13.12: Dispersion of Waves

Once formed, gravity waves keep on truckin’, even after the wind has subsided. The most energetic waves—the longest waves with the longest wave periods—move away from their point of origin faster than shorter waves. Thus, ocean swell with the longest wavelengths and periods separates from the slower waves with short wavelengths and periods, a process called wave dispersion. Most times, short-wavelength waves dissipate near the storm center. But fast-moving ocean swell will continue across the ocean until it meets an obstacle, such as a seamount, an island, or a distant beach.

Because swell sorts out according to its speed, waves of the same speed tend to travel together in a group called a wave train. Depending on the conditions that create swell, wave trains may have anywhere from 3 to 15 waves associated with them. Surfers know a wave train as a wave set, or simply a set—a series of similarly sized waves that arrive at the shore in close progression, one right after the other. Wave trains are the origin of sets. However, it’s simply not true that the seventh wave or the fifth wave or the third wave of a set is the largest. For a number of reasons, there will always be a wave or two that are bigger than the others in a set, but there is no mathematical consistency to which wave it will be. Sorry, dudes.

One of the interesting things about wave trains is that the train moves at half the speed of the individual waves. It’s not terribly important that you know why, but it has to do with the distribution of energy in the wave train. Just like a Tour de France cyclist, the lead wave does all the work.

In any wave the kinetic energy goes into moving water particles in their orbits. As they move, they lift the sea surface and create potential energy. The potential energy of the wave is released when the crest drops, and the released potential energy supplies energy to making wave orbitals—generating kinetic energy—and so on. In a wave train, the first wave has to lift the sea surface on its own. It uses kinetic energy to do that. But the second wave is the recipient of the potential energy generated by the first wave; the raised sea surface falls and releases energy to the second wave. In a wave train, the leading wave diminishes and disappears, but a new wave appears at the end of the train, because potential energy is released by the last wave in the train. In short, this backward trading of energy that goes on in a wave train results in the first wave disappearing and a new wave appearing at the end of the train, so that the forward progress of the entire train is slower. As a result, the group speed—the speed of the wave train—is half the speed of the individual waves.

One way to visualize a wave train is to imagine a conga line of dancers where the lead dancer exits and a new dancer joins the line at the rear when the line advances two steps. Even though individuals advance by two steps, the whole line only makes forward progress one step at a time. Try it at home with friends. Do the conga wave train. (“Come on, shake your body, baby, do the conga wave train!”)

Though swell moves hundreds to thousands of miles across the ocean, there is some loss of energy along the way. Frictional forces will dissipate some of the energy. But energy also dissipates by elongation of the wave front, the “edge” of the wave perpendicular to its direction of travel. The loss of energy due to expansion of the wave front is called spreading loss. Most of the energy generated by a storm, some 90 percent, will travel outward in a cone with an angle of about 30° to 45°. So the greater the distance you are from the vertex (the location where the two rays of the angle intersect), the greater the distance between the two rays, or sides, of the angle.

You can easily see this by making a peace sign with your hand. The distance between the knuckles of your fingers is shorter than the distance between your fingertips. Because swell has a fixed amount of energy, the widening of the wave front causes a reduction in the energy at any point along the wave front. The energy per unit length of wave front decreases with distance from the point of origin of the wave.

Close to the point of origin, spreading loss is minimal. Farther away from the point of origin, spreading loss can be significant. Some 60 percent of the energy of swell (per unit length of wave front) may be lost within the first 500 miles (805 km). That’s why killer surf for Hawaii might not be so epic once it reaches the US West Coast. Spreading loss reduces the size of the swell as it travels outward. The width of the wave front depends on the width of the fetch that created it, the fetch width. Typical storm systems across the ocean may range from 600 to nearly 2,000 miles in horizontal diameter (1,000–3,000 km; e.g., Bierly 2005). Swell-generating fetch will be on a similar scale. Thus, wave fronts for a typical ocean swell may extend hundreds of miles, if not a thousand miles or more, in length. What that means is that waves from a single storm system can affect the entire coastline of the western United States.

Storm systems rarely remain in one place. Generally, storm systems move west to east in both hemispheres, in the direction of the jet streams. Thus, the effective fetch of a storm may be much greater. The swell generated over a period of days will travel outward for the duration of the storm. Large storm systems at great distance may send waves for several days toward coastlines (e.g., Butt 2021).

The movement of storm systems also affects the swell direction—the direction the swell is coming from. Swell direction is identified according to directions on a compass rose, an illustration that depicts the cardinal directions—north, east, south, and west—and the ordinal directions, the points between the cardinal directions—northeast, southeast, southwest, and northwest. Compass directions are always given in degrees of a circle, where north is 0°, east is 90°, south is 180°, and west is 270°. The range of compass directions from which swell may arrive is known as the swell window. Surf forecasters calculate swell windows to determine which beaches may offer the best surfing conditions on a given day.

In California, swell windows may change from northwest to southeast, depending on the time of year. Storms in the North Pacific often occur in the winter and generate swell from west to northwest. In summer, winter storms in the Southern Hemisphere produce swell from the southwest to southeast. Hurricanes off the coast of Mexico swing into action in the summer and occasionally send swell our way. Of course, California has a tough time competing with Hawaii, which has to be one of the best places for surfing in the world. Situated in the middle of the Pacific, Hawaii can experience swell from just about any direction. As a result, there are surfable waves nearly year-round in Hawaii.

Swell direction also proves critical for places where islands or other land features may interfere with swell. Islands can block swell or change its direction. Gaps between the islands mean that some spots are going off, while other spots are snoozy. Because of the Channel Islands, it’s not uncommon for San Diego to experience big waves while Orange County is quiet, or vice versa. The islands produce what is called a swell shadow—a region over which swell is blocked from a particular direction.