39.7.2.4 Laplacian horizontal diffusion

The contribution from horizontal diffusion consists of three model processes:

• Nonzero horizontal diffusivity Ah
• Use of option isotropic_mixed (Section 34.1.9.3)
• Use of ahsteep in regions where the scaled isoneutral diffusivity is less than ahsteep (Section 34.1.9).

It is generally written

$$(\rho_{\theta})_{i,k,j} \, (diffhorz_{\theta})_{i,k,j} + (\rho_{s})_{i,k,j} \, (diffhorz_{s})_{i,k,j}.$$ diffhorz_i,k,j = (39.102)

The contribution from horizontal diffusion for each tracer takes the form

$$dx\_tr_{i,k,j} \, \left( diff\_fe_{i,k,j} - diff\_fe_{i-1,k,j} \right)$$ (diffhorz)_i,k,j =

$$dy\_tr_{i,k,j} \, \left( diff\_fn_{i,k,j} - diff\_fn_{i,k,j-1} \right)$$ + (39.103)

where

$$diff\_fe_{i,k,j} diff\_cet(i,k,j) \, (t_{i+1,k,j,n} - t_{i,k,j,n}) \, cstdxur_{i,j}$$ = (39.104)

$$diff\_fn_{i,k,j} diff\_cnt(i,k,j) \, (t_{i,k,j+1,n} - t_{i,k,j,n}) \, csu\_dyur_{j}.$$ = (39.105)

The  isotropic_mixed and ahsteep contributions are added where appropriate.