Mode conversion in the Gulf of Guinea

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 prop agation in one dimension (x), the local wavenumber k(x)(j) of each wave (j = a, b) varies with x; if these are equal at some x(R), the waves are local ly in phase, and resonant energy transfer can occur. We model wave propagat ion in the Gulf of Guinea, where wave a is an equatorially trapped Rossby-g ravity (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 couplin g 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 v ariational principle, and obtain an analytic expression for the wave-energy conversion coefficient, in terms of the wave frequency and the scale lengt h of the thermocline depth.