EM 1110-2-1100 (Part II)
30 Apr 02
allows treatment of the variability of waves with respect to period and direction of travel. The second
approach is to describe a wave record at a point as a sequence of individual waves with different heights and
periods and then to consider the variability of the wave field in terms of the probability of individual waves.
g. At the present time, practicing coastal engineers must use a combination of these approaches to obtain
information for design. For example, information from the Irregular Waves section will be used to determine
the expected range of wave conditions and directional distributions of wave energy in order to select an
individual wave height and period for the problem under study. Then procedures from the Regular Waves
section will be used to characterize the kinematics and dynamics that might be expected. However, it should
be noted that the procedures for selecting and using irregular wave conditions remain an area of some
uncertainty.
h. The major generating force for waves is the wind acting on the air-sea interface. A significant
amount of wave energy is dissipated in the nearshore region and on beaches. Wave energy forms beaches;
sorts bottom sediments on the shore face; transports bottom materials onshore, offshore, and alongshore; and
exerts forces upon coastal structures. A basic understanding of the fundamental physical processes in the
generation and propagation of surface waves must precede any attempt to understand complex water motion
in seas, lakes and waterways. The Regular Waves section of this chapter outlines the fundamental principles
governing the mechanics of wave motion essential in the planning and design of coastal works. The Irregular
Waves section of this chapter discusses the applicable statistical and probabilistic theories.
i. Detailed descriptions of the basic equations for water mechanics are available in several textbooks
(see for example, Kinsman 1965; Stoker 1957; Ippen 1966; Le Mhaut 1976; Phillips 1977; Crapper 1984;
Mei 1991; Dean and Dalrymple 1991). The Regular Waves section of this chapter provides only an
introduction to wave mechanics, and it focuses on simple water wave theories for coastal engineers. Methods
are discussed for estimating wave surface profiles, water particle motion, wave energy, and wave
transformations due to interaction with the bottom and with structures.
j. The simplest wave theory is the first-order, small-amplitude, or Airy wave theory which will hereafter
be called linear theory. Many engineering problems can be handled with ease and reasonable accuracy by
this theory. For convenience, prediction methods in coastal engineering generally have been based on simple
waves. For some situations, simple theories provide acceptable estimates of wave conditions.
k. When waves become large or travel toward shore into shallow water, higher-order wave theories are
often required to describe wave phenomena. These theories represent nonlinear waves. The linear theory
that is valid when waves are infinitesimally small and their motion is small also provides some insight for
finite-amplitude periodic waves (nonlinear). However, the linear theory cannot account for the fact that wave
crests are higher above the mean water line than the troughs are below the mean water line. Results obtained
from the various theories should be carefully interpreted for use in the design of coastal projects or for the
description of coastal environment.
l. Any basic physical description of a water wave involves both its surface form and the water motion
beneath the surface. A wave that can be described in simple mathematical terms is called a simple wave.
Waves comprised of several components and difficult to describe in form or motion are termed wave trains
or complex waves. Sinusoidal or monochromatic waves are examples of simple waves, since their surface
profile can be described by a single sine or cosine function. A wave is periodic if its motion and surface
profile recur in equal intervals of time termed the wave period. A wave form that moves horizontally relative
to a fixed point is called a progressive wave and the direction in which it moves is termed the direction of
wave propagation. A progressive wave is called wave of permanent form if it propagates without
experiencing any change in shape.
II-1-2
Water Wave Mechanics
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