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.
The present paper deals with separation of long-crested regular waves into incident and reflected components. Such methods have been available for several decades for linear waves, but have recently been extended to cover nonlinear waves over horizontal foreshores. The overall goal of the present paper is to extend the separation method for nonlinear regular waves to also cover sloping foreshores. This requires the combination of the existing method with a nonlinear shoaling model. A nonlinear shoaling model was very recently found valid for the shoaling of the primary and bound components in regular waves when the slope angle is positive and mild. In the present paper this shoaling model is utilized and assumed valid also for the de-shoaling of the reflected waves, ie on a negative mild slope angle. However, if the reflected waves are nonlinear the de-shoaling process is much more complicated and will for example cause the release of free waves. Interactions among those free reflected wave components may cause nonlinear interactions not included in the mathematical model. For that reason, the applicability range is limited to mildly nonlinear reflected waves. Using numerical model data with various foreshore slopes, wave nonlinearities and reflection coefficients the reliability of the developed model is examined in detail.