1. Pneumatic Breakwater System . 



The initial concept of the pneumatic breakwater was patented in 1907 

 (Brasher, 1915). Attenuation in this concept is the release of compressed air 

 through a submerged perforated pipe. Several prototype installations of this 

 system have been described as successful. A few model studies were conducted 

 before 1950, but the results were incomplete and in some cases contradictory. 

 These early tests indicated excessively large power requirements which were 

 probably true for the shallow-water waves under investigation at the time. 

 In addition to attenuating waves near the seacoast, there is a sufficient 

 requirement for reducing deepwater wave heights to warrant thorough investiga- 

 tions under deepwater conditions. For example, the offshore transfer of cargo 

 from conventional ships to amphibians in military discharge operations is 

 severely curtailed when wave heights exceed about 2 feet. If areas of rela- 

 tively calm water can be produced immediately around ships at anchor, the 

 capability of moving supplies ashore will increase substantially. 



a. Theoretical Analysis . At the request of the British Admiralty, Taylor 

 (1943) conducted an analysis of the pneumatic breakwater, and his development 

 became one of the most significant advances in this area of research. The 

 investigation was formulated around the superposition of a uniform current of 

 velocity, U, and thickness, h, on the velocity potential of a deepwater 

 wave. It was assumed that air bubbles had little effect on the attenuation, 

 and that the vertical-induced current caused by the rising bubbles diffusing 

 both upstream and downstream at the surface was solely responsible for the 

 attenuation of the incident waves. Taylor's analysis was aimed at determining 

 the current velocity necessary to attenuate waves of a given length, and he 

 found that for a given current, it was kinematically impossible to transmit 

 waves shorter than a given length. 



Taylor (1955) modified the theory by using a triangular velocity distri- 

 bution, which is more in accord with actual prototype distributions (Fig. 

 137). To relate the velocity and thickness of the current to the air dis- 

 charge and the submergence of the perforated pipe, Taylor used the analogous 

 solution for the convective currents above a horizontal line source of heat. 

 The maximum velocity of the current, U, was found to be related to the air 

 discharge, q, as 



q = 0.00454 U 3 (75) 



As the current reaches the surface, it spreads horizontally with maximum 

 velocity occurring at the water surface. It was determined that the depth of 

 air release plays only a minor role in the maximum velocity at the surface; 

 however, for maximum efficiency, the perforated pipe should be placed at the 

 bottom so that the rising bubbles will approach terminal velocity as nearly as 

 possible. The surface velocity will remain nearly the same for equal dis- 

 charges, but the effective current depth changes in proportion to the air- 

 release depth. Hence, for attenuating longer waves where a deeper current is 

 necessary, an increase in submergence is required. However, this entails 

 larger power requirements because the power necessary to release a given 

 amount of air is directly proportional to the depth of release. 



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