Propagation of Equatorially Trapped Waves on a Sloping Thermocline
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The WKBJ method and a multiple-scale expansion technique are used to study equatorially trapped waves propagating on a zonally sloping thermocline. Assuming that variations of the main thermocline depth (MTD) are slow (the change of the MTD over one wavelength is smaller than the wave amplitude), wave reflections can be neglected and the amplitudes of equatorially trapped waves can be derived by using the energy conservation law. It is found that the wavelengths and amplitudes of free waves are significantly modified by the MTD variations. While propagating eastward in an ocean basin (where the MTD is shallower), Kelvin waves shrink meridionally and zonally but their amplitudes increase to preserve wave energy; short Rossby waves behave in the opposite way. The wavelength of westward-propagating long Rossby waves becomes longer when they propagate into the deeper western ocean. The response of a Yanai wave to the changing thermocline depends on the sign of phase speed. A simple numerical method is designed to verify the WKBJ results and also to study the case of a relatively steep thermocline profile where the WKBJ method breaks down. Reflection of a Kelvin wave impinging on a thermocline front is also investigated in this work.