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3 An Introduction to Surface Waves
The size of wind generated waves is governed by the wind speed, Vw , wind
fetch, X, over which the wind blows and the length of time, t, the wind has
been blowing. In a sea of limited water depth, the wave size also depends on
water depth, h. To clarify how the combination of these parameters contributes
to wave growth in space and time, consider two points A and B on the sea
surface, at distances XA and XB from the shore, respectively, with wind of a
constant speed, Vw , blowing normally towards the shore. At the point A, for
time t < tA, waves are growing and at some time, tA, a saturation stage for
the given fetch, XA, and wind speed, Vw , is reached in which no more energy is
being received from the wind (see Fig. 3.9a). At the same time, wave energy
can still increase at the point B, which is located further from the shore line.
At time t > tA, wave height at a point A remains constant and is controlled by
fetch XA and wind speed Vw (more precisely by non-dimensional combination
9XA/V~), while for t < tA the wave height is controlled by duration time (more
precisely, by the non-dimensional duration time gt/Vw ). The first case (t > tA)
is called the fetch-limited stage of wave growth while the second case (t < tA)
is the time-limited stage of wave growth.
Consider now two instants of time, tA, and, tB, recalling that the wind has
been blowing at a constant speed, Vw . At time tA, the saturation stage reaches
point A, located at a distance XA from the shore, while at time tB, the saturation stage is a distance XB from the shore (see Fig. 3.9b). Therefore, we can
say that for X < XA, wave field is fetch-limited stage of wave growth and for
X > XA it becomes a time-limited stage of wave growth.
If the wind blows long enough, an equilibrium is eventually reached in which
energy is dissipated by the waves at the same rate as the waves receive energy
from the wind. Such a sea state is called a fully developed sea, in which
the size and characteristics of the waves are not changing. However, because
of wind speed variation, the ideal fully developed sea rarely occurs.
The relationships between the non-dimensional combinations (gX /V~) and
(gt/Vw ), and the resulting wave height, wave period and wave velocity for practical calculations, are given in the next chapter. Here we will only mention a
much simpler representation of this relationship, namely the traditional Beaufort Scale, which links wind speed with the state of the sea surface in grades
from 0 to 12 (see Table 3.1). In Table 3.1, wind speed is given in m/s and
knots (for definition of knots see Appendix B).
Even when there is no wind, the sea surface is not perfectly still. A more careful observer can notice waves of very large wavelength and sometimes only a few
centimeters amplitude. Such waves are known as swell, presumably because
of their smoother appearance. They are simply waves that have been generated elsewhere and have travelled far from their place of origin. Swell waves
are remarkably conservative; they can travel long distances without substantial
attenuation.
There is some experimental evidence that swell can travel nearly halfway
around the world, starting east of Australia and moving south, past New
3 An Introduction to Surface Waves
The size of wind generated waves is governed by the wind speed, Vw , wind
fetch, X, over which the wind blows and the length of time, t, the wind has
been blowing. In a sea of limited water depth, the wave size also depends on
water depth, h. To clarify how the combination of these parameters contributes
to wave growth in space and time, consider two points A and B on the sea
surface, at distances XA and XB from the shore, respectively, with wind of a
constant speed, Vw , blowing normally towards the shore. At the point A, for
time t < tA, waves are growing and at some time, tA, a saturation stage for
the given fetch, XA, and wind speed, Vw , is reached in which no more energy is
being received from the wind (see Fig. 3.9a). At the same time, wave energy
can still increase at the point B, which is located further from the shore line.
At time t > tA, wave height at a point A remains constant and is controlled by
fetch XA and wind speed Vw (more precisely by non-dimensional combination
9XA/V~), while for t < tA the wave height is controlled by duration time (more
precisely, by the non-dimensional duration time gt/Vw ). The first case (t > tA)
is called the fetch-limited stage of wave growth while the second case (t < tA)
is the time-limited stage of wave growth.
Consider now two instants of time, tA, and, tB, recalling that the wind has
been blowing at a constant speed, Vw . At time tA, the saturation stage reaches
point A, located at a distance XA from the shore, while at time tB, the saturation stage is a distance XB from the shore (see Fig. 3.9b). Therefore, we can
say that for X < XA, wave field is fetch-limited stage of wave growth and for
X > XA it becomes a time-limited stage of wave growth.
If the wind blows long enough, an equilibrium is eventually reached in which
energy is dissipated by the waves at the same rate as the waves receive energy
from the wind. Such a sea state is called a fully developed sea, in which
the size and characteristics of the waves are not changing. However, because
of wind speed variation, the ideal fully developed sea rarely occurs.
The relationships between the non-dimensional combinations (gX /V~) and
(gt/Vw ), and the resulting wave height, wave period and wave velocity for practical calculations, are given in the next chapter. Here we will only mention a
much simpler representation of this relationship, namely the traditional Beaufort Scale, which links wind speed with the state of the sea surface in grades
from 0 to 12 (see Table 3.1). In Table 3.1, wind speed is given in m/s and
knots (for definition of knots see Appendix B).
Even when there is no wind, the sea surface is not perfectly still. A more careful observer can notice waves of very large wavelength and sometimes only a few
centimeters amplitude. Such waves are known as swell, presumably because
of their smoother appearance. They are simply waves that have been generated elsewhere and have travelled far from their place of origin. Swell waves
are remarkably conservative; they can travel long distances without substantial
attenuation.
There is some experimental evidence that swell can travel nearly halfway
around the world, starting east of Australia and moving south, past New