Salty ocean dynamics within a Boussinesq framework

Seawater is a binary fluid, consisting of water and salt. However, the effects of salinity on ocean dynamics are neglected by the classical Boussinesq equations, which model fluid density as a passive tracer rather than, more accurately, a thermodynamic variable determined by an equation of state. This idealisation treats the ocean as being free of salt. Within this framework, one may wish to know what the inclusion of salinity can tell us about climatically important quantities, such as potential vorticity and available potential energy (APE), as well as the key results pertaining to them. This work is an investigation of the dynamical effects of salinity in the ocean, using as our basis the Seawater Boussinesq equations introduced by Young [1]. This model is a generalisation of the classical model that accounts for the salt present in seawater. By reformulating these equations as a Hamiltonian system, we show how to formally derive the APE of seawater. Since APE is key to understanding and diagnosing the small-scale mixing processes that drive ocean circulation, this work, therefore, provides insight into how current mixing parameterisations may be modified to accurately account for salinity. Further to this is the thermobaricity of seawater, which describes the weak pressure-dependence of the equation of state and arises due to the binary nature of the fluid. Using our model, we are also able to study and quantify the additional vertical mixing induced by thermobaricity.