APPENDIX G 



DOCUMENTATION OF THE COMPUTER PROGRAM MADSEN 



The computer program MADSEN (CERC program ninnber 752X1R1CPO) is used to 

 predict wave transmission through rubble-mound breakwaters using methods 

 developed by Madsen and White (1976). (Note: Equations and figures refer- 

 enced from that publication are identified by the symbol MW.) A wave 

 transmission by overtopping model is also included as discussed in the tejct 

 of this report. The program is organized as shown in Figure G-1. Whenever 

 possible the variable names used are a close approximation to the symbols 

 used by Madsen and White (1976). Table G-1 lists important variable names, 

 corresponding symbols used in Madsen and White, and gives a- description 

 including references to defining equations in Madsen and White (1976) . A 

 description of each of the program subroutines is given below: 



SUBROUTINE READI - This routine reads standard lookup tables corresponding 

 to MW Figures 2, 3, 15, 16, and 17 from Madsen and White (1976). Lookup tables 

 with a combination linear and logarithmic interpolation were selected to avoid 

 having to use Bessel functions with complex arguments. The 53 standard lookup 

 table cards are given in Tabl'e G-2 . 



SUBROUTINE REFL - This routine determines reflection coefficients from 

 rough impermeable slopes to account for energy dissipation on the breakwater 

 face (see-Ch. Ill of Madsen and White, 1976). MW equation (127) is solved 

 iteratively and the final result corrected by the corresponding correction 

 factor from MW Table 2 (a linear fit to these points is used) . Lookup tables 

 from MW Figures 15, 16, and 17 are employed in this routine. 



Loops 



Read standard lookup tables (53 cards) , CALL READI 

 Read number of breakwaters to analyze, NCOMP 

 For each NCOMP read breakwater geometry 



For each period, NT, read wave heights, (ill 



For each wave height loop to 100 



Determine dissipation on BW face, CALL REFL 



Iterate of AHg and AHy to find £g using MIV equations (172) and (161) 



Find equivalent breakwater (Sec. IV, 2, eq. 158), CALL EQBW 



Find internal transmission and reflection coefficients, (Sec. II), CALL INTER 

 AHg from MIV equation (161) — — 



Reestimate 



Determine transmission and reflection coefficients, 



equations (175) and (176) 

 Find wave transmission by overtopping coefficient, Ky^ 

 Print results 

 100 CONTINUE 



199 CONTINUE — 



200 CONTINUE 



STOP 



END 



SUBROUTINES 



53 standard lookup cards 



Input cards (see Table G-4) 



■Tt 



Figure G-1. General program organization, 



175 



