996.
Prislin, I., Zhang, J. and Johnson, P., “Deterministic Decomposition of Irregular Short-Crested Surface Gravity Waves,” Proceedings 6th ISOPE Conference, Vol. 3, pp. 57-64, 1996.
Prislin, I., Zhang, J. and Seymour, R.J., “Deterministic Decomposition of Short Crested Irregular Gravity Waves in Deep Water,” J. Geophys. Research, 1997, Vol. 102, C6, pp. 12.677-12.688.
Zhang, J., “Nonlinear Wave Interactions in Irregular Ocean Waves and their Applications,” Proc. of International Workshop on Modeling of Ocean Environments in Wave and current Basin, Taejon, Korea, February 3-4, 1998, pp. 40-61.
Zhang, J., Yang, J. and Wen, J., “Hybrid Wave Models and their Applications,” Ocean Wave Kinematics, Dynamics and Loads on Structures, Proc. 1998 International OTRC Symposium, April 30-May 1, 1998, Houston, TX, pp. 25-33.
Zhang, J., Yang, J., Prislin, I., Wen, J., and Hong, K. (1999) “Deterministic Wave Model for Short-Crested Ocean Waves, Part I. Theory and Numerical Scheme,” Applied Ocean Research, Vol.21, 167-188.
Zhang, J., Prislin, I., Yang, J., and Wen, J. (1999) “Deterministic Wave Model for short-Crested Ocean Waves, Part II. Comparison with Laboratory and Field Measurements,” Applied Ocean Research, Vol. 189-206.