Magnus Hieronymus

The nonlinear equation of state of sea water and the global water mass distribution

The role of nonlinearities of the equation of state (EOS) of seawater for the distribution of water masses in the global ocean is examined through simulations with an ocean general circulation model with various manipulated versions of the EOS. A simulation with a strongly simplified EOS, which contains only two nonlinear terms, still produces a realistic water mass distribution, demonstrating that these two nonlinearities are indeed the essential ones. Further simulations show that each of these two nonlinear terms affects a specific aspect of the water mass distribution: the cabbeling term is crucial for the formation of Antarctic Intermediate Water and the thermobaric term for the layering of North Atlantic Deep Water and Antarctic Bottom Water.

Water Mass Transformation in Salinity–Temperature Space

This article presents a new framework for studying water mass transformations in salinity temperature space that can, with equal ease, be applied to study water mass transformation in spaces define ...

The Buoyancy Budget with a Nonlinear Equation of State

The nonlinear equation of state of seawater introduces a sink or source of buoyancy when water parcels of unequal salinities and temperatures are mixed. This article contains quantitative estimates ...

Finding the Minimum Potential Energy State by Adiabatic Parcel Rearrangements with a Nonlinear Equation of State: An Exact Solution in Polynomial Time

AbstractThe problem of finding the state of minimum potential energy through the rearrangement of water parcels with a nonlinear equation of state is discussed in the context of a combinatorial optimization problem. It is found that the problem is identical to a classical optimization problem called the linear assignment problem. This problem belongs to a problem class known as P, a class of problems that have known efficient solutions. This is very fortunate since this study’s problem has been suggested to be an asymmetric traveling salesman problem. A problem that belongs to a class called NP-hard, for which no efficient solutions are known. The difference between the linear assignment problem and the traveling salesman problem is discussed and made clear by looking at the different constraints used for the two problems. It is also shown how the rearrangement of water parcels that minimizes the potential energy can be found in polynomial time using the so-called Hungarian algorithm. The Hungarian algori...

Arctic Ocean Water Mass Transformation in S–T Coordinates

AbstractIn this paper, water mass transformations in the Arctic Ocean are studied using a recently developed salinity–temperature (S–T) framework. The framework allows the water mass transformations to be succinctly quantified by computing the surface and internal diffusive fluxes in S–T coordinates. This study shows how the method can be applied to a specific oceanic region, in this case the Arctic Ocean, by including the advective exchange of water masses across the boundaries of the region. Based on a simulation with a global ocean circulation model, the authors examine the importance of various parameterized mixing processes and surface fluxes for the transformation of water across isohaline and isothermal surfaces in the Arctic Ocean. The model-based results reveal a broadly realistic Arctic Ocean where the inflowing Atlantic and Pacific waters are primarily cooled and freshened before exiting back to the North Atlantic. In the model, the water mass transformation in the T direction is primarily acco...

A Note on the Influence of Spatially Varying Diffusivities on the Evolution of Buoyancy with a Nonlinear Equation of State

AbstractThe oceanic buoyancy sinks from thermobaricity and cabbeling are quantified using hydrography and parameterized diffusive fluxes of heat and salt. A novelty in this study is that the effect of spatially varying diffusivities is considered and quantified. The spatial distribution as well as averages from different ocean basins of the cabbeling and thermobaricity sinks are shown and discussed. The contributions from isoneutral and dianeutral diffusion to the cabbeling and thermobaricity sinks are calculated separately, and their relative importance is seen to vary in the different ocean basins.

Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

AbstractThe steady-state energy and thermal variance budgets form the basis for most current methods for evaluating turbulent fluxes of buoyancy, heat, and salinity. This study derives these budgets for a double-diffusive staircase and quantifies them using direct numerical simulations; 10 runs with different Rayleigh numbers are considered. The energy budget is found to be well approximated by a simple three-term balance, while the thermal variance budget consists of only two terms. The two budgets are also combined to give an expression for the ratio of the heat and salt fluxes. The heat flux scaling is also studied and found to agree well with earlier estimates based on laboratory experiments and numerical simulations at high Rayleigh numbers. At low Rayleigh numbers, however, the authors find large deviations from earlier scaling laws. Last, the scaling theory of Grossman and Lohse, which was developed for Rayleigh–Benard convection and is based on the partitioning of the kinetic energy and tracer var...