134 Shallow Water Wave Transformation through External Factors 



Submarine ridges. Underwater ridges near shore have an effect opposite 

 to that of canyons. Waves passing over the ridge are in shallower water and 

 are therefore retarded, and on either side waves move ahead, creating a con- 

 vergence over the ridge. This is borne out by frequent observations of 

 unusually violent breakers over the shoal portion of underwater ridges. 



Other interesting cases are the influence of promontories, of bays and 

 islands on the surf, for which Munk and Taylor and Arthur (1946, 

 p. 168) have given good examples and which fully confirm the theory. It 

 seems quite possible to forecast the direction and force of the expected surf 

 with the aid of previously computed refraction diagrams for wave systems 

 of definite periods. The investigations are also of importance in connection 

 with the action of the surf on the topography of beaches, 

 (c) Surf Breaking against Cliffs 



If a wave train moves towards a vertical surface or against a shore sloping 

 down steeply into great depths at a sharp angle, it will be totally or partly 

 reflected. The reflected wave superimposes itself on the approaching one 

 and the result is a complete or incomplete standing wave. The water motion 

 in front of the wall then remains more or less at rest and, in an extreme 

 case, the wave attains twice the height of the approaching wave. With such 

 a simple reflection, there will be no shock from the approaching wave against 

 the vertical wall, because there are only vertical displacements of the water 

 particles (antinode). When there is such a motion, a vessel can venture to 

 come up close to the wall (breakwater, etc.) without risk of damage. In general, 

 however, the result of the reflection is not such a regular process, and the 

 incoming and reflected waves mix up confusedly. 



If the waves are high and move fast, they generally bounce against the 

 steep shore in breaking or shortly before; huge water-masses from the wave 

 crests are thrown jet-like against the wall. This is the shock or cliff surf. 



The shock waves are, of course, closely related to the place where the 

 wave crests overturn, and this place is dependent on the wave velocity and 

 on the slope of the beach, as well as on the latter's nature. The waves, when 

 hitting a barrier, exert a dynamic pressure, which is added to the generally 

 far smaller static pressure. When a liquid hits perpendicularly a large wall, 

 the particles change their motions gradually by a right angle, until the total 

 energy of motion in the direction of the pressure is counterbalanced by the 

 counterpressure of the wall. If the cross-section of the approaching water- 

 mass is F, then the mass of the shock in the unit of time with a velocity U 

 is oFU and its momentum qFU 2 , so that the shock pressure at the wall 

 becomes P = qFU 2 . Stevenson (1864, p. 285) was the first to determine 

 this shock pressure of surf waves and built a spring dynamometer which, 

 based on the principle of railway buffers, determined numerically the shock 

 pressure of the waves. Experiments made with such an instrument in 1843 

 and 1844 at the cliffs of Skerryvore (in the west of Scotland) gave an average 



