We linearize the governing equations by assuming small amplitudes for

yandq. Further, we expandyandqby a series of functions satisfying the boundary conditions and truncate up to the vertical wavenumber 1 (see Appendix B). As a result, we can easily obtain the approximate expression of the neutral curve of the system.The first term on the right hand side

(pdescribes the neutral curve for the case of the non-rotating system (center graph in figure). This neutral curve has a minimum at^{2}/8)(k^{2}+p^{2})^{2}. As the rotation rate increases, the effect of the second term (right graph in figure) appears and the neutral curve goes up in thek=0plane. However, since the effect of the second term vanishes atk-R, the critical horizontal wave number is zero even with the effect of rotation. Therefore, the critical values arek=0

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