Physical model tests are often conducted during the design process of coastal structures. The wave climate in such tests often includes short-crested nonlinear waves. The structural response is related to the incident waves measured in front of the structure. Existing methods for separation of incident and reflected short-crested waves are based on linear wave theory. For analysis of nonlinear waves, the existing methods are limited to separation of nonlinear long-crested waves. For short-crested waves, the only options so far have been to use estimates without the structure in place. The present paper thus presents a novel method for directional analysis of nonlinear short-crested waves: Non-Linear Single-summation Oblique Reflection Separation (NL-SORS). The method is validated on numerical model data, as for such data, the target is well defined as simulations may be performed with fully absorbing boundaries. Second- and third-order wave theory is used to demonstrate that small errors on the celerity of nonlinear components in the mathematical model of the surface elevation can be obtained if a double narrow-banded directional spectrum is assumed, ie the primary frequency and the directional spreading function must be narrow banded. As the increasing nonlinearity of the waves often arise from waves shoaling on a sloping foreshore, the directional spreading of the waves will decrease due to refraction, and a broad directional spreading function will thus not be experienced in highly nonlinear conditions. The new NL-SORS method is shown to successfully decompose nonlinear short-crested wave fields and estimate the directional spectrum thereof.
Physical model tests are often conducted during the design process of coastal structures. The wave climate in such tests often includes short-crested nonlinear waves. The structural response is related to the incident waves measured in front of the structure. Existing methods for separation of incident and reflected short-crested waves are based on linear wave theory. For analysis of nonlinear waves, the existing methods are limited to separation of nonlinear long-crested waves. For short-crested waves, the only options so far have been to use estimates without the structure in place. The present paper thus presents a novel method for directional analysis of nonlinear short-crested waves: Non-Linear Single-summation Oblique Reflection Separation (NL-SORS). The method is validated on numerical model data, as for such data, the target is well defined as simulations may be performed with fully absorbing boundaries. Second- and third-order wave theory is used to demonstrate that small errors on the celerity of nonlinear components in the mathematical model of the surface elevation can be obtained if a double narrow-banded directional spectrum is assumed, ie the primary frequency and the directional spreading function must be narrow banded. As the increasing nonlinearity of the waves often arise from waves shoaling on a sloping foreshore, the directional spreading of the waves will decrease due to refraction, and a broad directional spreading function will thus not be experienced in highly nonlinear conditions. The new NL-SORS method is shown to successfully decompose nonlinear short-crested wave fields and estimate the directional spectrum thereof.
The influence of directional spreading of waves is significant for wave-induced loads, wave breaking and nonlinearity of the waves. For physical model testing performed at test facilities such as the Ocean and Coastal Engineering Laboratory at Aalborg University, it is crucial to validate if the test conditions match the target sea states by measurement and analysis of the generated directional wave field. Most of the existing methods assume a double summation sea state to be present which is valid in the prototype. However, waves in the laboratory are usually generated by single summation. The current paper presents a method to analyze short-crested waves generated by the single summation method. Compared to similar methods oblique reflections are considered instead of only in-line reflections. The results show that the method successfully decomposes the incident and reflected wave fields in the time domain. Thus, for example the incident wave height distribution may be obtained. The sensitivity of the new method to additional reflective directions, noise, calibration errors and positional errors of the wave gauges was found small.
In hydraulic model tests, it is common practice to relate the response of the tested structure to the incident wave parameters at the toe. Estimation of the incident wave parameters at the toe is thus an essential part of the analysis of hydraulic model testing. In many cases, the design conditions at the toe are given by waves that are highly nonlinear or even depth limited. Modelling such conditions requires reproducing the prototype foreshore slope in the model. The present paper provide guidelines on the accuracy of a nonlinear reflection separation algorithm when applied to nonlinear waves over sloping foreshores. A simple methodology has been established to estimate the expected errors on the incident wave parameters.