The mother of all ocean waves

For ocean voyagers, one of the most important factors that impact travel on the sea is the sea state. There are waves of all sizes and shapes on the ocean, from small locally generated wind waves to larger, longer period swells which propagate away from their generation area.

The recent tsunami generated by the massive earthquake just east of the Japanese island of Honshu affected most of the Pacific Ocean in one way or another. While tsunamis are not meteorological phenomena, they do affect those with interests on and near the oceans, so I thought I would talk about them and their characteristics in this newsletter. Even though tsunamis are not meteorological, in the U.S. both the Pacific Tsunami Warning Center (http://ptwc.weather.gov) and the West Coast and Alaska Tsunami Warning Center (http://wcatwc.arh.noaa.gov) are part of NOAA’s National Weather Service. In Japan, the Japan Meteorological Agency (http://www.jma.go.jp/en/tsunami/) has responsibility for providing warnings. One of the main reasons that these meteorological organizations are involved in warning the public of tsunamis is that they have well-established communication systems in place (to disseminate regularly scheduled weather products) and it makes sense to take advantage of these systems to transmit tsunami information when it is needed.

To discuss tsunamis, I will first talk about the general characteristics of all ocean waves, including tsunamis. All waves can be defined by some basic characteristics. Many of these are familiar to mariners. The wave length is the horizontal distance from crest to crest of a wave. The wave height is the vertical distance from trough to crest of a wave. The wave period is the amount of time it takes for one full wave to pass a given point.

Using the physical properties of water, and knowing the force of gravity, as well as the physics of wave propagation, it is possible to relate the wave characteristics to one another and to some other parameters of interest, most notably the speed of propagation. These relationships depend to some extent on the depth of the water through which the waves are traveling. More particularly, the depth of the water compared to the wave length is important. Without going into the detail of the governing equations, in water which is much deeper than the wave length, the speed of propagation of a wave depends mainly on the period of the wave, and the longer the period, the faster the wave will travel. When waves move into shallower water (usually defined as about one half of the wave length), the speed of the wave depends largely on the depth of the water, and is roughly equal to the square root of the product of the acceleration of gravity and the depth of the water. Basically, this means that waves will travel slower in shallower water.

In terms of ordinary ocean waves that are experienced by mariners, wave periods tend to run from four seconds for smaller wind waves up to as high as 18 to 20 seconds for larger swells. In deep water, these waves will travel at speeds from 12 knots up to 60 knots. Also, these waves will have lengths ranging from about 80 feet up to 2,000 feet. As the waves move from deep water into shallower water, they will slow down, and will become steeper, eventually breaking. This is a process that is easily observed at any beach.

The typical waves that are experienced by mariners are produced by wind stress on the surface of the water. Basically, the wind moves the surface water around and in combination with gravity leads to the rising and falling of the water level. This process leads to the development of waves which propagate in the direction of the wind where they were generated. In the case of a tsunami, the displacement of water which results from a sudden underwater movement of the sea floor is much more massive and affects a much larger area. After this large volume of water is forced upward, gravity will pull it back down again, and the up and down oscillation of the sea surface, thus forming a wave, has begun.

The characteristics of tsunamis are going to follow the same general pattern as the ordinary waves noted above, but on a much different scale. If the sea floor movement covers an area of many miles, the area where the water is displaced will be similar, and this will translate into a wave length that is much longer than that of typical ocean waves. Many tsunamis have lengths of 100 miles or more and periods of several minutes, or even more than an hour. Because of the very long lengths, these waves are considered to be shallow water waves, even in the deepest parts of the ocean. Using the relationship for wave speed in shallow water, if the water in the middle of the ocean is about 14,000 feet deep (average depth of the Pacific), then a tsunami in that area will propagate at over 400 knots.

The wave height of a tsunami in the middle of the ocean is typically quite small, usually on the order of just a couple of feet, corresponding to the amount of displacement that the ocean floor underwent in an earthquake. Thus, in these regions, in combination with the very long wave length, a tsunami will be almost unnoticed. However, when the leading edge of the tsunami moves into shallower water as it approaches islands and coastlines it will slow down while following parts of the wave are still moving at a faster speed. This will cause the length of the wave to become shorter, and the displaced water (which in the deeper water was spread over a very long distance) will be compressed into a shorter distance, resulting in significant growth of the wave height. It’s the same process as when ordinary waves run up toward a beach, shorten, steepen, and break, but on a much larger scale and involving a lot more water.

The recent Pacific tsunami was generated by a huge earthquake, one that reportedly moved the ocean floor many feet. Thus the waves generated had a higher wave height than the “average” tsunami. As these waves moved into the shallow waters of coastal Japan, they slowed down and the heights became so large that they overwhelmed sea walls and other structures which the Japanese, generally very prepared for these phenomena, had constructed. The waves propagated at rapid speeds across the entire Pacific, causing damage for many islands as well as the mainland coasts of North America, Central America, and South America. Waves arrived at the U.S. West Coast around eight hours after the earthquake, and at the southern tip of Chile (over 10,000 miles away) less than 24 hours after the earthquake. These waves were not as high as those that affected Japan because their energy was able to spread out over a larger area before impacting coastal locations.

So, to sum up, tsunamis are ocean waves that have a much longer length than typical ocean waves, a much longer period, but a much shorter wave height when they are in the open ocean. When they move into shallower water in coastal zones, they slow down, and wave heights become significantly higher.

Categories: Weather