Consider a shallow-water wave of length 1.5km propagating in anocean 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 whichthere is a current of strength U that opposes the wave propagation.Explain how this modifies the dispersion relation and the wavespeed. (2P)
c) Assuming that the wave’s frequency ω remains constant, createa plot of the wavelength λ as a function of the current speed U. AsU 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 thespeed of the current U approaches the phase speed C that youcalculated in part a? Is this physical? What behavior would youexpect to see in real, nonlinear waves if they encountered such acurrent? (3P)
