Stokes Drift in Internal Equatorial Kelvin Waves: Continuous Stratification versus Two-Layer Models

Abstract

Abstract The Stokes drift in long internal equatorial Kelvin waves is investigated theoretically for an inviscid fluid of constant depth. While the Stokes drift in irrotational waves is positive everywhere in the fluid, that is, directed along the phase velocity, this is not always the case for internal Kelvin waves, which possess vorticity. For constant Brunt–Väisälä frequency, the Stokes drift in such waves is sinusoidal in the vertical with a negative value in the middle of the layer for the first baroclinic mode. For a pycnocline that is typical of the equatorial Pacific, this study finds for the first mode that the largest negative Stokes drift velocity occurs near the depth where the Brunt–Väisälä frequency has its maximum. Here, estimated drift values are found to be on the same order of magnitude as those observed in the Pacific Equatorial Undercurrent at the same level. In contrast, a two-layer model with constant density in each layer yields a positive Stokes drift in both layers. This contradicts the fact that, as shown in this paper, the vertically integrated Stokes drift (the Stokes flux) must be zero for arbitrary Brunt–Väisälä frequency.