On the frictional destabilization of abyssal overflows dynamically coupled to internal gravity waves

Abstract

In the immediate vicinity of a sill, abyssal overflows can possess current speeds greater the local long internal gravity wave speed with bottom friction and downslope gravitational acceleration playing a dominant role in the dynamics. The transition to instability is described of supercritical frictional abyssal overflows on a super-inertial time scale (where rotation, and hence along slope motion, is secondary), but where there is dynamic coupling between the overflow and gravest-mode internal gravity waves in the overlying water column. It is shown that dynamical coupling with ambient internal gravity waves leads to a significant ‘up or blue spectrum’ shift in the frequencies, wavelengths and growth rates as compared to an instability theory without dynamical coupling. For oceanographically relevant parameter values, the most unstable mode has been found to have a wavelength of about 484 m, an e-folding amplification time of about 13 min, a geostationary period of about 17 min and propagates in a retrograde manner with a co-moving period of about 19 min.

Keywords:

• Abyssal overflows
• Deep western boundary currents
• Baroclinic roll waves
• Internal gravity waves
• Deep water replacement

Acknowledgements

Preparation of this manuscript was supported in part by Research Grants awarded by the Natural Sciences and Engineering Research Council of Canada.