CHAPTER 2 



MECHANICS OF WAVE MOTION 



I. INTRODUCTION 



The effects of water waves are of paramount importance in the field of 

 coastal engineering. Waves are the major factor in determining the geometry 

 and composition of beaches and significantly influence the planning and design 

 of harbors, waterways, shore protection measures, coastal structures, and 

 other coastal works. Surface waves generally derive their energy from the 

 winds. A significant amount of this wave energy is finally dissipated in the 

 nearshore region and on the beaches . 



Waves provide an important energy source for forming beaches; sorting 

 bottom sediments on the shoreface; transporting bottom materials onshore, off- 

 shore, and alongshore; and for causing many of the forces to which coastal 

 structures are subjected. An adequate understanding of the fundamental physi- 

 cal processes in surface wave generation and propagation must precede any 

 attempt to understand complex water motion in the nearshore areas of large 

 bodies of water. Consequently, an understanding of the mechanics of wave 

 motion is essential in the planning and design of coastal works. 



This chapter presents an introduction to surface wave theories. Surface 

 and water particle motion, wave energy, and theories used in describing wave 

 transformation due to interaction with the bottom and with structures are 

 described to provide an elementary physical and mathematical understanding of 

 wave motion, and to indicate limitations of selected theories. A number of 

 wave theories have been omitted. References are cited to provide information 

 on theories not discussed and to supplement the theories presented. 



The reader is cautioned that man's ability to describe wave phenomena is 

 limited, especially when the region under consideration is the coastal zone. 

 Thus, the results obtained from the wave theories presented should be care- 

 fully interpreted for application to the actual design of coastal structures 

 or description of the coastal environment. 



II. WAVE MECHANICS 



1. General . 



Waves in the ocean often appear as a confused and constantly changing sea 

 of crests and troughs on the water surface because of the irregularity of wave 

 shape and the variability in the direction of propagation. This is particu- 

 larly true while the waves are under the influence of the wind. The direction 

 of wave propagation can be assessed as an average of the directions of indi- 

 vidual waves. The sea surface is difficult to describe because of the inter- 

 action between individual waves. Faster waves overtake and pass through 

 slower ones from various directions. Waves sometimes reinforce or cancel each 

 other by this interaction, often collide with each other, and are transformed 

 into turbulence and spray. When waves move out of the area where they are 

 directly affected by the wind, they assume a more ordered state with the 

 appearance of definite crests and troughs and with a more rhythmic rise and 



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