If it is a shallow water wave, use the D lessthan 1.25H breaking criterion to de
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Question
If it is a shallow water wave, use the D lessthan 1.25H breaking criterion to determine whether the wave would be breaking at that water depth If it is a deep water wave, then calculate the wave steepness. If the wave steepness is greater than 1/7, that means it is a breaking wave. For this problem we are looking at waves entering an area of very steep bottom, so there is no need to mess with the ugly math that describes "transitional waves. The city of Washaway Beach. Oregon, wants to install an artificial reef to protect their beach from wave erosion during winter storms. They plan to pile rocks underwater just off of the beach so as to cause large storm waves to break before they reach the beach, but still allow small, tourist-friendly waves to break on the beach. So they want the top of their reef to be deep enough to allow waves with heights of less than 2 m to pass over it, but waves 2 m and taller to break on it. Using our simplified shallow-water wave-breaking formula: How deep would the top of their underwater rock pile need to be to cause waves 2 m and taller to break, but waves less than 2 m tall to pass (we will ignore the affect of tides)'? A large earthquake off the coast of the Alaskan Peninsula in 1946 produced a deadly tsunami that reached Hawaii. 4260 km to the south, 6 hours later (see map below). How fast did the tsunami travel in km/hr?Explanation / Answer
Since the deep water wave is that in which the depth of water is greater than one half of the wavelength whereas if is less than half of the wavelength then it is shallow wave. Since the water depth is 20 m and the wavelength is 20 m. Here the depth of water i.e 20 m>10m which is half of the wavelength. So the waves are deep water waves. Also D/L would be 20/20=1.
H/L for the wave=2/20=0.1
To know if these deep water waves are breaking waves or not. If the steepness of these deep water waves i.e(H/L) is greater than 1/7 or 0.14 the wave is a breaking. But since the steepness ratio of the wave is lesser than 0.14 therefore this not a breaking wave
Water depth D (m) Wave length L(m) Wave height H(m) D/L Deep or shallow wave H/L Breaking
20 20 4 1 deep 4/20=0.2 yes
20 20 2 1 deep 2/20=0.1 no
9. The shallow water breaking criteria is D>1.25 H which means that the depth of water should be greater than 1.25 times the height of waves. Since we know that height of waves is 2m. So for that 2m and taller waves to break,the water depth should be greater than 1.25*2=5m.
10. Tsunami are water waves that generate deep in the ocean due to earthquakes or other disturbaces in the water and then these waves move towards the shore. Here the Tsunami moves 4260km to the south in 6 hours.
Speed of Tsunami=Distance travelled/time taken
=4260km/6h=710km/hr
Therefore speed of Tsunami=710km/hr
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