Equation of State (EOS)

The equation of state (EOS) for the ocean describes the relationship between specific volume of seawater (in \(\textrm{m}^3/\textrm{kg}\); the reciprocal of density) and temperature (in \(^{\circ}\textrm{C}\)), salinity (in \(\textrm{g/kg}\)), and pressure (in \(\textrm{dbar}\)). Through the hydrostatic balance (which relates density/specific volume gradients to pressure gradients), the equation of state provides a connection between active tracers (temperature and salinity) and the fluid dynamics.

Two choices of EOS are provided by Omega: a linear EOS and a TEOS-10 EOS. The linear EOS simplifies the relationship by excluding the influence of pressure and using constant expansion/contraction coefficients, making the specific volume a simple linear function of temperature and salinity. However, this option is only recommended for simpler idealized test cases as its accuracy is not sufficient for real ocean simulations. The TEOS-10 EOS is a 75-term polynomial expression from Roquet et al. 2015 that approximates the Thermodynamic Equation of Seawater 2010 , but in a less complex and more computationally efficient manner, and is the preferred EOS for real ocean simulations in Omega.

The user-configurable options are: EosType (choose either Linear or Teos-10), as well as the parameters needed for the linear EOS.

Eos:
   EosType : teos10
   Linear:
      DRhoDT: -0.2
      DRhoDS: 0.8
      RhoT0S0: 1000.0

where DRhoDT is the thermal expansion coefficient (\(\textrm{kg}/(\textrm{m}^3 \cdot ^{\circ}\textrm{C})\)), DRhoDS is the saline contraction coefficient (\(\textrm{kg}/\textrm{m}^3\)), and RhoT0S0 is the reference density at (T,S)=(0,0) (in \(\textrm{kg}/\textrm{m}^3\)).

In addition to SpecVol, the displaced specific volume SpecVolDisplaced is also calculated by the EOS. This calculates the density of a parcel of fluid that is adiabatically displaced by a relative k levels, capturing the effects of pressure/depth changes. This is primarily used to calculate quantities for determining the water column stability (i.e. the stratification) and the vertical mixing coefficients (viscosity and diffusivity). Note: when using the linear EOS, SpecVolDisplaced will be the same as SpecVol since the specific volume calculation is independent of pressure/depth.