(Photo from NOAA)
Wave Theories
Physical aspects such as bottom conditions, surface conditions, and flow and fluid conditions are important ones to note when analyzing water waves.
Bottom Conditions
Surface Conditions
Flow and Fluid Conditions
These factors show us that not just one analytical explanation can relate to every wave function. Instead, there are a variety of possible solutions over a given set of conditions. The simplest analytical solution is the Linear Wave Theory (LWT) which is also known as the small amplitude theory or the Airy Wave theory. However, for more extreme cases, the Linear Wave Theory should not be used because of the inaccuracies it obtains for aspects such as kinematics at the free surface. Instead, there are a set of Nonlinear Wave Theories that can be used to determine the forces of a nonlinear wave. Below are links to more detailed descriptions of the two types of theories.
References
