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The non-linear equation of state for the density of seawater leads to interesting phenomena, such as a gain in density when two water masses of equal density, but differing temperature and salinity, are mixed.
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Understanding the effect this gain in density upon mixing and ocean circulation in the high-latitudes was the focus of my PhD.
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For a real riot you can find my [thesis here](https://unsworks.unsw.edu.au/entities/publication/31923b90-a5fa-4c58-8202-d59c7434ef72) or just view the <button class="btn btnId btnPub--thesisabstract" id="thesis-abstract" style="outline:none; color:var(--info-color); border-color:var(--info-color);">abstract</button>
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<div class="dropDownThesisAbstract" id="thesis-abstract" style="display:none; font-size: 0.75rem;">
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<p>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. </p>
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For a real riot you can find my [thesis here](https://unsworks.unsw.edu.au/entities/publication/31923b90-a5fa-4c58-8202-d59c7434ef72) or you can read the published version of my [thesis abstract](https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/nonlinear-controls-on-ocean-circulation-and-mixing-in-the-highlatitude-oceans/D92C7157B62EE4616E59B4D874A2AB6B).
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One of the main findings was when, and how, influences the high-latitude oceans.
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When turbulent mixing is the dominant background mixing process in the high-latitude oceans, cabbeling will influence the thermohaline structure of the upper ocean by setting a limiting stability criteria.

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