| Summary: | The nonlinear nature of the equation of state of seawater leads to numerous interesting processes inthe ocean. Two of the more well-known processes caused by nonlinearities in the equation of stateare cabbeling and thermobaricity. Other nonlinearities lead to difficulties in analyzing water-masstransformation on continuous density surfaces due to the ill-defined nature of neutral surfaces.This ill-defined nature of neutral surfaces describes the problem of not being able to globallyconnect neutral tangent planes, i.e. planes which describe the local mixing direction of fluidparticles in the absence of diapycnal mixing, to form a well-defined surface in three-dimensionalspace. All these processes have been known to exist for quite some time but their impact on oceancirculation and its analysis remains elusive.In this work an algorithm is introduced which improves the description of existing density surfacesto ensure that the resulting surfaces are as close to approximating neutral tangent planes aspossible. Because of the remaining slope errors between these continuous density surfaces andthe neutral tangent planes, even in the absence of diapycnal mixing processes fluid trajectoriespenetrate through any continuous density surfaces. This leads to a fictitious diapycnal diffusivityand an extra physical mechanism that achieves mean vertical advection in the ocean through anycontinuous density surface.Using these accurate density surfaces, the effects of cabbeling, thermobaricity and the diapycnaladvection due to the ill-defined nature of neutral surfaces are quantified. It is shown that theseprocesses cause a significant downward diapycnal transport on the order of 6 Sv, concentrated inthe Southern Ocean. This additional production of dense water has implications on the oceansenergetics which is discussed in this work. A new form of vertical advection, similar to thediapycnal advection due to the ill-defined nature of neutral surfaces but caused by temporalchanges of the oceans hydrography instead of spatial changes, is also introduced here.Another consequence of the ill-defined nature of neutral surface is the non-existence of ageostrophic streamfunction. New approximate expressions for the geostrophic streamfunction are also developed and are shown to be significantly more accurate than previously availableexpressions.All the algorithms described and the used to quantify the diapycnal velocities caused bynonlinearities in the equation of state are implemented in Matlab. This code including a usermanual is part of this work.
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