Understanding the Physics of Tsunamis

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In summary, the speed of a tsunami is determined by the gravitational constant and the depth of the ocean, which is different from the constant speed of normal surface ocean waves. The derivation of the tsunami velocity equation can be found in the linear theory of ocean surface waves, specifically using equations 16.5 and 16.6. More information about ocean waves and tsunamis can be found in chapter 17 of the oceanography textbook.
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lagrange
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I read that the speed of a tsunami is given by

c = sqrt(G * d)

where G is the gravitational constant 9.8 m/sec^2 and
d is ocean depth in meters.

How is this derived? I had always thought that wave speed was a constant depending only on the medium.

Also, is there some fundamental mechanical difference between a tsunami and a "normal" surface ocean wave?
 
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Do you also know the formula for the height of the wave. (Of course in respect to the clifs stepping.)
 
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Hello lagrange,

The behaviour of tsunami is the behaviour of shallow-water waves.
Therefor the velocity of the waves is given by the equation for the shallow-water phase- and group velocity.

Here you'll find the linear theory of ocean surface waves:
http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_01.htm

The shallow-water velocity equation (16.8) and (16.11) in this paper are derived using the equations (16.5)and (16.6).

More about ocean waves and tsunami:
http://oceanworld.tamu.edu/resources/ocng_textbook/chapter17/chapter17_02.htm
 

1. How is the speed of a tsunami calculated?

The speed of a tsunami is calculated using the formula: speed = wavelength / period. The wavelength is the distance between two consecutive wave crests, and the period is the time it takes for one full wave cycle to pass. This calculation assumes that the water depth remains constant.

2. What factors affect the speed of a tsunami?

The speed of a tsunami can be affected by several factors such as the depth of the water, the distance from the earthquake source, and the shape of the coastline. In deeper water, the tsunami will travel faster, while shallower water can slow down the wave. The distance from the earthquake source also plays a role, as the longer the distance, the more the tsunami will spread out and decrease in speed. Additionally, the shape of the coastline can cause the wave to refract or reflect, altering its speed and direction.

3. Can the speed of a tsunami be predicted?

The speed of a tsunami can be estimated based on the characteristics of the earthquake that caused it, such as the magnitude and location. However, it is challenging to accurately predict the exact speed of a tsunami as it can be influenced by various factors such as local topography and ocean currents.

4. How does the speed of a tsunami compare to the speed of a regular ocean wave?

The speed of a tsunami is much faster than the speed of a regular ocean wave. While the speed of an ocean wave may range from 10-60 km/h, the speed of a tsunami can reach up to 800 km/h in deep water.

5. Are there any technologies used to measure the speed of a tsunami in real-time?

Yes, there are technologies such as deep-water buoys and coastal tide gauges that can measure the speed of a tsunami in real-time. These devices use sensors to detect changes in water level and pressure caused by the tsunami, providing valuable data for early warning systems.

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