Kinematic Free Surface Boundary Condition Errors, e^ 



The kinematic free surface boundary condition error is defined in dimensionless form 

 by Equation (35) and the root-mean-square (RMS) and maximum values are tabulated 

 (Table XI, Items 10 and 12) as defined by Equation (46). 



Dynamic Free Surface Boundary Condition Errors, e^ 



The dynamic free surface boundary condition error is defined by Equation (36) and is 

 represented in the following dimensionless form : 



£2 - j|- 



The RMS and maximum values are tabulated (Table XI, Items II and 13) as defined by 

 Equation (47). 



Kinematic Free Surface Breaking Parameter, |3j 



The kinematic free surface breaking parameter is tabulated (Table XI, Item 14) as 

 defined by Equation (48) (dimensionless form). 



Dynamic Free Surface Breaking Parameter, jS^ 



The dynamic free surface breaking parameter is tabulated (Table XI, Item 15) as 

 defined by Equation (49) in dimensionless form. 



Variables Presented in Graphical Form-Combined Effect of Shoaling and Refraction 

 In addition to developing the tabulated values previously described, tlie study included 

 the development of the combined effect of shoaUng and refraction for nonlinear waves 

 advancing toward shore with a deepwater direction, a^, over bathymetry characterized by 

 straight and parallel contours. 



For linear wave theory, it is possible to separate the shoahng and refraction effects, 

 because neither wave celerity, C (governing refraction), nor group velocity, C^ (governing 

 energy flux), is dependent on wave height. For nonlinear waves, both celerity and group 

 velocity at a certain location depend on wave height as weU as wave period and water depth. 

 The shoaUng-refraction effects for nonUnear waves are therefore not separable, and the 

 combined effect depends on the deepwater wave steepness, H^/L^, as well as the local 

 relative depth. 



Because the shoaling-refraction results are not readily presented in tabular form, graphs 

 are presented as Figures 25, through 29 for deepwater wave directions, a^ of ,10 ,20 

 40°, and 60°. A brief description of the use of these graphs follows. A wave with a 

 deepwater direction a^, will propagate toward shore such that the local H/L^ will fall 

 along a curve characterized by the deepwater value H^/L^. At any particular relative 

 depth, h/L^ , the local wave steepness W\ and direction a are read from the ordinate 



52 



