Biharmonic thickness mixing and backscatter by negative bolus velocity

Biharmonic (or higher order) mixing of potential vorticity (PV) combines biharmonic mixing of momentum and isopycnal thickness. It is applied in a realistic eddy-permitting model of the North Atlantic Ocean by a simple modification of the standard scheme for harmonic isopycnal thickness mixing or bolus velocity. The effect of biharmonic PV mixing is compared to the one of biharmonic mixing of momentum only. Results are similar except for more realistic mixed layer depths using PV mixing. It is also shown how harmonic isopycnal thickness mixing with negative definite dissipation representing an energy source, in short negative bolus velocity, can be implemented in existing ocean models by another simple modification of the standard scheme. While negative bolus velocity injects available potential energy to the model, previous backscatter formulations using negative definite harmonic momentum mixing inject kinetic energy by sharpening velocity gradients. Both backscatter formulations, combined with the more scale selective dissipation by biharmonic PV mixing and a subgrid-energy budget to control the energetics, reproduce previously reported positive effects by backscatter, such as a more realistic north-west corner of the North Atlantic Current and Gulf Stream path, but negative bolus velocity works better in our configuration. Furthermore, eddy production rates by baroclinic instability are enhanced by negative bolus velocity, but reduced to zero by backscatter using negative definite harmonic momentum mixing.