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 fall. These
waves may travel hundreds or thousands of miles after leaving the area in
which they were generated. Wave energy is dissipated internaily within
the fluid by interaction with the air above, by turbulence on breaking,
and at the bottom in shallow depths.
Waves which reach Coastal régions expend a large part of their energy
in the nearshore région. As the wave nears the shore, wave energy may be
dissipated as heat through turbulent fluid motion induced by breaking and
through bottom friction and percolation. While the heat is of little
concern to the Coastal engineer, breaking is important since it affects
both beaches and manmade shore structures. Thus, shore protection measures
and Coastal structure designs are dépendent on the ability to predict wave
forms and fluid motion beneath waves, and on the reliability of such
prédictions. Prédiction methods generally hâve been based on simple waves
where elementary mathematical functions can be used to describe wave motion
For some situations, simple mathematical formulas predict wave conditions
well, but for other situations prédictions may be unsatisfactory for
engineering applications. Many theoretical concepts hâve evolved in the
past two centuries for describing complex sea waves; however, complété
agreement between theory and observation is not always found.
In general, actual water-wave phenomena are complex and difficult
to describe mathematically because of nonlinearities, three-dimensional
characteristics and apparent random behavior. However, there are two
classical théories, one developed by Airy (1845) and the other by Stokes
(1880), that describe simple waves. The Airy and Stokes théories generally predict wave behavior better where water depth relative to wavelength
is not too small. For shallow water, a cnoidal wave theory often provides
an acceptable approximation of simple waves. For very shallow water near
the breaker zone, solitary wave theory satisfactorily predicts certain
features of the wave behavior. These théories will be described according
to their fundamental characteristics together with the mathematical équations which describe wave behavior. Many other wave théories hâve been
presented in the literature which, for some spécifie situations, may predict wave oehavior more satisfactorily than the théories presented here.
These other théories are not included, since it is beyond the scope of
this Manual to cover ail théories.
The most elementary wave theory, referred to as small-amplitude or
linear wave theory, was developed by Airy (1845). It is of fundamental
importance since it not only is easy to apply, but is reliable over a
large segment of the whole wave régime. Mathematically, the Airy theory
can be considered a first approximation of a complété theoretical description o wave behavior. A more complété theoretical description of waves
may e o tained as the sum of an infinité number of successive approximations, h ere each additional term in the sériés is a correction to preceding terms. For some situations, waves are better described by these
ig er or er théories which are usually referred to as finite amplitude
2-2
by the wind, they assume a more ordered State with the appearance of
definite crests and troughs and with a more rhythmic rise and fall. These
waves may travel hundreds or thousands of miles after leaving the area in
which they were generated. Wave energy is dissipated internaily within
the fluid by interaction with the air above, by turbulence on breaking,
and at the bottom in shallow depths.
Waves which reach Coastal régions expend a large part of their energy
in the nearshore région. As the wave nears the shore, wave energy may be
dissipated as heat through turbulent fluid motion induced by breaking and
through bottom friction and percolation. While the heat is of little
concern to the Coastal engineer, breaking is important since it affects
both beaches and manmade shore structures. Thus, shore protection measures
and Coastal structure designs are dépendent on the ability to predict wave
forms and fluid motion beneath waves, and on the reliability of such
prédictions. Prédiction methods generally hâve been based on simple waves
where elementary mathematical functions can be used to describe wave motion
For some situations, simple mathematical formulas predict wave conditions
well, but for other situations prédictions may be unsatisfactory for
engineering applications. Many theoretical concepts hâve evolved in the
past two centuries for describing complex sea waves; however, complété
agreement between theory and observation is not always found.
In general, actual water-wave phenomena are complex and difficult
to describe mathematically because of nonlinearities, three-dimensional
characteristics and apparent random behavior. However, there are two
classical théories, one developed by Airy (1845) and the other by Stokes
(1880), that describe simple waves. The Airy and Stokes théories generally predict wave behavior better where water depth relative to wavelength
is not too small. For shallow water, a cnoidal wave theory often provides
an acceptable approximation of simple waves. For very shallow water near
the breaker zone, solitary wave theory satisfactorily predicts certain
features of the wave behavior. These théories will be described according
to their fundamental characteristics together with the mathematical équations which describe wave behavior. Many other wave théories hâve been
presented in the literature which, for some spécifie situations, may predict wave oehavior more satisfactorily than the théories presented here.
These other théories are not included, since it is beyond the scope of
this Manual to cover ail théories.
The most elementary wave theory, referred to as small-amplitude or
linear wave theory, was developed by Airy (1845). It is of fundamental
importance since it not only is easy to apply, but is reliable over a
large segment of the whole wave régime. Mathematically, the Airy theory
can be considered a first approximation of a complété theoretical description o wave behavior. A more complété theoretical description of waves
may e o tained as the sum of an infinité number of successive approximations, h ere each additional term in the sériés is a correction to preceding terms. For some situations, waves are better described by these
ig er or er théories which are usually referred to as finite amplitude
2-2