Linear mode conversion is the partial transfer of wave energy from one wave type
(a) to another (b) in a weakly non-uniform background state. For propagation in
one dimension (x), the local wavenumber kjx
of each wave (j = a, b) varies with x;
if these are equal at some xR, the waves are locally in phase, and resonant energy
transfer can occur. We model wave propagation in the Gulf of Guinea, where wave
a is an equatorially trapped Rossby–gravity (Yanai) wave, and wave b is a coastal
Kelvin wave along the (zonal) north coast of the Gulf, both propagating in zonal
coordinate x. The coupling of the waves is due to the overlap of their eigenfunctions
(normal modes in y, the meridional coordinate). We derive coupled mode equations
from a variational principle, and obtain an analytic expression for the wave-energy
conversion coefficient, in terms of the wave frequency and the scale length of the
thermocline depth.