Group Velocity, Cq 



The group velocity is defined as the ratio of total energy flux to total energy 

 [Equation (42)] and is presented (Table XI, Item 6) in dimensionless form as: 



. = f 



[L/T 



The dimensionless group velocity is defined such that for linear wave theory the shallow and 

 deepwater values are I.O and 0.5, respectively. 



Average Momentum, M 



The total average momentum is defined by Equation (43) and is presented (Table XI, 

 Item 7) in dimensionless form as: 



8 L/T 



YH' 



The dimensionless momentum is defined such that for linear wave theory the result is unity. 

 Note that mass transport velocity, U = [M/ph] is proportional to the average momentum. 



Average Momentum Flux in Wave Direction, F^ 



The total average momentum flux in the wave direction is defined by Equation (44) 

 and is tabulated (Table XI, Item 8) in the following dimensionless form: 



yH' 



The above definition reduces to 1.5 and 0.5 for linear wave theory for shallow and 

 deepwater waves, respectively. 



Average Momentum Flux Transverse to Wave Direction, F^ 



The total average momentum flux in a direction perpendicular to the wave advance 

 direction is needed to define the radiation stress tensor, (discussed by Bowen 1969), is 

 defined by Equation (45), and is tabulated (Table XJ, Item 9) in the following dimensionless 

 form: 



r 



YH' 



For linear wave theory, the above definition reduces to 0.5 and 0.0 for shallow and 

 deepwater waves, respectively. 



51 



