Insights into the Mixing Efficiency of Submesoscale Centrifugal-Symmetric Instabilities

Submesoscale processes provide a pathway for energy to transfer from the balanced circulation to turbulent dissipation. One class of submesoscale phenomena that has been shown to be particularly effective at removing energy from the balanced flow is centrifugal-symmetric instabilities (CSIs), which grow via geostrophic shear production. CSIs have been observed to generate significant mixing in both the surface boundary layer and bottom boundary layer flows along bathymetry, where they have been implicated in the mixing and water mass transformation of Antarctic Bottom Water. However, the mixing efficiency (i.e., the fraction of the energy extracted from the flow used to irreversibly mix the fluid) of these instabilities remains uncertain, making estimates of mixing and energy dissipation due to CSI difficult. In this work we use large-eddy simulations to investigate the mixing efficiency of CSIs in the submesoscale range. We find that centrifugally dominated CSIs (i.e., CSI mostly driven by horizontal shear production) tend to have a higher mixing efficiency than symmetrically dominated ones (i.e., driven by vertical shear production). The mixing efficiency associated with CSIs can therefore alternately be significantly higher or significantly lower than the canonical value used by most studies. These results can be understood in light of recent work on stratified turbulence, whereby CSIs control the background state of the flow in which smaller-scale secondary overturning instabilities develop, thus actively modifying the characteristics of mixing by Kelvin-Helmholtz instabilities. Our results also suggest that it may be possible to predict the mixing efficiency with more readily measurable parameters (viz., the Richardson and Rossby numbers), which would allow for parameterization of this effect.

Automated summary

Submesoscale centrifugal-symmetric instabilities (CSIs) play an important role in transferring energy from balanced circulation to turbulent dissipation. These instabilities generate significant mixing in boundary layer flows and are implicated in the mixing and transformation of Antarctic Bottom Water. However, the mixing efficiency of CSIs remains uncertain, making estimates of mixing and energy dissipation difficult. This study uses large-eddy simulations to investigate the mixing efficiency of CSIs and finds that it can vary significantly depending on the dominant shear production mechanism. These findings suggest that it may be possible to predict the mixing efficiency using more readily measurable parameters.