A two dimensional hydrodynamic and morphological model is applied to the Natori River mouth to predict sand spit flushing and resulting topography change during the floods in September 1982 and August 1989. Time-variation of water level in the mouth can be simulated quite well by means of the present model, in which sediment movement due to streamwise current as well as that induced by secondary current is considered.
Linear and nonlinear sets of equations of long waves in the Lagrangian description are solved numerically to obtain run-up heights. Numerical results are compared with theoretical ones in case of simple topographies and the agreement is quite satisfactory. As a practical application, the computation is carried out for the Okkirai Bay in Japan. The computed run-up heighs agree fairly well with the recorded ones.
ABSTRACTABSTRACTThe Kakutani equation is rewritten in retaining the relative weights of terms: non-linearlity, dispersion and the effect of unevenness of bottom.Laws of shoaling are derived from the equation. Linear long waves and nonlinear long waves without the effect of dispersion give the "—1/4 power" law without regard to the initial wave profile. Shoaling of a solitary wave is solved to give the "—1 power" law. Boundary between the two laws depends on the bottom slope and the ratio of wave height to water depth.Comparison with experimental results supports these conclusions.
ABSTRACTABSTRACTThe feasibility of quantitatively forecasting a near-field tsunami prior to its arrival is examined, provided that the initial tsunami profile can be determined from fault parameters calculated using a method similar to that of Izutani and Hirasawa. Examination of basic equations, boundary conditions and grid lengths has led to the conclusion that the following combination is the best to perform rapid, accurate, and detailed numerical forecasting; the linear long wave theory discretized with the staggered leap-frog scheme, perfect reflection at the land boundary, and a grid length varying from 5.4 km out at deep sea to 0.2 km at the shoreline. With the aid of a super computer, tsunami heights along every 200 m of Japan's Sanriku coast (250 km long) can be obtained within 7 minutes after the occurrence of an earthquake. This method gives enough time for warning transmission and for evacuation of residents because the standard arrival time of tsunamis in this district is 25 to 30 minutes.
A commonly observed feature of pocket beaches confined by two rocky headlands is that river mouths are located at either end of beaches adjacent to one of headlands. This study presents a theoretical model of instability of river mouth locations in pocket beaches in terms of a linear stablity analysis. The theory shows that river mouths cannot exist stably around the central region of beaches and only can be located at either end of beaches when the load of river sediment supply relative to the dimensions of rivers are comparatively larger than the capability of longshore sediment transport relative to the dimensions of beaches.
