Spurious Dianeutral Advection and Methods for Its Minimization

Abstract

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 nonneutral directions. However, there is also a spurious dianeutral advection that arises when lateral advection is applied nonneutrally 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 nonzero 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 10−5 m2 s−1 background diffusivity. Thus, we also develop a method to minimize a combination of esp and Df, yielding the 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.