depth, h, and wave period, T, a (symmetrical) representation can be developed to describe 

 the kinematics and dynamics of the motion and (2) for a given measured water surface 

 displacement, i?(t) representing a single oscillation (e.g., trough-to-trough), a representation 

 can be determined which completely defines the kinematics and dynamics of the wave 

 motion. The first case is, of course, of more interest to designers; in another application, the 

 second case has been employed for the analysis of hurricane-generated wave and wave-force 

 data. Only the first mode has been explored under the present study. 



Formulation 



The water-wave phenomenon of interest here can be idealized as a two-dimensional 

 boundary value problem of ideal flow. The assumption of ideal flow is essential to a 

 mathematical formulation that can be readily solved by known techniques. Figure 1 defines 

 terms employed in the formulation. 



Mean 

 Level- 



Water 



UNI nnfunf/n ni > n nnr/ n n n /?/ n / 



Figure 1 . Definition sketch, progressive wave system 



Differential Equation 



Ideal flow incorporates the assumptions of an incompressible fluid and irrotational 

 motion. For pressures normally experienced in progressive water-wave motions, the 

 incompressibility assumption can be shown to be valid. Shock pressures due to a wave 

 breaking against a seawall may be an important exception; however these are not 

 encompassed by the results of this research. The assumption of irrotational flow may be 

 questioned. Probably the best reason for this assumption, at this stage, is that it allows 

 formulation of a boundary -value problem that can be solved in an approximate manner. The 

 solutions can then be compared with measurements to determine the apparent need for the 

 refinement to include a nonzero rotation. 



The differential equation (DE) for two-dimensional ideal flow, the Laplace equation, can 

 be presented in terms of either the velocity potential, or stream function, t//. 



V2(|, = 

 V^(|; = 



(1) 



(2) 



