waves (Sec. II, 5, c), or the fact that wave crests depart farther from the mean 

 water level (MWL) than do the troughs. More general theories such as fin-ite- 

 amplitude, or nonlinear wave theories are required to account for these 

 phenomena as well as most interactions between waves and other flows. Non- 

 linear wave theories also permit 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 the waveform is invariant in 

 time and space. 



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



The first three assumptions are acceptable for virtually all coastal engineer- 

 ing 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 considered later in 

 this chapter. 



In applying assumption (g) to waves in water of varying depth as is 

 encountered when waves approach a beach, the local depth is usually used. 

 This can be justified, but not without difficulty, for most practical cases in 

 which the bottom slope is flatter than about 1 on 10. A progressive wave 

 moving into shallow water will change its shape significantly. Effects due to 

 viscosity and vertical velocity on a permeable bottom may be measurable in 

 some situations, but these effects can be neglected in most engineering 

 problems. 



3. Elementary Progressive Wave Theory (Small-Amplitude Wave Theory) . 



The most fundamental description of a simple sinusoidal oscillatory wave 

 is by its length L (the horizontal distance between corresponding points on 

 two successive waves), height H (the vertical distance to its crest from the 

 preceding trough), period T (the time for two successive crests to pass a 



2-6 



