A number of wave theories have been adopted in an effort to describe the kine- 

 matics of waves. The most accessible and frequently used of these is Airy wave theory 

 (also known as linear theory or first order Stokes theory). Airy wave theory is easy 

 to use, but has a number of limitations. The source of these limitations is the sim- 

 plifications of the governing equations of gravity waves that are made to linearize the 

 equations, allowing a straightforward solution. These simplifications are made in the 

 free surface boundary conditions and are justified by an assumption of small wave 

 amplitude. Simplifying the free surface boundary conditions reduces the accuracy 

 of the predicted kinematics. Unfortunately, this compromise is at the free surface, 

 which is the location of the greatest fluid velocities and accelerations in waves, and 

 thus frequently the most important to the forcing of structures. The assumption of 

 small amplitude also renders the theory inadequate for large waves, exactly those of 

 greatest interest to coastal engineers. 



In order to address these limitations, a number of high order steady wave theo- 

 ries have been developed. Commonly in use are Stokes, Cnoidal, and Fourier wave 

 theories. For a review of these, see Fenton (1990). In general, Stokes methods are 

 successful in deep water, Cnoidal methods in shallow water, and Fourier methods in 

 all depths of water. Within their limitations, all three of these methods provide ex- 

 cellent predictions of the kinematics of steady waves, but are not directly applicable 

 to the irregular waves commonly found in the field. With the possible exception of 

 swell conditions on a very mild-sloped bottom, waves in the sea are neither steady, 

 unidirectional nor monochromatic. 



Methods for the interpretation of measurements of real sea states rely on Airy wave 

 theory even more heavily than do steady wave methods. With modern computer sys- 

 tems, even the most complicated of high order steady wave theories is quite accessible. 

 However, such higher order theories are not directly applicable to multi-directional or 

 multi-chromatic waves. The linearity of Airy theory allows superposition, in which 

 any combination of waves of different frequencies or directions can be combined to 

 form a solution. Superposition allows real sea states to be easily characterized by 

 frequency and direction spectra. While accessible, this method results in solutions 

 for the kinematics of the waves that do not satisfy the full free surface boundary 



