Search

Abstract An efficient semi-analytical solution to the problem of nonlinear water waves propagating at a constant depth is derived using parallel computing techniques. The approach is based on the assumptions of an irrotational flow of an inviscid and incompressible fluid. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series satisfying a formulated initial boundary-value problem by a proper selection of time-dependent coefficients. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher-order time-stepping procedure to provide an efficient spectral collocation method of computation of wave-induced free-surface flows. The application of the Fourier transform qualifies the semi-analytical algorithm for efficient parallelization. Hence, the numerical model performance is improved using the computing capabilities of a GPU. The derived semi-analytical approach is easy to implement and may be straightforwardly extended to cover the generation of waves in a flume or a basin. The ability of the model to reproduce nonlinear phenomena is demonstrated in simulations of two- and three-dimensional instabilities of a modulated Stokes wave. The model can be used to solve standard as well as complex wave problems in large computational domains considerably faster than its CPU-based counterpart. [ABSTRACT FROM AUTHOR]

Abstract: The problem of wave propagation and wave damping in a channel with side porous mattresses of arbitrary shape protruding from the walls is studied. The solution was achieved by applying 3-D boundary element method and was employed to study wave field in the channel and to analyze the effect of the geometry of the mattresses and physical and hydraulic properties of porous material on wave damping. The results show that wave damping in the channel strongly depends on wave parameters, especially, on the wave number. Wave reflection and transmission decrease with increasing the wave number. The results also show that the wave field in the channel strongly depends on the geometry of the mattresses as well as on physical and hydraulic properties of porous material used to build these wave dampers. The geometry of the mattresses and physical and hydraulic properties of porous material have a moderate effect on wave reflection and a significant effect on wave transmission. The results show that wave transmission down the channel decreases with increasing the length and thickness of the mattresses. Moreover, wave transmission decreases with increasing the porosity and damping properties of porous media used to build the mattresses. The analysis shows that porous mattresses protruding from the channel walls are very efficient in damping water waves propagating down the channel and may be built in channels to reduce high waves and achieve desired wave conditions. Theoretical results are in reasonable agreement with experimental data. [Copyright &y& Elsevier]

Abstract: A semi-analytical nonlinear wavemaker model is derived to predict the generation and propagation of transient nonlinear waves in a wave flume. The solution is very efficient and is achieved by applying eigenfunction expansions and FFT. The model is applied to study the effect of the wavemaker and its motion on the generation and propagation of nonlinear waves. The results indicate that the linear wavemaker theory may be applied to predict only the generation of waves of low steepness for which the nonlinear terms in the kinematic wavemaker boundary condition and free-surface boundary conditions are of secondary importance. For waves of moderate steepness and steep waves these nonlinear terms have substantial effects on wave profile and wave spectrum just after the wavemaker. A wave spectrum corresponding to a sinusoidally moving wavemaker possesses a multi-peak form with substantial nonlinear components, which disturbs or may even exclude physical modeling in wave flumes. The analysis shows that the widely recognized weakly nonlinear wavemaker theory may only be applied to describe the generation and propagation of waves of low steepness. This is subject to further restrictions in shallow and deep waters because the kinematic wavemaker boundary condition as well as the nonlinear interaction of wave components and the evolution of wave energy spectrum is not properly described by weakly nonlinear wavemaker theory. Laboratory experiments were conducted in a wave flume to verify the nonlinear wavemaker model. The comparisons show a reasonable agreement between predicted and measured free-surface elevation and the corresponding amplitudes of Fourier series. A reasonable agreement between theoretical results and experimental data is observed even for fairly steep waves. [Copyright &y& Elsevier]

Abstract: A theoretical approach is applied to predict the propagation and transformation of nonlinear water waves. A semi-analytical solution was derived by applying an eigenfunction expansion method. The solution is applied to analyze the effect of wave frequencies and wave steepness on the propagation of nonlinear waves. The main attention is paid to the wave profile, the wave energy spectrum, and the changes of wave profile and energy spectrum due to the interaction of wave components in a wave train. The results show that for waves of low steepness the nonlinear wave effects and effects associated with the interaction of water waves in a wave train are of secondary importance. For waves of moderate steepness and steep waves the effects associated with the interactions between waves in a wave train are becoming significant and a train of initially sinusoidal waves may drastically change its form within a short distance from its original position. The evolution of wave components has substantial effects on the wave spectrum. A train of initially very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short period of time. Laboratory experiments were conducted in a wave flume to verify theoretical approaches. The free-surface elevation recorded by a system of wave gauges was compared with the results provided by the semi-analytical solution. Theoretical results are in a fairly good agreement with experimental data. A reasonable agreement between theoretical results and experimental data is observed often even for relatively steep waves. [Copyright &y& Elsevier]