next up previous

5.4 Transformation to Sigma Coordinates     continued...

The expression for is similar to equation (85) except that S replaces in equations (86) and (87). The expressions for and are also similar except that in addition, we can safely ignore the second term in square brackets of equations (86) and (87) since along isopycnal diffusion of and is quite small in the deep ocean, because of the very small magnitudes of and . Therefore, unlike and S, there is not a threat of significant drift in water mass properties for long term integrations.

The expressions for horizontal viscosities and can also be simplified to considerable computational advantage and negligible loss in accuracy [41]: