Buoyancy model and equations of state

The buoyancy model determines the relationship between tracers and the buoyancy in the momentum equation.

Buoyancy tracer

The simplest buoyancy model uses buoyancy itself as a tracer: obeys the tracer conservation equation and is used directly in the momentum equations.

Seawater buoyancy

For seawater buoyancy is, in general, modeled as a function of conservative temperature , absolute salinity , and depth below the ocean surface via

where is gravitational acceleration, is the reference density. The function in the seawater buoyancy relationship that links conservative temperature, salinity, and depth to the density perturbation is called the equation of state. Both and obey the tracer conservation equation.

Linear equation of state

Buoyancy is determined from a linear equation of state via

where is gravitational acceleration, is the thermal expansion coefficient, and is the haline contraction coefficient.

Nonlinear equation of state

Buoyancy is determined by the simplified equations of state introduced by Roquet et al. (2015).