Spurious dianeutral advection and methods for its minimization

Abstract An existing approximately neutral surface, the ω-surface, minimizes the neutrality error and hence also exhibits very small fictitious dianeutral diffusivity, Df, that arises when lateral diffusion is applied along the surface, in non-neutral directions. However, there is also a spurious dianeutral advection that arises when lateral advection is applied non-neutrally along the surface; equivalently, lateral advection applied along the neutral tangent planes creates a vertical velocity esp through the ω-surface. Mathematically, esp = u ⋅ s, where u is the lateral velocity and s is the slope error of the surface. We find that esp produces a leading order term in the evolution equations of temperature and salinity, being similar in magnitude to the influence of cabbeling and thermobaricity. We introduce a new method to form an approximately neutral surface, called an ωu⋅s-surface, that minimizes esp by adjusting its depth so that the slope error is nearly perpendicular to the lateral velocity. The esp on a surface cannot be reduced to zero when closed streamlines contain non-zero neutral helicity. While esp on the ωu⋅s-surface is over 100 times smaller than that on the ω-surface, the fictitious dianeutral diffusivity on the ωu⋅s-surface is larger, nearly equal to the canonical 10‒5m2s‒1 background diffusivity. Thus, we also develop a method to minimize a combination of esp and Df, yielding the ωu⋅s+s2-surface, which is recommended for inverse models since it has low Df and it significantly decreases esp through the surface, which otherwise would be a leading term that cannot be ignored in the conservation equations.