high waves that we would find very impressive while watching the surf crashing ashore.
Meteorological reports typically provide wave periods (T) and wave heights (H). The speed, period, and wavelength of an “ideal” wave are related mathematically. However, it should be understood that the periods and wave heights given in weather reports are “typical” values, meaning they represent the preponderance of waves of various sizes and periods that the mariner may encounter. Thus, the most likely height wave and the most likely period wave bear no mathematical relationship to each other.
The wavelength is related to how fast waves travel but has another useful purpose as a measure of when water is deep for a particular wave. As a rule of thumb, oceanographers say that water is deep if the depth is greater than one-half a wavelength. Since the average depth of the oceans is around 2.5 miles (13,115 feet, or 4,000 meters), for most waves in the open ocean the water is deep and the effect of the wave does not extend more than 300 to 600 feet below the surface. A submarine at this depth would not sense the turbulent seas of a major storm above it; here the sea remains calm. However, there are certain waves—earthquake-produced waves known as tsunami, for example—that have very long wavelengths; thus, even midocean is considered “shallow” for these waves. The passage of such long-wavelength waves roils the entire sea, from the surface to the depths, but this is generally of no major consequence until the wave enters shallow coastal water, where it slows down and piles up into towering and destructive walls of water capable of sweeping all before them.
Another important wave parameter is wave steepness. The steepness is a measure of how dangerous a wave can be. Thus, a very high wave with a short wavelength is said to be very steep. Wind or sea bottom conditions can increase steepness. In contrast, a high wave with a very long wavelength (such as an ocean swell) presents less of a threat to vessels since they can ride up and over the gradual slope. Theoretical studies of the idealized wave shown in Figure 2 indicate that there is a limit to the steepness of a wave traveling in deep water. Once the height of the wave reaches one-seventh of the wavelength, the wave is so steep that it will break.2