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The biharmonic filter is an extra term that is added in the horizontal turbulent viscous flux, J, that filters high frequency oscillations in a numerical model of advection-diffusion of a property C(i.e. oscillations with a wave-length equal to one or two widths of the horizontal resolution):

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

where \mathrm{K} is Fick's law diffusivity. A ready made formula that would estimate the order of magnitude of the \kappa_4 coefficient for momentum 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.


In mohid, you need to add in the Hydrodynamic_x.dat the following keywords:

BIHARMONIC        : [0/1] <-- Activates de biharmonic viscous flux
BIHARMONIC_COEF   : [Real] <-- Sets the value of \kappa_4


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.