Trapping of Low Frequency Oscillations in an Equatorial “Boundary Layer”

A thin layer of water (thickness h) and its spherical boundaries (mean radius R) rotate with uniform angular velocity Ω. Using an asymptotic expansion in the parameter h/R ⪡ 1 we investigate the inertial oscillations of “large scale” disturbances at the equator. It is found that the vertical constraints on the motion inhibit the lateral (poleward) propagation of low frequency energy. Solutions of the non-separable eigenvalue problem give standing oscillations whose longest period is (R/h)^½ (2π/Ω) and which are self-confined within a distance of order (Rh)^½ on either side of the equator. This axial symmetric calculation is probably valid for disturbances whose eaet-west wave-length is large compared with the width of the “boundary layer” (Rh)^½. t is suggested that a trapped wave can transfer energy to a mean flow at the equator, as the result of the correlation between the velocity components of the eigenfunction.

In the bottom water of the equatorial ocean, where, the stratification is small, there might be oscillations whose period is of the order of a month and which extended some 300 km north and south of the equator. When the static stability is appreciable the effect can only be expected if, on thie time scale, the fluid dissipates temperature perturbations much more rapidly than momentum.