EFFECTS OF TRANSIENT LONG WAVES ON NONLINEAR PROCESSES IN RANDOM WAVES
Abstract
Much effort has been devoted to the numerical modeling of nonlinear wave propagation in shallow water during the last several years. Boussinesq equations are important because they balance the effect of nonlinear terms and dispersion relation and make it possible to find solutions including waves of permanent form. However, Boussinesq equations are not valid in intermediate and deep water depth. There are generally two methods to extend the limitation. One approach is to extend the Boussinesq equation by improving the linear properties. The other one is the nonlinear mild-slope equation, which has the fully dispersion relation and shoaling property. Kaihatu and Kirby’s mild-slope nonlinear wave transformation model is a parabolic model in frequency domain. The time series measurement should be treated with Fast Fourier Transformation before simulation. The model is built for random wave fields. In Kaihatu and Kirby (1995), the model has been proved good simulation performance on the basis of the data of random wave field from Mase and Kirby (1992) experiments. However, if the model is applied in field work, it can be an interesting question whether the transient long wave will affect the model simulation. The NEES Tsunami and Swell experiments conducted at Oregon State University produced solitary waves in random wave fields and recorded the wave heights at different gauges. Hence, this thesis makes use of Kaihatu and Kirby (1995) model to simulate this soliton plus random waves data to investigate the effect of transient long waves on the simulation of random waves. The performance of the model will be evaluated when handling the soliton plus random wave field. A MATLAB code of the model is built in reference to the original code in Fortran fixed format.
The spectra of the data and model results are compared to evaluate the performance of model qualitatively. The frequency scale is divided into three areas, infragravity area (0 ≤ f ≤ fpeak 2 ), swell area ( fpeak 2 ≤ f ≤ 3fpeak 2 ) and sea area ( 3fpeak 2 ≤ f), and the energy in each area is calculated on the basis of both experiment data and model results for comparison. The root-mean-square of the wave height is calculated to evaluate the energy prediction of the model. The skewness and the asymmetry are calculated to evaluate the performance of the model in prediction of the wave shape change during the propagation. Generally, the addition of the soliton has a significant influence on the wave field and the performance of the model. The larger the amplitude of the soliton, the larger the effect of the soliton on the nonlinear processes in random waves, and with that the poorer the performance of the model in prediction of spectra.
Citation
Yang, Xin (2019). EFFECTS OF TRANSIENT LONG WAVES ON NONLINEAR PROCESSES IN RANDOM WAVES. Master's thesis, Texas A&M University. Available electronically from https : / /hdl .handle .net /1969 .1 /186384.