Modeling of Propagation and Transformation of Transient Nonlinear Waves on A Current

A novel theoretical approach is applied to predict the propagation and transformation of transient nonlinear waves on a current. The problem was solved by applying an eigenfunction expansion method and the derived semi-analytical solution was employed to study the transformation of wave profile and the evolution of wave spectrum arising from the nonlinear interactions of wave components in a wave train which may lead to the formation of very large waves. The results show that the propagation of wave trains is significantly affected by a current. A relatively small current may substantially affect wave train components and the wave train shape. This is observed for both opposing and following current. The results demonstrate that the application of the nonlinear model has a substantial effect on the shape of a wave spectrum. A train of originally linear and very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short distance from an initial position. The discrepancies between the wave trains predicted by applying the linear and nonlinear models increase with the increasing wavelength and become significant in shallow water even for waves with low steepness. Laboratory experiments were conducted in a wave flume to verify theoretical results. The free-surface elevations recorded by a system of wave gauges are compared with the results provided by the nonlinear model. Additional verification was achieved by applying a Fourier analysis and comparing wave amplitude spectra obtained from theoretical results with experimental data. A reasonable agreement between theoretical results and experimental data is observed for both amplitudes and phases. The model predicts fairly well multi-peak spectra, including wave spectra with significant nonlinear wave components.

Modelling of wave transmission through a pneumatic breakwater

A theoretical approach is derived to study interaction of linear water waves with an air bubble curtain used as a pneumatic breakwater. Modelling of wave transmission through an aerial barrier is a complex task due to a need to cover processes associated with wave-current interaction, effects of two-phase flows, wave damping, etc.. An initial boundary-value problem is solved by applying an efficient eigenfunction expansion method and a time-stepping procedure. The derived semi-analytical solution is used to study the effect of basic parameters of the model on wave dissipative properties of the pneumatic breakwater. Results show that wave damping by the breakwater is mainly affected by an air flow rate. The increased air discharge results in higher velocities of ascending bubbles and increases aerial barrier width. This leads to a substantial reduction of transmitted wave heights, especially for waves of intermediate length and short waves. In order to verify the applicability of the presented theoretical approach, laboratory experiments are conducted in a wave flume for different wave regimes and pneumatic breakwater characteristics. The analysis of a wave trans- mission coefficient calculated numerically and measured in the laboratory confirms that the derived model can be used for a certain range of wave conditions.