Shigeaki Tsutsui

MODEL EQUATIONS OF NONLINEAR DISPERSIVE WAVES IN SHALLOW WATER AND AN APPLICATION OF ITS SIMPLIFIED VERSION TO WAVE EVOLUTION ON THE STEP-TYPE REEF

The system of integro-differential equations, which combines long wave nonlinearity with full linear dispersion, is presented as new model equations for studying nonlinear evolution of shallow water waves. The dispersion term is represented by an integral with the kernel of the Fourier transform of phase velocity. Among the nonlinear wave equations developed from the system for spectral-wave components, the simplified version is applied to waves over the step-type reef in two-dimensions. Comparisons between present numerical results and experimental data are made. The results show that there occurs modulation chiefly in the amplitude and the phase of the first harmonic because of nonlinear interaction between wave components and bathymetry of the reef. Consequently, there may be the resonance of incident waves on the step-type reef due to vertical bathymetric variation.

PREDICTION OF THE MAXIMUM WAVE ON THE CORAL FLAT

A special reflecting wall 12 m long and 2.1 m high was built off the beach at Reggio Calabria, and 30 wave gauges were assembled before the wall and were connected to an electronic station on land. It was possible to observe the reflection of wind waves generated by a very stable wind over a fetch of 10 Km. The experiment aimed to verify the general closed solution for the wave group mechanics (Boccotti, 1988, 1989), for the special case of the wave reflection.Significant features on Wadden Sea wave climate are evaluated in respect of the state of the art. Main emphasis was laid on an analysis of the governing boundary conditions of local wave climate in island sheltered Wadden Sea areas with extensions being sufficient for local wind wave growth. Explanatory for significant wave heights a reliable parametrization of local wave climate has been evaluated by using generally available data of water level and wind measurements.

COASTAL WAVE-DEFORMATION MODELS COMBINED WITH INTEGRABLE-TYPE INFINITE ELEMENTS

An assumption of collinear straight coastlines in the far field, traditionally used in wave models for harbors, is a limitation to wave simulations in the domain extending to infinity, since this assumption is invalid for most real coastlines. By alleviating this limitation based on the geometric-optics approximation, functions of these coastal wave-deformation models are extended to be able to predict wave patterns around the semi-infinite breakwater and convex and concave coasts, such as bulkheads with discontinuous alignment. Mapped infinite elements are also formulated for exterior wave problems. A basic concept in developing is that the true decaying property of scattered waves, i.e. with the modes of r −1/2, r −3/2,…, where r is the radial distance, must be represented directly in infinite elements. To do so, a complementary element is introduced to the infinite element. Infinite element integrals can be expressed explicitly because of analytical integrability due to weak singularity in the infinite mapping. Three test problems for coastal wave-deformation models are solved combined with the cubic infinite element with r −1/2 and r −3/2 decays; this combination technique is found to be effective and accurate for problems of wave scattering.

Jump Condition of Energy Flux at the Line of Bathymetric Discontinuity and Wave Breaking on the Reef Flat

ABSTRACTThe wave reflection from a submerged vertical wall along the line of bathymetric discontinuity is beyond the postulation of the mild-slope equation; i.e., weak horizontal variations in water depth. The present paper offers the approximate jump condition of energy flux at the bathymetric discontinuity point and the corresponding functional, for the application to wave height prediction based on the mild-slope equation. We can then handle the problem of wave propagation as a two-dimensional problem. The most important feature of the jump condition is that it is independent of the direction of wave incidence, whether waves are incident from a deeper or shallower region. The jump condition is verified through prediction of the wave height distribution around a variety of bottom topographies including a submerged breakwater. Secondly, the present paper deals with wave breaking due to bathymetric discontinuity. The preceding results on the breaking criteria and on the wave energy damping after breaking ...

A PERFECTLY MATCHED LAYER ABSORBING BOUNDARY CONDITION AND WAVE-MAKER MODELING FOR WAVE PROPAGATION PROBLEMS IN INHOMOGENEOUS INFINITE-DOMAINS

For wave propagation problems in infinite-domains, truncation of the far-field by an artificial boundary is essential to define a bounded domain of interest; resultant difficulties are the radiation condition and generation of incident waves. Instead of the radiation condition, an absorbing boundary condition (ABC) is implemented in an inhomogeneous exterior domain, based on the perfectly matched layer (PML) technique. Complex coordinate stretching, a key PML concept, analytically continues a governing equation in the domain of interest into a PML equation as an anisotropic absorbing boundary in the exterior domain; a system of equivalent equations governs waves in the whole computational domain, and thus the PML is reflectionless at the artificial boundary, an interface between the PML and the domain of interest. For generation of incident waves, wave-maker modeling is proposed based on an idea of plain topography and wave-ray tracing. A source function along the interface is a curvilinear integral in a weak form for the governing equation. Finite element examples for wave propagation in one-dimension verify ability and efficiency of techniques with PML ABCs; besides, those for wave scattering by a circular cylinder on a slope show effectiveness of the wave-maker modeling.