A storm generates large waves in the Pacific Ocean. On November 25, 2008, 6pm, s

Question

A storm generates large waves in the Pacific Ocean. On November 25, 2008, 6pm, swell with a wave height of 5m reaches an exposed location at the coast of Southern California. At 6am of the next day, the wave height is 4m. The water depth within 100 km of the coast is 1000 m and 3000 m everywhere else. All waves have a steepness of ak=0.25. [For formulas please refer to notes from the lecture slides].
a) How far offshore were the waves generated by that storm?
b) How long did it take the waves to travel from the storm area, where they were generated, to the coast?
c) At what date and time do waves with a height of 2m reach the same location at the coast?
d) How long does it take a tsunami with a wave

Explanation / Answer

Wave ht at 6pm - 5m

After 12 hrs at 6am - 4m

Water depth - 3000m and 1000m near the coast.

Wave steepness (ak) =0.25

Calculations -

a) According to the data given, storm generated will depend on the wind speed and other factors such as pressure , temperature etc. Considering the steepness of wave as 0.25 and the wave ht at different periods being 5 or 5m , the distance between the coast and storm source is more than 60 km.

b) It took more than 2 days for the waves to travel from the storm source to the coast.

c)Wave reaches the coast on 27th November around 6am in the morning.

d)Tsunamis are unlike wind-generated waves , with long periods and wave lengths. It usually has a wavelength in excess of 100 km and period on the order of one hour.

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