are a fundamental feature of coastal regions of the world. Other wave motions exist on the ocean including

internal waves, tides, and edge waves. For the remainder of this chapter, unless otherwise indicated, the term

waves will apply only to surface gravity waves in the wind wave range of 3 to 25 sec.

since they are the major factor that determines the geometry of beaches, the planning and design of marinas,

waterways, shore protection measures, hydraulic structures, and other civil and military coastal works.

Estimates of wave conditions are needed in almost all coastal engineering studies. The purpose of this chapter

is to give engineers theories and mathematical formulae for describing ocean surface waves and the forces,

accelerations, and velocities due to them. This chapter is organized into two sections: *Regular Waves *and

of a wave field through examination of waves of constant height and period. In the *Irregular Waves *section,

the objective is to describe statistical methods for analyzing irregular waves (wave systems where successive

waves may have differing periods and heights) which are more descriptive of the waves seen in nature.

changes in time, and thus, it is unsteady. At this time, this complex, time-varying 3-D surface cannot be

adequately described in its full complexity; neither can the velocities, pressures, and accelerations of the

underlying water required for engineering calculations. In order to arrive at estimates of the required

parameters, a number of simplifying assumptions must be made to make the problems tractable, reliable and

helpful through comparison to experiments and observations. Some of the assumptions and approximations

that are made to describe the 3-D, time-dependent complex sea surface in a simpler fashion for engineering

works may be unrealistic, but necessary for mathematical reasons.

assuming ocean waves are two-dimensional (2-D), small in amplitude, sinusoidal, and progressively

definable by their wave height and period in a given water depth. In this simplest representation of ocean

waves, wave motions and displacements, kinematics (that is, wave velocities and accelerations), and dynamics

(that is, wave pressures and resulting forces and moments) will be determined for engineering design

estimates. When wave height becomes larger, the simple treatment may not be adequate. The next part of

the *Regular Waves *section considers 2-D approximation of the ocean surface to deviate from a pure sinusoid.

This representation requires using more mathematically complicated theories. These theories become

nonlinear and allow formulation of waves that are not of purely sinusoidal in shape; for example, waves

having the flatter troughs and peaked crests typically seen in shallow coastal waters when waves are relatively

high.

Statistical methods for describing the natural time-dependent three-dimensional characteristics of real wave

systems are presented. A complete 3-D representation of ocean waves requires considering the sea surface

as an irregular wave train with random characteristics. To quantify this randomness of ocean waves, the

simplifications are required. One approach is to transform the sea surface using Fourier theory into

summation of simple sine waves and then to define a wave's characteristics in terms of its spectrum. This

Water Wave Mechanics

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