39.7.2.6 Biharmonic skew-diffusion

If the option biharmonic_rm is enabled (Section 34.1.8), then the convergence of the Roberts and Marshall biharmonic skew-flux of temperature and salinity is diagnosed. The contribution from the biharmonic skew-flux is given by

$$(\rho_{\theta})_{i,k,j} \, (diffbihskew_{\theta})_{i,k,j} + (\rho_{s})_{i,k,j} \, (diffbihskew_{s})_{i,k,j}.$$ diffbihskew_i,k,j = (39.108)

The contribution from temperature and salinity each take the form

$$(diffbihskew_{\theta})_{i,k,j} dx\_tr_{i,k,j} \, \left( bihskew\_fe_{i,k,j} - bihskew\_fe_{i-1,k,j} \right)$$ =

$$dy\_tr_{i,k,j} \, \left( bihskew\_fn_{i,k,j} - bihskew\_fn_{i-1,k,j} \right)$$ +

$$dz\_tr_{i,k,j} \, \biggl( bihskew\_fb_{i,k-1,j} - bihskew\_fb_{i,k,j} \biggr).$$ + (39.109)

The biharmonic skew-flux components are computed just as in the solution of the tracer equation (Section 34.1.8.8).