This paper presents the theory for freely propagating and forced Rossby waves in a continuously stratified ocean where the bouyancy frequency, N, varies with longitude and depth. In this study zonal variations in N occur because the climatological mixed layer depth, h, varies with longitude. With the assumption that changes in h occur on a length scale which is large compared to a horizontal wavelength the free modes on a -plane are examined. It is found that realistic mixed layer depth changes can cause amplitude modulations, the largest amplitudes occurring where the mixed layer is shallowest. The requirement that h variations occur slowly is removed by employing a numerical model to study the free modes in a continuously stratified meridional channel. A criterion, based on the ratio of a horizontal length scale associated with the wave packet and the internal Rossby radius, is derived for determining when a free mode may be affected by the zonal variations in the stratification. Using climatological mixed layer depth data at 35N in the Atlantic (taken from Lamb, 1984) the basin modes are numerically determined. The major response is now concentrated where the mixed layer is deepest. This apparent contradiction is explained. A general theory is presented for calculating the forced basin mode response in terms of the free modes. As an example, a wind stress curl is applied as a body force over the mixed layer for a finite duration. After the forcing is removed the percentage that each basin mode contributes to the total solution is calculated. It is found that the dominant response to wind stress curl forcing can be significantly affected by the presence of a variable depth mixed layer. The implication of this study for the interaction between baroclinic Rossby waves and mixed layer dynamics is discussed.
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