A tsunami is a series of ocean waves generated by the rapid displacement of a massive volume of water, typically resulting from a submarine earthquake or landslide. Unlike common wind-driven waves that only disturb the ocean’s surface, a tsunami involves the movement of the entire water column from the surface to the seafloor. In the deep ocean, tsunamis are characterized by a long wavelength, often hundreds of kilometers, and a low wave height, frequently less than a meter. They travel unnoticed at speeds comparable to a jet airliner. A tsunami is classified as a “shallow-water wave” because its immense wavelength is much larger than the ocean’s depth, meaning its speed is governed solely by the water depth. The dramatic transformation of this wave begins precisely when it encounters the continental shelf, where the ocean floor begins to rise toward the land.
Speed Reduction and Wave Drag
The physical principle dictating a tsunami’s speed is directly tied to the depth of the water. When a tsunami travels across the deep ocean, where depths can be 4,000 meters or more, its speed can exceed 800 kilometers per hour. This speed dramatically changes as the wave encounters the continental shelf, which marks a rapid reduction in the water depth from thousands of meters to just a few hundred.
As the wave moves into this shallower water, the decreasing depth forces a deceleration of the wave front. For example, in water 4,000 meters deep, the wave moves at around 713 kilometers per hour, but in water just 100 meters deep, that speed drops to about 113 kilometers per hour. This rapid reduction in speed means the trailing parts of the wave, which are still traveling faster in deeper water, begin to catch up to the slower front. The increasing proximity of the seafloor also introduces more friction and drag, which further slows the wave. The transformation of the wave is not primarily caused by friction but by the conservation of momentum as the water column height decreases.
Height and Wavelength Changes
The slowing of the tsunami over the continental shelf initiates energy concentration due to the principle of energy conservation. A tsunami carries kinetic energy, and as the wave slows down, this energy must be converted into potential energy, specifically gravitational potential energy. This energy conversion is manifested as a dramatic increase in the wave’s vertical height, or amplitude.
The immense wavelength, which may span 500 kilometers in the open ocean, is simultaneously compressed as the rear of the wave overtakes the front. As the wave moves across the shelf, the wavelength can shrink significantly, sometimes to less than 20 kilometers, causing the water to pile up. This compression and height amplification mean a wave that was imperceptible in the deep ocean can grow from less than one meter to tens of meters in height by the time it reaches the shoreline. The resulting wave often does not resemble a typical breaking surf wave but instead appears as a rapidly advancing tide or a turbulent wall of water known as a bore.
Coastal Run-Up and Inundation
The final stage of the tsunami’s interaction with the land involves draw-down, run-up, and inundation. If the trough of the tsunami wave arrives first, the water recedes dramatically from the shoreline, exposing the seafloor for a significant distance. This phenomenon, known as draw-down, is a natural precursor to the arrival of the wave crest that follows.
Run-up is the maximum vertical height the water reaches above the normal sea level once it hits the shore and rushes inland. The horizontal distance the water travels inland is called inundation. These final effects are highly dependent on the local underwater topography, or bathymetry, and the shape of the coastline.
A gently sloping continental shelf and a shallow bay can focus the wave energy, leading to a much higher run-up in that specific area. Conversely, a steeper continental slope may cause the wave to lose energy more rapidly. Therefore, the destructive power of the tsunami, which is determined by the maximum run-up and inundation distance, can vary widely over just a few miles of coastline due to these localized geographical factors.