Wataru Kioka

Applicability of numerical models to nonlinear dispersive waves

Abstract The applicability of three different wave-propagation models in nonlinear dispersive wave fields has been investigated. The numerical models tested here are based on three different wave theories: a fully nonlinear potential theory, a Stokes second-order theory, and a Boussinesq-type theory with an improved dispersion relation. Physical experiments and computations were conducted for wave evolutions during passage over a submerged shelf under various wave conditions. As expected, the fully nonlinear solutions agree better with the measurements than do the other solutions. Although the second-order solution has sufficient accuracy for smaller-amplitude wave cases, the truncation after the third harmonics causes significant discrepancies in wave form for larger waves. In addition, the second-order model markedly overestimates the first- and second-harmonic amplitudes in transmitted waves. The Boussinesq model provides excellent predictions of wave profile over the shelf even in larger wave cases. However, this model also overestimates the magnitudes of several higher harmonics in transmitted waves. These facts may indicate that energy transfer from bound components into free waves in these higher harmonics cannot be accurately evaluated by the Boussinesq-type equations.

TRANSMISSION OF LONG WAVES INDUCED BY SHORT-WAVE GROUPS THROUGH A COMPOSITE BREAKWATER

Theoretical findings and laboratory evidences are presented regarding the transmission of long waves induced by short-wave groups through the rubble base of an infinitely long composite breakwater. Multiple-scale perturbation method is applied in describing the long-wave fields in terms of velocity potential, and an analytical solution is derived for transmitted and reflected long waves induced by wave groups. Dependency of the reflection and transmission of free long waves on several parameters is examined through the numerical calculations. It is found that the linear friction factor, the rubble-base height and the modulation of short waves affect the transmission of free long waves significantly. Theoretical results are then compared with the results from laboratory experiments. It is shown that although the conventional rubble-mound breakwaters can reflect short wave energy efficiently, a significant part of the bound long-wave energy associated with shortwave groups is transmitted to the leeward side of the breakwater as free waves.

Theory of Significant Wave Period Based on Spectral Integrals

A formula for the significant wave period is derived. This containes the complex value integral of energy spectrum, and thus depends on the spectral shape asymetry. For the wind waves characterized by a Pierson-Moskowitz spectrum the spectral asymetry becomes remarkable, so that the significant wave period T 1/3 deviates from the mean period T m . The empirical ratio T 1/3 / T m of 1.2 is well interpreted by the proposed theory.

LONG WAVES AND THE CHANGE IN CROSS-SHORE SEDIMENT TRANSPORT RATES ON A SHEET FLOW DOMINATED BEACH

In this paper, at first results of experiments in sheet flow conditions under nonlinear asymmetric irregular oscillations with and without long wave components are presented and a method for estimating the net transport rates is proposed. Then the importance of phase lag between free long waves and irregular short waves as well as the effect of steady currents on the magnitude of transport rate are discussed. Implications of the results are further demonstrated by applying the proposed formulation to calculating the cross-shore distributions of sediment transport rates on a sheet flow dominated beach under incident irregular waves with low frequency components. It is found that long waves can significantly enhance the seaward transport of sediments inside the surf zone during a storm. It is also shown that the presence of a standing long wave system may lead to large spatial gradients in the cross-shore transport rates and eventually, to formation of a multiple longshore bar system.

LONG-PERIOD OSCILLATIONS IN A HARBOUR CAUSED BY TYPHOON

A study of alternatives including a shoreline evolution numerical modelization has been carried out in order to both diagnose the erosion problem at the beaches located between Cambrils Harbour and Pixerota delta (Tarragona, Spain) and select nourishment alternatives.Engineers and scientists at the U.S. Army Engineer Waterways Experiment Station (WES) are developing a Rapidly Installed Breakwater (RIB) System specifically designed to address problems associated with the militarys efforts to offload ships during Logistics Over The Shore (LOTS) operations. Problems arise with these operations when seas become energetic and limit capabilities of crane operators and stevedore crews. The RIB System is designed to solve this problem by creating a pool of calmer water where these operations occur so that crews can continue to function. A series of small-scale laboratory experiments conducted in 1995 and 1996 at WESs facilities in Vicksburg, Miss., and at the O. H. Hinsdale Wave Research Laboratory at Oregon State University in Corvallis, laid the groundwork for the RIB System development and yielded an optimum RIB System configuration known as the Double Delta. Laboratory results, obtained with the Double Delta configuration, showed that wave heights could be reduced by more than 80 percent. During the spring and summer of 1996, a mid-scale RIB System successfully demonstrated its capabilities during a field deployment, with wave height reduction on the order of 75 percent. Based on these results, it is believed that the RIB System will be integrated into the Armys LOTS asset inventory and become a key part of the solution to the militarys LOTS problems.

Numerical Analysis of Breaking Waves in a Shallow Water

ABSTRACTThe deformation of shallow-water breaking waves is studied from the exact theory of irrotational flow. The method used here is based on the mixed Eulerian-Lagrangian technique developed by Longuet-Higgins and Cokelet. To generate the breaking waves a sufficiently large wave steepness is used as initial conditions for the computation. The deformation of unsteady waves and the resultant two types of breaker, plunging and spilling breakers, are shown for various relative depths. The velocity field of these breaking waves are also given.

DIFFRACTIVE UNCERTAINTY TOWARD THE FUTURE ESTIMATION OF RETURN WAVE HEIGHT

Freshness is very important factor, which is not exceptional for the observation data. The data ready for statistical analyses, is observed in the past, while the return period is laid on the future for the predicting return levels. It is natural that the farther ahead in the future the return level is predicted, the larger the statistical variety becomes. Thus, the freshness of the record is falling down as the pass of time. In the point of view, the statistical uncertainty becomes wide, as entering into the shadow area distinguished by the straight lines of confidence regions by the conventional method. The proposed method will give a potential trend even for the stationary model. It will be useful tool because in many cases it is very difficult to detect the faint trend in short records of wave heights and sea levels due to the climate change, as one of the applications.