Consider a shallow-water wave of length 1.5km propagating in an ocean that is 62.5m deep. a)...

Consider a shallow-water wave of length 1.5km propagating in an ocean that is 62.5m deep.

a) Calculate the wave’s speed C and period T. (3P)

b) Now suppose that this wave propagates into a region in which there is a current of strength U that opposes the wave propagation. Explain how this modifies the dispersion relation and the wave speed. (2P)

c) Assuming that the wave’s frequency ω remains constant, create a plot of the wavelength λ as a function of the current speed U. As U increases, what do you expect to happen to
i) the wave’s length?
ii) the wave’s amplitude?

iii) the wave’s steepness? (5P)

d) Still assuming that ω remains constant, what happens as the speed of the current U approaches the phase speed C that you calculated in part a? Is this physical? What behavior would you expect to see in real, nonlinear waves if they encountered such a current? (3P)

Expert Solution

genius_generous answered 1 year ago

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