To determine whether a wave is a shallow water wave or a deep water wave, first

Question

To determine whether a wave is a shallow water wave or a deep water wave, first determine its D/L. If its D/L is less than 1/20 then it is a shallow-water wave. If its D/L is greater than 1/2 then it is a deep-water wave. 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)?_______

Explanation / Answer

First of all to know whether the wave is shallow or deep water we will calculate its D/L. If the D/L <1/20 or 0.05 then it is a shallow water wave, whereas if the D/L >0.5 then it is a deep water wave. Since the value of D/L here is 20/20=1 which means that it is greater than 0.5 so it is a deep water wave.

Now H/L = depth of water/wavelength=2/20=0.1. To know whether the deep water wave is breaking wave or not, the steepness or H/L should be known. If the steepness of the wave is greater than 1/7 or 0.14 that means that waves are breaking. Since the H/L is 0.1 which is less than 1/7 or 0.14 so these waves are not breaking waves.

Water depth(m) Wave length(m) Wave height(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 criteria for shallow water breaking wave is D<1.25H which means that the for the shallow water wave to break the depth of water should be less than 1.25 times the height wave. Since for the 2m and the taller waves to break the water depth should be less than 1.25*2=2.5m. So the depth of the underwater rock pile should be 2.5m so to cause 2m and taller waves to break and lesser than 2m waves to pass.

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