What are tsunamis?

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Special Public Seminar on Earthquakes and TsunamisTsunami from the Perspective of Ocean Waves Professor K. W. Chow Department of Mechanical Engineering University of Hong Kong

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GOAL: Try to understand how tsunamis can cause so much damage and destruction from the perspective of ocean waves: (A) water waves in the open oceans, (B) their dynamics near the seashore.

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General ideas about wave motion Very often, a ‘fluid’ (liquid or gas) transmits energy and information by small disturbances or waves. Sound waves – a sequence of compressions and relaxations in a gas.

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How about waves in water?Try to classify them through the periods of wave motion: (1) We jump up and return to the ground in a few seconds, due to gravity. The same principle applies to water particles. Hence ordinary gravity waves on the sea surface have a period of a few seconds. (2) Tides have periods of roughly 12 hours. (3) Anything in between?

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In fact a whole spectrum of wave motions is possible:

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IMPLICATIONS:

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What are tsunamis?Commonly asked questions: (1) How high do the waves need to be to qualify as a ‘tsunami’? (2) Will we see a 10-meter high wall of water in the open ocean? (3) Waves shown in television news reports are not particularly huge, why are they so damaging? (4) Will I see a 10-foot tsumami in Hong Kong?

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These are not the most appropriate questions. The proper question to ask, perhaps, is: How can Nature transfer a huge amount of energy from the epicenter to the coast through water waves?

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The answer: Through ‘long oceanic waves’, since such long waves are: (1) moving very fast; (2) non-dispersive; and (3) can excite motion through a large depth of water. Results: most dissipation mechanisms (geometry, friction, scattering…) do not have time to attenuate this flow of energy.

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Moving Fast?? (1) Generally, any disturbance or pattern in water consists of various components with different wavelengths. (2) Water waves: Long waves travel at a HIGH velocity. Short waves travel at a LOW velocity.

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Long waves are thus the first wave group observed at the coast. All long wave components travel at the speed of square root (g H), where g = acceleration due to gravity, 9.8 m s–2, H = water depth.

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For the Japan earthquake: (1) At a depth of around 1000 meters, the speed is around 100 m s–1. Speed of a Boeing 747 at cruising altitude is approximately 150 – 250 m s–1. (2) At the shore, the depth is zero. Let us simplify the dynamics by taking an ‘average depth’ of 500 meters, an average speed is then 70 m s–1. (3) Time to travel 100 km ≈ 1400 seconds ≈ 23 minutes!!

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THANK YOU

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Non-dispersive?? Dispersion of white light (sunlight) into components: as light rays of different colors have different refractive indices (or speeds) inside the glass prism.

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DISPERSION (1) Components of different wavelengths move with different speeds. (2) Example: Many students are walking to the canteen. If they all walk at the same speed, they arrive at the same time. If each student walks at a different speed, the group will ‘disperse’.

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DispersionIf dispersion is present, the pulse broadens.Animation courtesy of Dr. Dan Russell, Kettering University

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Long waves are non–dispersive In the case of water waves, all long waves travel at the same speed (= square root of (g H)), and are thus non–dispersive. The various long wave components do NOT separate from each other, and pound on the coast at the same time.

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Particle paths?? As the wave form progresses, each particle oscillates in a circular or elliptic path, with dimensions decreasing with depth.

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IMPLICATIONS:Dimensions of particle trajectories decrease exponentially as we go deeper into the fluid. Typically these paths will become very small at a water depth larger than a few wavelengths.

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A water wave moving from left to right. Each particle moves in an elliptical path of decreasing dimension.

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For short waves of say 1 meter, water motion is negligible in water deeper than say 5 meters. Motions in such a small region are easily scattered or dissipated.

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For long waves of say 10 km (which is greater than the ocean depth), this motion will persist throughout most of the ocean!!

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Last Updated: 8th March 2018

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