Ocean waves are complex. Many aspects of fluid mechanics necessary 

 to a complete discussion have only a minor influence on solving most 

 coastal engineering problems. Thus, a simplified theory which omits most 

 of the complicating factors is useful. The assumptions made in developing 

 the simple theory should be understood, because not all of the assumptions 

 are justified in all problems. When an assumption is not valid in a 

 particular problem, a more complete theory should be employed. 



The most restrictive of common assumptions is that waves are small 

 perturbations on the surface of a fluid which is otherwise at rest. This 

 leads to a wave theory which is variously called, small-amplitude theory, 

 linear theory, or Airy theory. The small-amplitude theory provides in- 

 sight for all periodic wave behavior and a description of the periodic flow 

 adequate for most practical problems. This theory is unable to account for 

 mass transport due to waves (Section 2.253 Mass Transport Velocity), or the 

 fact that wave crests depart further from the mean water level than do the 

 troughs. A more general theory, usually called the finite amplitude, or 

 nonlinear wave theory is required to account for these phenomena as well as 

 most interactions between waves and other flows. The nonlinear wave theory 

 also permits a more accurate evaluation of some wave properties than can be 

 obtained with linear theory. 



Several assumptions, commonly made in developing a simple wave theory 

 are listed below. 



(a) The fluid is homogeneous and incompressible; therefore, the 

 density p is a constant. 



(b) Surface tension can be neglected. 



(c) Coriolis effect can be neglected. 



(d) Pressure at the free surface is uniform and constant. 



(e) The fluid is ideal or inviscid (lacks viscosity) . 



(f) The particular wave being considered does not interact with 

 any other water motions. 



(g) The bed is a horizontal, fixed, impermeable boundary which 

 implies that the vertical velocity at the bed is zero. 



(h) The wave amplitude is small and wave form is invariant in 

 time and space. 



(i) Waves are plane or long crested (two-dimensional) . 



The first three are acceptable for virtually all coastal engineering 

 problems. It will be necessary to relax assumptions (d) , (e), and (f) 

 for some specialized problems not considered in this Manual. Relaxing 

 the three final assumptions is essential in many problems, and is con- 

 sidered later in this chapter. 



2-6 



