On the Propagation of Flood Waves

In natural rivers, the forms of the channels, --the bed slopes, the breadth, the forms of cross sections, etc.--are all very irregular and incessantly changing. It is impossible to grasp them defimtely. Yet the flow in rivers is steady and nearly uniform in the broad means. The disturbances on the flow caused by these irregularities damp away within a few kilometres and have certain limited dimensions and durations. The stochastic character of the collective of these elementary disturbances causes a large scale longitudinal mixing. The order of magnitude of the diffusion coefficient may be estimated to be 106 ~ 108 c. g. s. according to the scale of a river. Introducing the effect of longitudinal diffusion caused by the mixing into the equation of continuity and assuming the mean flow taken over a suitable range to be steady and uniform, the differential equation of flood waves was derived. It is an equation of diffusion containing a term of advection. As the equation is non-linear, an approximate method of solution was discussed and solutions were obtained under several conditions. They well explain the properties of flood waves. The approximate equation of flood waves is linear, a flood of any form is, therefore, supposed to be composed of many elementary flood waves of simple character, -- unit graph, or unit flood. A method of computing the unit graph was described and some numerical examples were shown. In the last, some of the results of observations made on an artificial unit flood in the Yedo River were compared with the theoretical computations. Their agreement is excellent

Some Studies on Beach Erosions

For some years now the writers have engaged in the field study on some important topics of beach erosions. The purport of this paper is to report briefly the main results obtained therein. Following an introduction, in Chapter 2, wave observations made along the beaches of Toyama Bay and of Ise Bay around Tsu City are described. The observed breaker heights were well explained by the effect of wave refraction. From the wave observations made along the beach of Tsu City, it was further suggested that the mean wave energy is proportional to breaker heights just at the moment of breaking. In Chapter 3 another factor which causes, besides the wave refraction, the distribution of breaker heights, that is, the effect of fetch, is discussed along the southern beaches of the east coast of Ōsaka Bay, and it was suggested that for the beach erosion of this region the effect of fetch played an important role. In Chapter 4, the grain size distributions of the beach sediments together with the beach profiles along the same beaches in Chapter 2, are discussed. From the sand ridge towards the shore the beach profile has two distinct slopes, the one corresponding to the surf zone, the other corresponding to the up-rush zone--a zone over which the breakers at the shore rush up after breaking. The grain size of the sediments increases rapidly in the surf zone towards the shore and in the up-rush zone it becomes abruptly large. It was noticed that different hydraulics must be applied to these two zones. In Chapter 5, the results of wave observations at the beach of Sano City along the same coast in the previous chapters are described. The wave profiles were recorded simultaneously with the particle velocity associated with a wave by the wave profile recorder and current recorder. Two distinct types of breakers were found, one which is called flow type has the maximum of velocity in the fore side of a wave, and seems to develop to a bore after breaking, while the other which is called wave type has the maximum of velocity at the crest of a wave and seems to crush after breaking. These two types of breakers are compared with the results of wave observations made in a wave tank. In Chapter 6, some results of observations of the sediment transportation along the up-rush zone at the same beach are described. It was found that for the breakers of flow type the net transfer of sediments is on-shore, that is, beach sedimentation takes place, whereas for the breakers of wave type the net transfer of sediments is off-shore, that is, beach erosion takes place