Scalar properties in the ocean are stirred (and subsequently mixed) rather efficiently by mesoscale eddies and two-dimensional turbulence along “neutral surfaces”, defined such that when water parcels are moved small distances in the neutral surface, they experience no buoyant restoring forces. By contrast, work would have to be done on a moving fluid parcel in order to keep it on a potential density surface. The differences between neutral surfaces and potential density surfaces are due to the variation of α/β with pressure (where α is the thermal expansion coefficient and β is the saline contraction coefficient). By regarding the equation of state of seawater as a function of salinity, potential temperature, and pressure, rather than in terms of salinity, temperature, and pressure, it is possible to quantify the differences between neutral surfaces and potential density surfaces. In particular, the spatial gradients of scalar properties (e.g., S, θ, tritium or potential vorticity) on a neutral ... Abstract Scalar properties in the ocean are stirred (and subsequently mixed) rather efficiently by mesoscale eddies and two-dimensional turbulence along “neutral surfaces”, defined such that when water parcels are moved small distances in the neutral surface, they experience no buoyant restoring forces. By contrast, work would have to be done on a moving fluid parcel in order to keep it on a potential density surface. The differences between neutral surfaces and potential density surfaces are due to the variation of α/β with pressure (where α is the thermal expansion coefficient and β is the saline contraction coefficient). By regarding the equation of state of seawater as a function of salinity, potential temperature, and pressure, rather than in terms of salinity, temperature, and pressure, it is possible to quantify the differences between neutral surfaces and potential density surfaces. In particular, the spatial gradients of scalar properties (e.g., S, θ, tritium or potential vorticity) on a neutral ...