is obtained from equation (95) and is presented in graphical form in 

 Figure 16. 



The solutions for R and R^ were obtained through the use of complex 

 computer programs for Bessel functions with complex arguments which are 

 part of the Massachusetts Institute of Technology (MIT) Information 

 Processing Center's IBM System 370 computer library routines. 



With the solution for R as presented graphically in Figure 15 it 

 is seen that knowledge oi^ilg/L and (f) enables one to determine the value 

 of R or conversely, if R and l^/L were known Figure 15 may be used to 

 obtain the corresponding value of . 



a. Determination of the Friction Angle, j) . The value of the 

 linearized friction factor, f^, or the friction angle, <j) , was considered 

 constant (i.e., independent of jc and t) in the analysis presented in the 

 preceding section. This friction factor was introduced through 

 equation (81) and corresponds to a linearized bottom shear stress as 

 given by equation (82) 



T^ = pfj^whU = pwhU tan2(}) . (99) 



With the rate of energy dissipation per unit area of the slope 

 given by Eq = t^^U, as discussed in Appendix A, the average rate of 

 energy dissipation per unit area of the slope is given by 



s -' s -^0 



in which U is the real part of the solution given by equation (84) with 

 u given by equation (91). Since U is necessarily periodic the time 

 averaging in equation (100) is readily performed so that 



= 1 ^^"^s f ^s 2 



Ej^ = J poj tan24) — — ^ ^ ^ |u| dx . (101) 



From equation (91) it is seen that 



J, (2k J, /1-i tan2d) y^'^^) 

 u = -iA ^ ° ^ -1 1 



/1-i tan2<J>/-^ y^/2 



(102) 



54 



