Energetically consistent rotated diffusion and lateral stirring surfaces in the ocean

The definition of isopycnal surfaces in the ocean has long remained ambiguous, complicating the parameterisation of subgridscale mixing in ocean models and rigorous development of isopycnic-coordinate frameworks. Here we show that balancing sources and sinks of subgridscale turbulent available potential energy (TAPE) constrains isopycnal surfaces to align with the Lorenz reference density (LRD) surfaces that define the reference state in APE theory. Building on this, comparisons in ( S , θ ) space confirm that LRD surfaces form the underlying physical basis for empirical approximately neutral surfaces ( γ n and Ω ), except in colder waters. In our theory, deviations from neutrality are the signatures of thermobaric forces rather than ‘errors’. Consequently, constructing rotated (Redi) diffusion tensors using neutral directions is unphysical, as it introduces spurious diapycnal mixing via the Veronis effect — particularly significant in the Southern Ocean. This highlights APE theory as a fundamental framework for developing energetically consistent ocean models and parameterisations, offering a pathway to reduce or eliminate artificial diapycnal mixing in ocean general circulation models (OGCMs). • Veronis effect rigorously defined and linked to observable ocean mixing. • Eddy APE budget constrains lateral stirring surfaces. • Traditional isoneutral mixing causes spurious diapycnal mixing. • APE theory provides clear pathways to reducing unphysical mixing.