Destabilization of the thermohaline circulation by transient perturbations to the hydrological cycle

We reconsider the problem of the stability of the thermohaline circulation as described by a two-dimensional Boussinesq model with mixed boundary conditions. We determine how the stability properties of the system depend on the intensity of the hydrological cycle. We define a two-dimensional parameters' space descriptive of the hydrology of the system and determine, by considering suitable quasi-static perturbations, a bounded region where multiple equilibria of the system are realized. We then focus on how the response of the system to finite-amplitude surface freshwater forcings depends on their rate of increase. We show that it is possible to define a robust separation between slow and fast regimes of forcing. Such separation is obtained by singling out an estimate of the critical growth rate for the anomalous forcing, which can be related to the characteristic advective time scale of the system.Comment: 37 pages, 8 figures, submitted to Clim. Dy

On acceleration of Krylov-subspace-based Newton and Arnoldi iterations for incompressible CFD: replacing time steppers and generation of initial guess

We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. This operator can be inverted by the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose to generate an initial guess of steady flow, leading eigenvalue and eigenvector using orthogonal projection on a divergence-free basis satisfying all boundary conditions. The approach, including the two proposed techniques, is illustrated on the solution of the linear stability problem for laterally heated square and cubic cavities

Sensitivity of the Atlantic meridional overturning circulation to South Atlantic freshwater anomalies

The sensitivity of the Atlantic Meridional Overturning Circulation (AMOC) to changes in basin integrated net evaporation is highly dependent on the zonal salinity contrast at the southern border of the Atlantic. Biases in the freshwater budget strongly affect the stability of the AMOC in numerical models. The impact of these biases is investigated, by adding local anomaly patterns in the South Atlantic to the freshwater fluxes at the surface. These anomalies impact the freshwater and salt transport by the different components of the ocean circulation, in particular the basin-scale salt-advection feedback, completely changing the response of the AMOC to arbitrary perturbations. It is found that an appropriate dipole anomaly pattern at the southern border of the Atlantic Ocean can collapse the AMOC entirely even without a further hosing. The results suggest a new view on the stability of the AMOC, controlled by processes in the South Atlantic. <br/

Global instability in the Ghil--Sellers model

The Ghil--Sellers model, a diffusive one-dimensional energy balance model of Earth's climate, features---for a considerable range of the parameter descriptive of the intensity of the incoming radiation---two stable climate states, where the bistability results from the celebrated ice-albedo feedback. The warm state is qualitatively similar to the present climate, while the cold state corresponds to snowball conditions. Additionally, in the region of bistability, one can find unstable climate states. We find such unstable states by applying for the first time in a geophysical context the so-called edge tracking method, which has been used for studying multiple coexisting states in shear flows. This method has a great potential for studying the global instabilities in multistable systems, and for providing crucial information on the possibility of transitions when forcing is present. We examine robustness, efficiency, and accuracy properties of the edge tracking algorithm. We find that the procedure is the most efficient when taking a single bisection per cycle. Due to the strong diffusivity of the system, the transient dynamics, is approximately confined to the heteroclininc trajectory, connecting the fixed unstable and stable states, after relatively short transient times. Such a constraint dictates a functional relationship between observables. We characterize such a relationship between the global average temperature and a descriptor of nonequilibrium thermodynamics, the large scale temperature gradient between low and high latitudes. We find that a maximum of the temperature gradient is realized at the same value of the average temperature, about 270 K, largely independent of the strength of incoming solar radiation. Due to this maximum, a transient increase and nonmonotonic evolution of the temperature gradient is possible and not untypical. We also examine the structural properties of the system defined by bifurcation diagrams describing the equilibria depending on a system parameter of interest, here the solar strength. We construct new bifurcation diagrams in terms of quantities relevant for describing thermodynamic properties such as the temperature gradient and the material entropy production due to heat transport. We compare our results for the energy balance model to results for the intermediate complexity general circulation model the Planet Simulator and find an interesting qualitative agreement

Phase behaviour of a model of colloidal particles with a fluctuating internal state

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal particles, with a simple phenomenological model to account for these degrees of freedom, is studied. It is found that the interaction between the particles is not pairwise additive. It is even possible that the interaction between a triplet of particles is attractive while the pair interaction is repulsive. When this is so the liquid phase is either stable only in a small region of the phase diagram or absent altogether.Comment: 12 pages including 4 figure

Modeling the dynamics of glacial cycles

This article is concerned with the dynamics of glacial cycles observed in the geological record of the Pleistocene Epoch. It focuses on a conceptual model proposed by Maasch and Saltzman [J. Geophys. Res.,95, D2 (1990), pp. 1955-1963], which is based on physical arguments and emphasizes the role of atmospheric CO2 in the generation and persistence of periodic orbits (limit cycles). The model consists of three ordinary differential equations with four parameters for the anomalies of the total global ice mass, the atmospheric CO2 concentration, and the volume of the North Atlantic Deep Water (NADW). In this article, it is shown that a simplified two-dimensional symmetric version displays many of the essential features of the full model, including equilibrium states, limit cycles, their basic bifurcations, and a Bogdanov-Takens point that serves as an organizing center for the local and global dynamics. Also, symmetry breaking splits the Bogdanov-Takens point into two, with different local dynamics in their neighborhoods

Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials

In this paper it is shown that unique solutions to the relativistic Boltzmann equation exist for all time and decay with any polynomial rate towards their steady state relativistic Maxwellian provided that the initial data starts out sufficiently close in $L^\infty_\ell$. If the initial data are continuous then so is the corresponding solution. We work in the case of a spatially periodic box. Conditions on the collision kernel are generic in the sense of (Dudy{\'n}ski and Ekiel-Je{\.z}ewska, Comm. Math. Phys., 1988); this resolves the open question of global existence for the soft potentials.Comment: 64 page

Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism

This is the author accepted manuscript. The final version is available from The Royal Society via the DOI in this record.Data access: The codes supporting this article have been uploaded as part of the supplementary material. They can also be found on the online repository figshare: https://doi.org/10.6084/m9.figshare.8085683.v1Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through an ad-hoc physical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism is introduced as a way to systematically derive delay models from systems of partial differential equations and hence provides a better justification for using these delay-type models. The Mori-Zwanzig technique gives a formal rewriting of the system using a projection onto a set of resolved variables, where the rewritten system contains a memory term. The computation of this memory term requires solving the orthogonal dynamics equation, which represents the unresolved dynamics. For nonlinear systems, it is often not possible to obtain an analytical solution to the orthogonal dynamics and an approximate solution needs to be found. Here, we demonstrate the Mori-Zwanzig technique for a two-strip model of the El Nino Southern Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The resulting nonlinear delay model contains an additional term compared to previously proposed ad-hoc conceptual models. This new term leads to a larger ENSO period, which is closer to that seen in observations.European Union Horizon 2020Dutch Science Foundation (NWOEngineering and Physical Sciences Research Council (EPSRC

EU Support for Robust, Effective, and Democratic Global Governance: A Conceptual Framework

The ENSURED project addresses the following research question: How can the EU and its members, in a contested world in transition, transform and defend global governance to make it more robust, effective, and democratic? This conceptual framework provides the basis for the empirical analysis of the project, which includes case studies, comparative analyses, and an expert survey. It starts by operationalising the three core concepts of the project – robust, effective, and democratic global governance – and considers their interactions. The conceptual framework then identifies the unexploited potential for global governance reform by unpacking the positions of major international actors. It also clarifies alternative pathways to global governance transformation and specifically considers the role that the EU and its members play in these processes

EU Support for Robust, Effective, and Democratic Global Governance: A Conceptual Framework

The ENSURED project addresses the following research question: How can the EU and its members, in a contested world in transition, transform and defend global governance to make it more robust, effective, and democratic? This conceptual framework provides the basis for the empirical analysis of the project, which includes case studies, comparative analyses, and an expert survey. It starts by operationalising the three core concepts of the project – robust, effective, and democratic global governance – and considers their interactions. The conceptual framework then identifies the unexploited potential for global governance reform by unpacking the positions of major international actors. It also clarifies alternative pathways to global governance transformation and specifically considers the role that the EU and its members play in these processes