£. Pneumatic Breakwaters . Pneumatic breakwaters reduce incident 

 wave heights by generating horizontal surface currents, a part of which 

 flows counter to the orbital velocities of the oncoming waves. The hori- 

 zontal surface currents are generated by the action of vertically rising 

 air bubbles discharged from a pipe manifold system placed on or near the 

 bottom. The waves from which protection is desired are propagated by the 

 restoring force of gravity and are, therefore, modeled from Froude's law. 

 However, since the generation of the counter surface currents, on which 

 the reduction of wave action depends, is the result of rising air bubbles, 

 viscous shear and surface tension forces must be considered. According to 

 Kurihara (1956), the viscous forces in the turbulent area where the sur- 

 face currents encounter the orbital velocities of the waves are also in- 

 volved to some extent in the reduction of wave heights. Thus, pneumatic 

 breakwater models must be designed and operated based on model laws that 

 consider the forces of inertia, gravity, viscous shear, and surface 

 tension. Pressure forces are also involved in the bubble formation. 



When waves pass through a bubble screen, with the manifold located on 

 the bottom, the reduction in wave heights may be assumed a function of the 

 following variables: 



Hj, H^, X, d, g, Q^, p^, p^, p^^, II, and a, 



where 



Hj^ = incident wave height 



H^ = transmitted vi^ave height 



A = incident wavelength 



d = depth of water 



g = acceleration of gravity 



Qair ~ quantity of air emerging per second per foot from the 

 orifices of the manifold; the quantity of free air 

 delivered by the compressor to the manifold system per 

 foot of manifold is 





Pair ~ mass density of air 



p^^ = mass density of the water 



Pat ~ atmospheric pressure 



y = dynamic viscosity of the water 



a = surface tension of the water 



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