With longitudinal displacement of the ends of adjacent tubes relative to 

 each other, the flow in the tube is induced with various phase shifts, thus 

 distributing the flows and pressure forces on the tubes with respect to time. 

 Any reflecting forces are randomized, as well as the kinetic energies of the 

 jets leaving the tubes. In addition, the presence of the tubes affects that 

 part of the wave energy passing between the tubes. The effect of such a tube 

 array is a scattering of a train of waves incident on the system. This array 

 of tubes should perform in this fashion for all wavelengths; it is most 

 efficient, however, when the maximum pressure gradient exists between the ends 

 of the tubes. A highly efficient breakwater system can thus be theoretically 

 maintained for a range of wavelengths by using tubes of different lengths in a 

 single floating breakwater configuration. 



Ippen and Bourodimos (1964) conducted an experimental study to determine 

 reflection and transmission coefficients, and power losses through the appli- 

 cation of a floating breakwater system composed of random length tubes. The 

 reflection coefficient, C r , was determined by obtaining the envelope of 

 the wave amplitudes on the oceanside of the breakwater. The reflection 

 coefficient is defined as the difference between the maximum and the minimum 

 amplitudes of the wave envelope, divided by the sum of the maximum and the 

 minimum amplitudes of the wave envelope. Correspondingly, the transmission 

 coefficient, C t , is the ratio of the same amplitude quantities on the lee 

 side of the breakwater. 



In analyzing the effects of the tube system on the waves, the power (lost 

 or dissipated) per wave cycle can be considered as the average time rate of 

 change of energy within an element of fluid through which the wave passes. 

 The power dissipated by the breakwater can be computed by using an expression 

 equating the power incident on the breakwater, the power transmitted through 

 the breakwater, and the power reflected from the breakwater. Defining P Q as 

 the fraction of incident wave power dissipated, it can be shown that 



P D = 1 - C2 - C 2 (74) 



As for other types of breakwaters, the theoretical aspects of the floating 

 tube system pertaining to effects of partial reflection and transmission of 

 wave energy, and to the balance of power transmission, apply as derived. How- 

 ever, the amount of dissipation is subject to complex influences which cannot 

 be specified by analytical expressions. Hence, the experimental investigation 

 was conducted on a model scale, but the results can be extrapolated to proto- 

 type behavior on the basis of the usual similarity principles. 



a. Reflection and Transmission Coefficients . The experimental arrange- 

 ment of the open-tube floating breakwater concept (Fig. 130) was installed in 

 a two-dimensional wave flume and subjected to a range of wave characteristics. 

 The dissipative action of the breakwater is due to the combination of dissipa- 

 tion of the kinetic energy of the flow induced in the tubes, boundary resist- 

 ance of the flow generated in and around the tubes, and general interference 

 with the normal transient velocity field of the waves in both the vertical 

 and horizontal directions. The results of the study are presented graphically 

 in Figures 131 and 132. While the data exhibit apparent scattering, tests 

 under the same test conditions were highly repeatable, indicating consistent 

 accuracy in measurements. Much of the apparent scatter can therefore be 

 attributed to inherent changes in performance of the various models with 



191 



