Decomposition of incident and reflected higher harmonic waves using four wave gauges

This study proposes a new technique to separate incident and reflected higher harmonic waves using four or more spatially separated probes. Both the free and locked modes in the higher harmonics of the regular waves can be isolated. The complex waves are decomposed into individual frequency components using the Fourier transform. The least squares method is applied to minimize the error caused by possible signal noise and to obtain the equations for solving the unknown parameters related to the wave amplitudes. Probe spacing condition for preventing singularity in the calculation is provided. The accuracy of this method is verified by applying it to resolve artificial waves with arbitrarily selected amplitudes. The sensitivity of this method to the noise inevitably associated with the experiments is also tested. The free surface elevation data collected from probes located upstream and downstream of a submerged breakwater in a numerical wave tank are analyzed to demonstrate the applicability of this method. The results are compared with those obtained using the methods of Goda and Suzuki [Goda, Y., Suzuki, Y., 1976. Estimation of incident and reflected waves in random wave experiments. Proc. 15th Costal Eng. Conf., ASCE, pp. 828-845] and Mansard and Funke [Mansard, E.P.D., Funke, E.R., 1980. The measurement of incident and reflected spectra using a least squares method. Proc. 17th Costal Eng. Conf., ASCE, pp. 154-172]. The comparison indicated that this method gives exactly the same first harmonic incident and reflected wave amplitudes as the other two methods. The full modes in the higher harmonics can be determined using this method, while the higher harmonics are presumed to be free waves in the other two methods.