Ageostrophic effects on large scale circulation, eddy mixing and dissipation in the ocean

This thesis aims to provide a better understanding of the role of ageostrophic processes in ocean dynamics by analyzing three different case studies - the large-scale circulation, the mixing of eddies in the upper ocean and the ability of ageostrophic dynamics to feature a direct route to dissipation. Furthermore, it examines to which extent parameterizations can yield adequate simplifications of the more complex ageostrophic phenomena. The first case study concerns zonally averaged models of the large-scale meridional overturning circulation. Ageostrophic processes need to be considered here to correctly describe the dynamics in western boundary currents, while the interior ocean can be described by a geostrophic balance. Both, interior geostrophic and ageostrophic dynamics in the western boundary current need to be considered for the zonally averaged flow. It is illustrated that many zonally averaged models which do not consider both regimes show dynamical inconsistencies in comparison with zonally resolved models. A new parameterization for the zonally averaged flow is developed, in which both dynamical regimes are directly represented and which does not suffer from those inconsistencies. Zonally resolved models show good agreement with the new zonally averaged model, demonstrating that the new parameterization is dynamically consistent. The second case study deals with the mixing of eddies in the upper ocean. Since the stratification is often weak within the mixed layer, ageostrophic processes are likely to occur here. Two parameterizations for the eddy mixing are compared, which especially take ageostrophic dynamics into account. The first is based on linear stability analysis while the second is based on a scaling of the potential energy release. Numerical simulations for a wide range of dynamical conditions are used to diagnose the ability of these parameterizations to predict the mixing effect of the eddies. It turns out that the mean difference between both parameterizations and the diagnosed eddy fluxes is less than a factor of two. While the parameterization based on linear stability analysis performs slightly better in an equilibrated forced-dissipative flow scenario, the parameterization based on the scaling of the potential energy release performs better in a scenario of a re-stratifying density front. In addition it is found that the vertical structure of the eddy fluxes is better described by the former in both scenarios. The third case study investigates the role of ageostrophic dynamics for kinetic energy dissipation. Numerical simulations for a wide range of different dynamical conditions characterized by their Richardson number are used to diagnose the energy flux in wavenumber space. It is found that quasi-geostrophic dynamics feature an upscale kinetic energy flux while kinetic energy is transferred towards smaller scales for ageostrophic dynamics. Horizontal divergent velocities evolving under ageostrophic conditions can be identified to be responsible for the downscale flux. An important consequence is that the small-scale dissipation is larger in the presence of ageostrophic dynamics. To quantify the effect of ageostrophic dynamics on the small-scale dissipation, its dependency on the Richardson number is investigated and a power law relating the energy dissipation with the Richardson number is estimated

The impact of advection schemes on restratifiction due to lateral shear and baroclinic instabilities

This paper quantifies spurious dissipation and mixing of various advection schemes in idealised experiments of lateral shear and baroclinic instabilities in numerical simulations of a re-entrant Eady channel for configurations with large and small Rossby numbers. In addition, a two-dimensional barotropic shear instability test case is used to examine numerical dissipation of momentum advection in isolation, without any baroclinic effects. Effects of advection schemes on the evolution of background potential energy and the dynamics of the restratification process are analysed. The advection schemes for momentum and tracers are considered using several different methods including a recently developed local dissipation analysis. As highly accurate but computationally demanding schemes we apply WENO and MP5, and as more efficient lower-order total variation diminishing (TVD) schemes we use among others the SPL-max-View the MathML source13 and a third-order-upwind scheme. The analysis shows that the MP5 and SPL-max-View the MathML source13 schemes provide the most accurate results. Following our comprehensive analysis of computational costs, the MP5 scheme is approximately 2.3 times more expensive in our implementation. In contrast to the configuration with a small Rossby number, in which significant differences between schemes are apparent, the different advection schemes behave similarly for a larger Rossby number. Regions of high numerical dissipation are shown to be associated with low grid Reynolds numbers. The major outcome of the present study is that generally positive global numerical dissipation and positive background potential energy evolution delay the restratification process

Evaluating Different Parameterizations for Mixed Layer Eddy Fluxes induced by Baroclinic Instability

In this study, the authors discuss two different parameterizations for the effect of mixed layer eddies, one based on ageostrophic linear stability analysis (ALS) and the other one based on a scaling of the potential energy release by eddies (PER). Both parameterizations contradict each other in two aspects. First, they predict different functional relationships between the magnitude of the eddy fluxes and the Richardson number (Ri) related to the background state. Second, they also predict different vertical structure functions for the horizontal eddy fluxes. Numerical simulations for two different configurations and for a large range of different background conditions are used to evaluate the parameterizations. It turns out that PER is better suited to capture the Ri dependency of the magnitude of the eddy fluxes. On the other hand, the vertical structure of the meridional eddy fluxes predicted by ALS is more accurate than that of PER, while the vertical structure of the vertical eddy fluxes is well predicted by both parameterizations. Therefore, this study suggests the use of the magnitude of PER and the vertical structure functions of ALS for an improved parameterization of mixed layer eddy fluxes

Concentrations of Cobalt, Chromium and Titanium and Immunological Changes after Primary Total Knee Arthroplasty—A Cohort Study with an 18-Year Follow-Up

Background: Total knee arthroplasty (TKA) generates elevated metal ion concentrations, but long-term changes in the concentrations of cobalt (Co), chromium (Cr) and titanium (Ti) after primary TKA and potential subsequent immune system activation—not limited to the joint but systemically—are not known. Patients and Methods: We conducted a cohort study on 26 patients with TKA (19 women; 16 with metal-backed and 10 with all-polyethylene tibial components) 18.3 years (min. 16.7, max. 20.5) after index TKA. A total of 69% of patients additionally underwent subsequent arthroplasty of the contralateral knee or either hip after the index surgery. Blood samples were analysed by inductively coupled plasma–mass spectrometry, and leukocytes were characterised by flow cytometry. Patients were clinically assessed using the Knee Society score and by plain radiography of the knee. Results: The median metal ion concentrations were 0.7 (0.1–13.0) µg/L for Co, 0.9 (0.4–5.0) µg/L for Cr, and 1.0 (0.2–13.0) µg/L for Ti. There was no relevant difference in systemic metal ion concentrations between patients exposed to single and multiple arthroplasties. The absolute count and proportion of CD3+CD4+CD8+ T cells was inversely correlated with both Co (rho −0.55, p = 0.003) and Cr concentrations (rho −0.59, p = 0.001). Conclusions: Between the first and second decades after primary TKA, in most patients, the concentrations of Co, Cr and Ti in blood samples were below the thresholds that are considered alarming. The negative correlation of Co and Cr concentrations with a subset of lymphocytes that commonly increases during immune activation is reassuring. This represents a worst-case scenario, underscoring that the investigated metal ions remain within reasonable ranges, even after additional hardware exposure

Impact of advection schemes on restratification

A host of studies has recognized that truncation errors of the discretized advection terms lead to spurious mixing and dissipation (Fig. 1) and may interact nonlinearly with turbulent mixing and transport. To investigate the impacts of spurious mixing and dissipation, we implemented some of the most novel advection schemes into the coastal ocean model GETM. We quantified spurious dissipation [Klingbeil, 2014] and mixing of the advection schemes (Fig. 3) in idealized experiments of baroclinic instabilities (Fig. 2) ranging from mesoscales (small Rossby number) to sub-mesoscales (order-one Rossby number). The processes at submesosales are distinct from mesoscale by their contribution to restratification of the mixed layer. Such analyses (Fig. 4) help to choose between highly accurate but complex schemes and lower-order less complex schemes balancing accuracy and computational costs. The major outcome of the present study is that both, numerically induced dissipation (leading to a decrease of kinetic energy) and numerically induced mixing (leading to an increase of background potential energy), artificially delay the restratification process [Mohammadi-Aragh, 2015], an effect that needs to be taken into account if parameterizations for eddy-induced mixing and dissipation are compared with numerical model simulations

Kennzahlen zur Wertorientierung

Wer in ein Unternehmen investiert, tut dies, um in Zukunft Geld zu verdienen. Er rechnet mit einer risikoadäquaten Rendite. Die Auswahl der Kennzahlen, die diese Wertsteigerung transparent machen, ist allerdings nicht trivial. Denn von ihnen hängt ab, ob die Unternehmensziele richtig vorgegeben und ob die Anreize für das Management richtig gesetzt werden

Performance-Maße zur risikoadjustierten Steuerung

Risiken sind per se nichts Schlechtes, wenn der dadurch erzielte Ertrag für das eingegangene Risiko angemessen ist. Dieser Zusammenhang wird allerdings nicht immer verstanden – einer der Gründe für die Finanzkrise von 2008/09. Die in diesem Beitrag vorgestellten Kennzahlen zeigen, wie man Risiken mit erzielten oder möglichen Erträgen ins Verhältnis setzen kann

Unternehmensbewertung mittels Multiples

Umsatz und Gewinne stagnieren auf hohem Niveau, und dennoch steigen der Aktienkurs und der Gewinn pro Aktie – eine Entwicklung, die sich etwa bei Apple oder Ebay beobachten lässt. Aktionäre sollten wissen, welche Arithmetik sich hinter solchen Entwicklungen verbirgt und mit welchen Verfahren sie den Unternehmenswert am besten ermitteln können