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 and BruntVaisalaFreq are also calculated by the EOS.

Displaced Specific Volume

The Eos class 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 option, SpecVolDisplaced will be the same as SpecVol since the specific volume calculation is independent of pressure/depth.

Brunt Vaisala Frequency

The Eos class also calculates the Brunt Vaisala Frequency, which is used by the VertMix class to determine water column stability for both the convective adjustment and shear-induced mixing. When using the Linear EOS option, the BruntVaisalaFreq is calculated using with linear coefficients. When using the Teos-10 EOS option, the BruntVaisalaFreq is calculated with non-linear coefficients according to the TOES-10. For both options, SpecVol must be calculated prior to calculating BruntVaisalaFreq, as it is an input to the BruntVaisalaFreq calculation.