EM 1110-2-1100 (Part II)
30 Apr 02
Water Wave Mechanics
a. Waves on the surface of the ocean with periods of 3 to 25 sec are primarily generated by winds and
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.
b. Knowledge of these waves and the forces they generate is essential for the design of coastal projects
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
c. In the Regular Waves section, the objective is to provide a detailed understanding of the mechanics
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.
d. In looking at the sea surface, it is typically irregular and three-dimensional (3-D). The sea surface
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.
e. The Regular Waves section of this chapter begins with the simplest mathematical representation
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
f. The Irregular Waves section of this chapter is devoted to an alternative description of ocean waves.
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
Irregular Waves section employs statistical and probabilistic theories. Even with this approach,
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