82
3 An Introduction to Surface Waves
3.4 Basic Wave Characteristics
3.4.1 Definition of Surface Wave Dimensions
In general, there are many forms of wave type oscillations of water mass in the
ocean. We will start here with the simple form of periodic waves. The water
particle motion resulting from the restoring force acting during one wave cycle
provides the displacing force for the next cycle. Such alternate displacements
and restorations establish oscillatory motion. The simplest form of such motion
is the sinusoidal form.
Consider, for example, a narrow wave tank equipped with a wave-maker at
the end of the tank. A 'snapshot' taken through the glass wall of the tank, or
recording water oscillations at a given point, provides a picture of wave motion
in the tank. In particular, the surface displacement, (, of water particles
from the undisturbed water level varies with distance at a fixed instant of time
(Fig. 3.2a), as well as varying with time at a fixed point in the tank (Fig. 3.2b).
A simulation given in computer program D.31 (see Appendix D) clarifies the
difference between representations of wave motion in both time and space.
The basic horizontal wave dimension is a wavelength, L. This is the distance
between two successive crests (or two successive troughs). On the other hand,
wave height, H, is the overall vertical change in surface displacement between
the wave crest and the wave trough. For a sinusoidal profile, the wave height
is twice the wave amplitude, A. The wave profiles observed in nature usually
show some asymmetry with respect to the still water level and the wave crests
are larger than the troughs. However, the wave height is always the sum of
the wave crest and wave trough elevations. The ratio of wave height, H, and
wavelength, L, is known as the wave steepness, s = H / L.
For later convenience we will introduce another quantity related to wavelength, namely the wave number, k, such that:
27r
k=-.
L
(3.1)
From a physical point of view, the wave number, k, represents the number of
waves per unit length.
Let us now consider a time history of wave profile changes at a fixed point
in the wave tank. This history will also have a periodic character, however,
instead of distance as the horizontal axis, we now have a time axis (Fig. 3.2b).
The time interval between two successive crests (or two successive troughs)
passing a fixed point is known as the wave period, T. The number of crests
(or number of troughs) which pass a fixed point per second is called the frequency, f. Thus,
1
f =-.
T
(3.2)
3 An Introduction to Surface Waves
3.4 Basic Wave Characteristics
3.4.1 Definition of Surface Wave Dimensions
In general, there are many forms of wave type oscillations of water mass in the
ocean. We will start here with the simple form of periodic waves. The water
particle motion resulting from the restoring force acting during one wave cycle
provides the displacing force for the next cycle. Such alternate displacements
and restorations establish oscillatory motion. The simplest form of such motion
is the sinusoidal form.
Consider, for example, a narrow wave tank equipped with a wave-maker at
the end of the tank. A 'snapshot' taken through the glass wall of the tank, or
recording water oscillations at a given point, provides a picture of wave motion
in the tank. In particular, the surface displacement, (, of water particles
from the undisturbed water level varies with distance at a fixed instant of time
(Fig. 3.2a), as well as varying with time at a fixed point in the tank (Fig. 3.2b).
A simulation given in computer program D.31 (see Appendix D) clarifies the
difference between representations of wave motion in both time and space.
The basic horizontal wave dimension is a wavelength, L. This is the distance
between two successive crests (or two successive troughs). On the other hand,
wave height, H, is the overall vertical change in surface displacement between
the wave crest and the wave trough. For a sinusoidal profile, the wave height
is twice the wave amplitude, A. The wave profiles observed in nature usually
show some asymmetry with respect to the still water level and the wave crests
are larger than the troughs. However, the wave height is always the sum of
the wave crest and wave trough elevations. The ratio of wave height, H, and
wavelength, L, is known as the wave steepness, s = H / L.
For later convenience we will introduce another quantity related to wavelength, namely the wave number, k, such that:
27r
k=-.
L
(3.1)
From a physical point of view, the wave number, k, represents the number of
waves per unit length.
Let us now consider a time history of wave profile changes at a fixed point
in the wave tank. This history will also have a periodic character, however,
instead of distance as the horizontal axis, we now have a time axis (Fig. 3.2b).
The time interval between two successive crests (or two successive troughs)
passing a fixed point is known as the wave period, T. The number of crests
(or number of troughs) which pass a fixed point per second is called the frequency, f. Thus,
1
f =-.
T
(3.2)