After explaining the mechanism producing double diffusion, its representation analytically is developed and applied to linear stability analysis to determine conditions for double diffusion to occur. Laboratory observations of salt fingers are summarized, as well as the existence of thermohaline staircases produced by fingers in the thermocline. A similar development for the diffusive regime includes layering in Lake Kivu and in polar regions. Lastly, the role of double diffusion in thermohaline intrusions is explored.

This chapter explores how mixing is measured, focusing on what can be measured and how accurately. It begins with probes measuring dissipation scales, i.e. thermistors and airfoils, but also includes other devices not used routinely, such as pitot tubes. Finescale sensors are also examined, with an emphasis on absolute accuracy and salinity spiking. Then the vehicles carrying the probes are described, i.e. profilers, tows, AUVs, and submersibles. Moorings and fixed platforms are also briefly examined. Finally, remote sensing, principally using backscatter from high-frequency acoustics, is reviewed, along with tracer releases for measuring net diffusivity.

Dimensional analysis for stratified turbulence defines the variables describing turbulence in the ocean, which are then used with the Reynolds decomposition to develop equations of motion and define key parameters, such as turbulent kinetic energy and the viscous dissipation rate. These are used in developing the Kolmogorov energy cascade and the accompanying cascade of scalar variance. Considering turbulent evolution and decay leads to consideration of strongly stratified turbulence and pancake eddies. Turbulent intermittence and statistics include expressions for estimating confidence limits. The turbulent equations are then used to develop expressions for estimating turbulent eddy coefficients from what can be measured. The chapter ends with a consideration of mixing efficiency.

The last chapter combines themes from earlier chapters to summarize what has been learned about mixing in the stratified ocean. The nature of finestructure is explored first, as it contains signatures of the processes producing the mixing, as well as modulating the development of turbulent patches. After exploring how patches are identified, their characteristics are discussed. Evidence for the other major mixing process, double diffusion, is presented, principally as signatures in horizontal tows. The chapter concludes with summaries of mixing in three important regions differing from the open ocean pycnocline: the Southern Ocean, the Arctic, and ocean ridges.

Beginning with the equation of state of seawater, the chapter proceeds to apply the first and second laws of thermodynamics to seawater. These, in turn, lead to the equilibrium and well-mixed states that provide references for the mixed state of the ocean. Molecular flux laws also follow from the thermodynamic discussion, and then the turbulent buoyancy flux and its effect on potential energy is considered. After exploring TS diagrams, expressions for water mass conversion are discussed, including thermobaricity, cabbeling, and dianeutral velocity.

After explaining the mechanism producing double diffusion, its representation analytically is developed and applied to linear stability analysis to determine conditions for double diffusion to occur. Laboratory observations of salt fingers are summarized.