39.7.2.5 Laplacian skew-diffusion

If the Gent-McWilliams transport is enabled (Section 34.1.6), then the convergence of the GM skew-flux of temperature and salinity are diagnosed. Note that the contribution from GM is computed in terms of the GM skew-flux regardless of whether the GM scheme is actually implemented with the default option gm_skew, or with option gm_advect. The reason is that the computation of the skew flux is much easier than the alternative advective flux.

The contribution from the skew-flux is given by

$$(\rho_{\theta})_{i,k,j} \, (diffgmskew_{\theta})_{i,k,j} + (\rho_{s})_{i,k,j} \, (diffgmskew_{s})_{i,k,j}.$$ diffgmskew_i,k,j = (39.106)

The contribution from temperature and salinity each take the form

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

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

$$dz\_tr_{i,k,j} \, \biggl( skew\_fb_{i,k-1,j} - skew\_fb_{i,k,j} \biggr).$$ + (39.107)

The skew-flux components are computed just as in the solution of the tracer equation (Section 34.1.6 and Appendix C).