Océan waves are complex. Many aspects of fluid mechanics necessary
to a complété discussion hâve only a minor influence on solving most
Coastal engineering problems. Thus, a simplified theory which omits most
of the complicating factors is useful. The assumptions made in developing
the simple theory should be understood, because not ail of the assumptions
are justified in ail problems. When an assumption is not valid in a
particular problem, a more complété theory should be employed.
The most restrictive of common assumptions is that waves are small
perturbations on the surface of a fluid which is otherwise at rest. This
leads to a wave theory which is variously called, small-amplitude theory,
linear theory, or Airy theory. The small-amplitude theory provides insight for ail periodic wave behavior and a description of the periodic flow
adéquate for most practical problems. This theory is unable to account for
mass transport due to waves (Section 2.253 Mass Transport Velocity), or the
fact that wave crests départ further from the mean water level than do the
troughs. A more general theory, usually called the finite covpZi/tude3 or
nonlinear wave theory is required to account for these phenomena as well as
most interactions between waves and other flows. The nonlinear wave theory
also permits a more accurate évaluation of some wave properties than can be
obtained with linear theory.
Several assumptions, commonly made in developing a simple wave theory
are listed below.
(a) The fluid is homogeneous and incompressible; therefore, the
density p is a constant.
(b)
Surface tension can be neglected.
(c)
Coriolis effect can be neglected.
(d)
Pressure at the free surface is uniform and constant.
(e)
The fluid is idéal or inviscid (lacks viscosity).
(f) The particular wave being considered does not interact with
any other water motions.
(g) The bed is a horizontal, fixed, imperméable boundary which
implies that the vertical velocity at the bed is zéro.
(h) The wave amplitude is small and wave form is invariant in
time and space.
(i)
Waves are plane or long crested (two-dimensional).
nrohi^r tb"ea"acceptable for virtually ail Coastal engineering
problems. It will be necessary to relax assumptions (d), (e), and (fl
the three'fîn1?
d proble"ls not considered in this Manual. Relaxing
side^ed î.tèr Jnathl"’PtiOnS “ essential in manX Problems, and is consiaerea later in this chapter.
2-6
to a complété discussion hâve only a minor influence on solving most
Coastal engineering problems. Thus, a simplified theory which omits most
of the complicating factors is useful. The assumptions made in developing
the simple theory should be understood, because not ail of the assumptions
are justified in ail problems. When an assumption is not valid in a
particular problem, a more complété theory should be employed.
The most restrictive of common assumptions is that waves are small
perturbations on the surface of a fluid which is otherwise at rest. This
leads to a wave theory which is variously called, small-amplitude theory,
linear theory, or Airy theory. The small-amplitude theory provides insight for ail periodic wave behavior and a description of the periodic flow
adéquate for most practical problems. This theory is unable to account for
mass transport due to waves (Section 2.253 Mass Transport Velocity), or the
fact that wave crests départ further from the mean water level than do the
troughs. A more general theory, usually called the finite covpZi/tude3 or
nonlinear wave theory is required to account for these phenomena as well as
most interactions between waves and other flows. The nonlinear wave theory
also permits a more accurate évaluation of some wave properties than can be
obtained with linear theory.
Several assumptions, commonly made in developing a simple wave theory
are listed below.
(a) The fluid is homogeneous and incompressible; therefore, the
density p is a constant.
(b)
Surface tension can be neglected.
(c)
Coriolis effect can be neglected.
(d)
Pressure at the free surface is uniform and constant.
(e)
The fluid is idéal or inviscid (lacks viscosity).
(f) The particular wave being considered does not interact with
any other water motions.
(g) The bed is a horizontal, fixed, imperméable boundary which
implies that the vertical velocity at the bed is zéro.
(h) The wave amplitude is small and wave form is invariant in
time and space.
(i)
Waves are plane or long crested (two-dimensional).
nrohi^r tb"ea"acceptable for virtually ail Coastal engineering
problems. It will be necessary to relax assumptions (d), (e), and (fl
the three'fîn1?
d proble"ls not considered in this Manual. Relaxing
side^ed î.tèr Jnathl"’PtiOnS “ essential in manX Problems, and is consiaerea later in this chapter.
2-6