HOMEWORK:

1) Show that when the equatorial thermocline tilts (for example, $h_x<0$, where $h$ is the thermocline depth below $z=0$, the location of the ocean surface at rest), the ocean surface height tilts in the opposite way (in this example, $\eta_x<0$, where $\eta$ is the surface elevation relative to $z=0$).  Find the ratio of the amplitudes of the tilts ($\eta_x/h_x$).

2) A storm occurs in the middle of the Pacific ocean at a time $t=0$, exciting all shallow water equatorial modes at a wavelength of 300 km.  Calculate and plot the times of arrival of equatorial wave mode numbers $n=-1,1,2\ldots,10$ at both the eastern and western boundaries, as function of mode number.  Feel free to make reasonable assumptions and approximations as needed.  Hint: Should you use group velocity or phase velocity for this calculation?  Why?