Question

Consider a shallow-water wave of length 1.5km propagating in an ocean that is 62.5m deep . The speed of the wave is 25m/s and the period T= 60 sec .

a) 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.

b) 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?

c) 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?

Answer 1