Shallow Water Wave Transformation through External Factors 135 



0-298 kg/cm 2 (611 lb./sq ft) for five summer months and 1018 kg/cm 2 

 (2090 lb./sq ft) for six winter months, with a maximum of 2 97 (6090 lb./sq ft). 

 At Dunbar on the north coast of Scotland, the maximum found was 383 

 (7840 lb./sq ft) and near Buckie, over several years of reading, 3-28 kg/cm 2 

 (6720 lb.). As a result of experiments on how the pressure varies with height, 

 it was found that the shock pressure of the waves is strongest at high-water 

 level and decreases rapidly with increasing water depth. Off the German 

 coast of the North Sea, Franzius and Schilling (1901, p. 22) found as 

 largest shock pressure 15 kg/cm 2 , at the Baltic coast 10 kg/cm 2 , so that 

 it can be assumed that at points exposed to the beating of the waves the 

 largest shock pressure varies between 1-5 and 2-5 kg/cm 2 . More recently, 

 experiments have been made with manometer and oscillograph pressure 

 gauges respectively, which have given values of the same order of magnitude ; 

 the highest pressure hitherto recorded of 6-9 kg/cm 2 was observed on the 

 east mole of the harbour of Dieppe on 23rd February 1933, by means of 

 a recording device which was located 35 cm above the base of the vertical 

 wall, and which was hit by a wave 5 m high (horizontal velocity 8-50 m/sec, 

 initial vertical velocity 23 m/sec). The breaker had a height of 36 m, a length 

 of 40 m and a wave velocity of 6 m/sec (De Rouville, 1938). Other mea- 

 surements, made simultaneously with several recording dynamometers, were 

 reported from the east coast of North America (Portland, Maine). However, 

 the pressure values remained far below the maximum value observed at 

 Dieppe. A comprehensive survey has been compiled by d'Arrigo (1940). 



Gaillard (1904), at North Beach (Florida), studied the relationship between the dimensions 

 of the waves and the shock pressure. The shore line at that point is straight, the beach is flat, and 

 the pressure gauges were mounted on upright poles, 8x8in., in such a manner that they received 

 the full shock of the waves. When we take p = kqi^if) as dynamical pressure, the pressure coef- 

 ficient k = Iplgii 1 and, theoretically, it can attain a maximum value 2. Gaillard assumes it is the 

 sum of the wave velocity c and the velocity v of the water particles in their orbit, so that 



c+v = 



V&V^h 



in which a and b are the semi-axis of the orbit at the surface. He thus obtains Table 18, from which 

 we can see that the shock pressure, even with relatively large waves, hardly attains the average 

 value of 0-5 kg/cm 2 ; the pressure coefficient here is 1-2, which is considerably below the theoretical 

 maximum value. The destructive force by a breaker is estimated by d*Auria (1890-1891) as follows: 

 a breaker with a frontal height h, a length A, with a velocity u (approximately equal to c) has per 

 unit width the kinetic energy (qIiK)u 2 . The onrush occurs during the time K:u. If during this time 

 the total kinetic energy has been used up, then, according to the impulse theorem, 



P k qhlu P q/i 

 = mass x velocity = or — = — ii 2 , 



2 w 2 2 2 



where the average resistance = %P. The greatest resistance may be approximately twice as much. 

 If spread at the vertical wall over an area of the height h, the maximum shock pressure per unit 

 surface of a breaker will be p = u 2 , which is in agreement with the result obtained by Gaillard. 



