20. 河口近傍における長波について[I] : buffer domainの方法による解析

In this paper, a long wave in the vicinity of an estuary istreated by use of the method of the buffer domain. Dividing the whole domain into three parts, the equation of along wave is solved analytically by use of the Fourier Besselexpansion. Then an electronic computer was used to obtain the wave heights and phases in each domain. The conclusions obtainedin the present purview are :- (1) For the waves propagating into the canal, when kd(k: the wave number of the incident waves ; d: half the width of the canal) approaches to zero, the wave height tends to double that of the incident waves, the phase becomes zero and the waves in the canal are propagated as if they originated at an infinite point. When kd increases in amount, the wave height diminishes monotonically to reach that of the incident waves at about kd=1.0, the phase takes a maximum value at about kd=0.3 and later decreases monotonically to zero value at kd=1.0, and the supposed origin of the waves propagated into the canal approaches the estuary. (2) For the waves in front of the mouth of the canal, the equi-amplitude and phase lines run parallel to the coast facing the open sea and the amplitude of the waves increases in the direction of the offing. Provided that the linear approximations for sine and cosine functions are possible, it is found that the waves in front of the mouth of the canal are propagated with the speed of a long wave into the canal. (3) As far as the waves in the open sea are concerned, our greatest interest is in damping reflected waves(instead of merely reflected waves). Regarding these waves, the following facts are known. When kd is small, the amplitude of the damping reflected waves is also small. As kd becomes large, a contribution of these waves to reflected waves is augmented. For the rates of the damping of these waves versus a variation of position, a similar tendency is seen. That is to say, the damping rate is gentle for small kd and rapid for large kd. And the rate is remarkable, in magnitude, in the surrounding part of the mouth of the canal. The surface composed by the amplitudes of the damping reflected waves tends to an asymptotic surface as kd becomes large. Finally, concerning the directivity of the damping reflected waves, the fact is known that a contribution of these waves to reflected ones is small in the direction along the coast and becomes large as a line, along which a variation of the damping reflected waves is examined, is directed to the offing.本論文においては河口附近における長波に関する研究が,buffer domainの方法を用いてなされている.まず全領域は3つの部分に分けられる.そのうち1つはbuffer domainである.そして河口部と広海(open sea)はベッセル函数を用いて解が求められ,水路の部分は三角函数を用いて解が表現されている.得られた解の数値計算には電子計算機が用いられ,次のような結論を得た.(1)水路に進入する波についてkd(kは広海における進入波の波数,dは水路の幅の半分の長さ)が零に近づくにつれて水路の波の波高は広海における進入波の波高の2倍に近づき,位相のずれは零に近づく,そして水路の進入波は恰も無限遠点を起点としているかのごとくである