Narrowband oscillations in the upper equatorial ocean. Part II: Properties of shear instabilities

Narrowband oscillations observed in the upper equa-torial Pacific are interpreted in terms of a random ensemble of shear instability events. Linear pertur-bation analysis is applied to hourly averaged profiles of velocity and density over a 54-day interval, yield-ing a total of 337 unstable modes. Composite pro-files of mean states and eigenfunctions surrounding the critical levels suggest that the standard hyper-bolic tangent model of Kelvin-Helmholtz (KH) insta-bility is a reasonable approximation, but the symme-try of the composite perturbation is broken by the stratification and vorticity gradient of the underlying equatorial undercurrent. Unstable modes are found to occupy a range of frequencies with a peak near 1/700 s, consistent with the frequency content of the observed oscillations. A probabilistic theory of random instabilities pre-dicts this peak frequency very closely. An order of magnitude estimate suggests that the peak fre-quency is of order N, in accord with the observations. This results not from gravity wave physics but from the balance of shear and stratification that governs shear instability in geophysical flows. More generally, we conclude that oscillatory signals with frequency bounded by N can result from a process that has nothing to do with gravity waves.