Though it is tempting to jump directly into discussing ocean waves — or at least what most of us think of when we visualize the sea — it is worthwhile to begin more slowly with a discussion of the basics of wave theory.

Wave Definitions

There are several components to a basic wave (Figure 7.1.1):

• Still water level: where the water surface would be if there were no waves present and the sea was completely calm.
• Crest: the highest point of the wave.
• Trough: the lowest point of the wave.
• Wave height: the distance between the crest and the trough.
• Wavelength: the distance between two identical points on successive waves, for example crest to crest, or trough to trough.
• Wave steepness: the ratio of wave height to length (H/L). If this ratio exceeds 1/7 (i.e. height exceeds 1/7 of the wavelength) the wave gets too steep, and will likely break. (This will be discussed with more nuance in a future chapter.)

There are also a number of terms used to describe wave motion:

• Period: the time it takes for two successive crests to pass a given point.
• Frequency: the number of waves passing a point in a given amount of time, usually expressed as waves per second. This is the inverse of the period.
• Speed: how fast the wave travels, or the distance traveled per unit of time. This is also called celerity (c), where

c = wavelength  x  frequency

Therefore, the longer the wavelength, the faster the wave.

Types of Waves

Waves generally begin as a disturbance of some kind, and the energy of that disturbance gets propagated in the form of waves. When we think of ocean waves, most of us think of the waves at the surface because they are the ones we can see and have perhaps interacted with when swimming, boating, or sitting at a beach. This course focuses on exactly these waves because they exist and propagate in the precisely location where our engineering applications live — boats, ships, offshore wind turbine platforms, oil rigs, etc — at the surface. 

While we are most familiar with the kind of waves that break on shore, or rock a boat at sea, but there are many other types of waves that are important to oceanography, including but not limited to:

• Internal waves form at the boundaries of water masses of different densities pycnocline, and propagate at depth. These generally move more slowly than surface waves, and can be much larger, with heights exceeding 100 m. However, the height of the deep wave would be unnoticeable at the surface.
• Tidal waves are due to the movement of the tides. What we think of as tides are basically enormously long waves with a wavelength that may span half the globe. Tidal waves are not related to tsunamis, so don’t confuse the two.
• Tsunamis are large waves created as a result of earthquakes or other seismic disturbances. They are also called seismic sea waves.

As mentioned above, waves are created by disturbances. The waves we see at the beach or from the deck of a boat are created by the wind blowing across the surface of the water. We know that waves do not continue growing indefinitely, such that there must be some opposing force. We call this the restoring force. Sometimes the wave at the surface are referred to as wind waves, as shown in Table 7.1.1 below, because of the mechanism by which they are generated. More often these waves are referred to as gravity waves, or wind-driven gravity waves, because of their restoring mechanism. Just as waves vary over a wide range of spatial and temporal domains, there are also variety of mechanisms that act as restoring forces. In fact, many ocean engineers use these restoring mechanisms to categorize wave types, as shown in Table 7.1.1 below.

Table 7.1.1 Waves categorized by restoring mechanism, period (s), and region of activity.