Thermodynamic neutral density: A new physically-based, energy-constrained, materially conserved neutral density variable for quantifying mixing and tracking water masses in the ocean

A new materially-conserved quasi-neutral density variable has been constructed, called thermodynamic neutral density. It is composed of two parts. The first part is the Lorenz reference density entering Lorenz theory of available potential energy, which can be interpreted as the potential density of a fluid parcel referenced to the pressure it would have in Lorenz reference state of minimum potential energy. The second part is an empirical correction for pressure, which can be suitably chosen to make thermodynamic neutral density a very good approximation of Jackett and McDougall (1997) neutral density over most of the ocean water masses for which the latter is defined.

Thermodynamic neutral density possesses many advantages over the empirically constructed Jackett and McDougall (1997) neutral density: 1) it is physically-based; 2) it is easily computed using fast and efficient methods for arbitrary states of the ocean, not just the present state, using the recently developed methodology by Saenz et al. (2015); 3) it is exactly neutral in a state of rest, and approximately neutral in the present ocean; 4) it is exactly materially conserved (it is a function of salinity and potential temperature only) and not plagued by unphysical nonmaterial effects, so can be used unambiguously to define and diagnose diapycnal and isopycnal mixing; 5) it is based on available potential energy, and therefore is the most suitable variable to discuss the energy cost of adiabatic stirring; 6) it is the variable that should be used to define the isopycnal and diapycnal directions in rotated diffusion tensor, as it can be shown that using the directions defined by the local neutral tangent plane as currently done causes spurious destruction of water masses.

References:

J. A. Saenz, R. Tailleux, E.D. Butler, G.O. Hughes, and K.I.C. Oliver, 2015: Estimating Lorenz’s reference state in an ocean with a nonlinear equation of state for seawater. J. Phys. Oceanogr., 45, 1242—1257