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Mixing along sloping isopycnals plays a key role in the transport and uptake of heat and carbon by the ocean. This mixing is quantified by a lateral diffusivity, which can be measured by tracking the lateral spreading of point release tracer patches. We present a definition for the area of a tracer patch, the time derivative of which provides the lateral diffusivity. To accurately estimate the diffusivity, an ensemble mean concentration field of many tracer release experiments is required. We use numerical experiments to quantify how accurately the “true” lateral diffusivity (obtained from the ensemble mean concentration field) can be estimated from a single tracer release experiment (one ensemble member). To simulate observational campaigns, we also estimate the diffusivity from a single tracer release that is spatially and/or temporally subsampled, quantifying how the error between the estimated diffusivity and the true diffusivity grows as this sampling resolution worsens. We perform these numerical experiments in a two-layer quasigeostrophic model of turbulent flow on a β plane, using an ensemble of 50 passive tracer release experiments, each initialized as a 2D Gaussian but with differing realizations of the turbulent flow. We find that the diffusivity estimates from the single tracer releases have a relative root-mean-square error (RMSE) of 1.43% from the true diffusivity. Subsampling a single tracer release experiment every 956 km increases the relative RMSE from the true diffusivity to 3.1%; also subsampling every 277 days raises this figure to 6.5%.

At constant pressure, a mixture of water parcels with equal density but differing salinity and temperature will be denser than the parent water parcels. This is known as cabbeling and is a consequence of the nonlinear equation of state for seawater density. With a source of turbulent vertical mixing, cabbeling has the potential to trigger and drive convection in gravitationally stable water columns and there is observational evidence that this process shapes the thermohaline structure of high-latitude oceans. However, the evolution and maintenance of turbulent mixing due to cabbeling has not been fully explored. Here, we use turbulence-resolving direct numerical simulations to investigate cabbeling’s impact on vertical mixing and pathways of energy in closed systems. We find that cabbeling can sustain convection in an initially gravitationally stable two-layer configuration where relatively cold/fresh water sits atop warm/salty water. We show the mixture of the cold/fresh and warm/salty water is constrained by a density maximum and that cabbeling enhances mixing rates by four orders of magnitude. Cabbeling’s effect is amplified as the static stability limit is approached, leading to convection being sustained for longer. We find that available potential energy, which is classically thought to only decrease with mixing, can increase with mixing due to cabbeling’s densification of the mixed water. Our direct numerical dimulations support the notion that cabbeling could be a source of enhanced ocean mixing and that conventional definitions of energetic pathways may need to be reconsidered to take into account densification under mixing.

The uptake and vertical redistribution of heat and carbon is a crucial component of the ocean's role in regulating Earth's climate. Turbulent mixing, triggered by gravitational instability, enhances vertical transport of heat and carbon between the sea surface and deep ocean. Non-linearities in the equation of state for seawater density result in processes that can alter local gravitational stability, possibly leading to enhanced mixing. In this thesis I explore the impact of these non-linearities on the thermohaline structure and mixing in the high-latitude oceans.In chapter 2, I seek to establish if the gain in density upon mixing, known as cabbeling, is having an impact in high-latitude oceans. A hypothesis from a 1957 study by N. Fofonoff is extended to investigate if a gravitationally stable profile can become unstable after mixing due to cabbeling creating denser waters i.e. if a profile is unstable to cabbeling. In both observational data and output from a data constrained global circulation model, profiles are rarely unstable to cabbeling suggesting cabbeling sets a limiting threshold for vertical profile stability.Cabbeling's effect on small-scale mixing is explored using Direct Numerical Simulation (DNS) in chapter 3. The simulations show that a cabbeling instability can trigger and drive convection from an initially gravitationally stable state. Further, cabbeling driven convection is the same order of magnitude as convection driven by static instability indicating parametrisations of convection in global ocean models may need updates to take into account cabbeling instability, particularly at the high-latitudes.In chapter 4, the interaction between cabbeling and double diffusion is investigated using DNS. At high-latitudes, when turbulent mixing is weak and salinity and temperature increase with depth, conditions are favourable for \"diffusive\" convection. With a linear equation of state, this double diffusive instability forms equal density anomalies within layers either side of a \"diffusive\" interface. With a non-linear equation of state, our DNS results show a larger density anomaly forms in the lower layer, and the interface migrates upward, consistent with previous laboratory experiments. The temperature difference is found to be the main driver of the asymmetric density anomalies.