Biharmonic

The biharmonic coefficient is an extra term that is added to the horizontal turbulent viscous flux, J:

$\mathrm{J} = -\mathrm{K}\cdot \nabla C + \nabla_{h}\left( \kappa_4 \nabla_{h}^2 C \right)$

A ready made formula that would estimate the order of magnitude of the k_4 coefficient would be

$\kappa_4 \sim \frac{U}{16} \Delta x^3$

where U is a typical flow velocity and $\Delta x$ is the numerical model horizontal resolution.

References

Delhez, E., & Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing. 
Ocean Modelling, 17(3), 183-198. doi: 10.1016/j.ocemod.2007.01.002.