 Solution

Use Earth's rotation rate $\Omega =7.292\times 10^{-5}{\mathrm{s}}^{-1}$ and the Coriolis parameter $f=2\Omega \sin \varphi$. At $|\varphi |=10^{\circ }$,The Kelvin waves propagate polewards along the eastern boundary: northwards at $10^{\circ }$ N and southwards at $10^{\circ }$ S. The positive Rossby deformation radius uses $|f|$; the source's expression $c/f$ must be interpreted as a magnitude in the southern hemisphere.

The east-west e-folding distance is approximately $100$ km, orof longitude. With the coast at $x=0$ and ocean at $x<0$, a northern-hemisphere snapshot can be writtenAt a positive thickness crest, the thermocline is depressed and the alongshore velocity points polewards; a negative thickness trough reverses that velocity. In the southern hemisphere replace $c$ by $-c$ in the propagation and in $v/\eta$. The envelopes of both thickness and alongshore velocity decay offshore, and the cross-shore velocity vanishes.