Barotropic, wind-driven circulation in a small basin

We study the asymptotic behavior (large time) of a simple, wind-driven, barotropic ocean model, described by a nonlinear partial differential equation with two spatial dimensions. Considered as a dynamical system, this model has an infinite-dimensional phase space. After discretization, the equivalent numerical model has a phase space of finite but large dimension. We find that for a considerable range of friction, the asymptotic states are low-dimensional attractors. We describe the changes in the structure of these asymptotic attractors as a function of the eddy viscosity of the model. A variety of different types of attractor are seen, with chaotic attractors predominating at higher Reynolds numbers. As the Reynolds number is increased, we observe a slow increase in the dimension of the chaotic attractors. Using an energy analysis, we examine the nature of the instability responsible for the Hopf bifurcation that initiates the transition from asymptotically steady states to time-dependent states

Instabilities of a steady, barotropic, wind-driven circulation

We explore the stability characteristics of a single, barotropic, wind-driven gyre as a function of the strength of the wind forcing and the size and shape of the basin. We find steady solutions for the barotropic flow in a basin driven by a steady wind stress over a range of values of the Reynolds number and the strength of the wind stress. For those solutions that are close to the stability boundary, we examine the form of the most unstable normal mode. We find that for sufficiently weak forcing, the form of the first instability seen is an instability of the western boundary current. However, for larger values of the forcing, the first instability to set in, as the Reynolds number is reduced, is centered on a standing meander that forms on the continuation of the boundary current after it has left the boundary. Both types of instability are oscillatory. There are several different modes of standing meander instability each associated with Rossby wave-like disturbances in the eastern half of the basin. Each of these modes is most unstable when its frequency is close to a resonance with a basin mode with similar spatial scales

On the stability of the wind-driven circulation

This work examines the instabilities of steady circulations driven by stationary single-gyre wind forcing in closed rectangular basins with different aspect ratios. The stratified ocean is modeled with quasi-geostrophic 1.5-layer (equivalent-barotropic) and two-layer models. As friction is reduced, a stability threshold is encountered. In the vicinity of this threshold, unstable steady states and their unstable eigenmodes are determined. The structures of the eigenmodes and their associated energy conversion terms allow us to characterize the instabilities. In each case, the loss of stability is associated with an oscillatory instability. Several different instability mechanisms are observed. Which of these is responsible for the onset of instability depends upon the basin aspect ratio and the choice of stratification (1.5- or two-layer). The various mechanisms include instability of the western boundary current, baroclinic instability of the main recirculation gyre, instability of a standing meander located downstream of the main recirculation gyre and a complex instability involving several recirculations and the standing meander. The periods of the eigenmodes range from several months to several years depending upon the kind of instability and type of model. Additional insight into the western boundary current and baroclinic gyre instabilities is provided by an exploration of the stability of (a) the Munk boundary layer flow in 1.5- and two-layer models in an unbounded north-south channel, and (b) an isolated baroclinic vortex on an f-plane

The dynamics of an equivalent-barotropic model of the wind-driven circulation

Various steady and time-dependent regimes of a quasi-geostrophic 1.5 layer model of an oceanic circulation driven by a steady wind stress are studied. After being discretized as a numerical model, the quasi-geostrophic equations of motion become a dynamical system with a large dimensional phase space. We find that, for a wide range of parameters, the large-time asymptotic regimes of the model correspond to low-dimensional attractors in this phase space. Motion on these attractors is significant in determining the intrinsic time scales of the system. In two sets of experiments, we explore the dependence of solutions on the viscosity coefficient and the deformation radius. Both experiments yielded a succession of solutions with different forms of time dependence including chaotic solutions. The transition to chaos in this model occurs through a modified classical Ruelle-Takens scenario. We computed some unstable steady regimes of the circulation and the associated fastest growing linear eigenmodes. The structure of the eigenmodes and the details of the energy conversion terms allow us to characterize the primary instability of the steady circulation. It is a complex instability of the western boundary intensification, the western gyre and the meander between the western and central gyres. The model exhibits ranges of parameters in which multiple, stable, time-dependent solutions exist. Further, we note that some bifurcations involve the appearance of variability at climatological time scales, purely as a result of the intrinsic dynamics of the wind-driven circulation

Classification Algorithms Framework (CAF) to enable Intelligent Systems using JetBrains MPS domain-specific languages environment

This paper describes the design and development of a Classification Algorithms Framework (CAF) using the JetBrains MPS domain-specific languages (DSLs) development environment. It is increasingly recognized that the systems of the future will contain some form of adaptivity therefore making them intelligent systems as opposed to the static systems of the past. These intelligent systems can be extremely complex and difficult to maintain. Descriptions at higher-level of abstraction (system-level) have long been identified by industry and academia to reduce complexity. This research presents a Framework of Classification Algorithms at system-level that enables quick experimentation with several different algorithms from Naive Bayes to Logistic Regression. It has been developed as a tool to address the requirements of British Telecom’s (BT’s) data-science team. The tool has been presented at BT and JetBrains MPS and feedback has been collected and evaluated. Beyond the reduction in complexity through the system-level description, the most prominent advantage of this research is its potential applicability to many application contexts. It has been designed to be applicable for intelligent applications in several domains from business analytics, eLearning to eHealth, etc. Its wide applicability will contribute to enabling the larger vision of Artificial Intelligence (AI) adoption in context

Customised computerised clinical protocol guidelines for medical education: the case of Chronic Kidney Disease (CKD) using domain-specific languages

Educating healthcare professionals to correctly manage long-term conditions such as Chronic Kidney Disease (CKD) can be complex [1]. Converting theoretical understanding of clinical concepts into logical steps for identifying and managing a disease is not straightforward [2]. There is a risk to patients if guidelines and protocols are not followed correctly, for example through not identifying a condition like CKD in a timely fashion [3] or sub-optimally managing key risks such as hypertension [4]. In addition, during both initial training and in later professional development, professionals need to adapt to changing clinical guidelines and emerging findings from research [5]. Therefore, there is a strong need to support medical professionals with learning and adopting current and emerging clinical protocol guidelines, particularly for complex conditions such as CKD. From the technical perspective, and although specialised software solutions that are customised for complex clinical protocols and verified by medical professionals can be extremely valuable tools towards this aim, there are several challenges. More rigorous validation and verification processes for the software developed are required to ensure correctness [6]. The whole software development process and the resulting artefact need to be “understandable” and “accessible” by the non-technical users to ensure validity and adoption. Domain-specific languages (DSLs) are an advanced technique that can address both above issues. They allow “correct-by-constriction” software development [7] and non-technical domain users to interface with complex technological systems bringing technology to non-technical audiences [8]. In this project, using CKD as an exemplar, we used open-source DSL for the development of clinical protocol software: the Guidelines Definition Language (GDL) DSL [9] by Cambio CDS [10]; the PROforma [11] and a custom DSL developed in our research group. Commercial DSLs, such as those developed by Voluntis [12], also exist. Initial evaluation of the developed artefacts will take place within the University of Southampton medical school. Experiential software engineering methods through surveys and co-creation workshops with co-developed domain-specific criteria was the approach followed. This is a new approach developed and trialled in this project. All existing approaches focus on DSL usability aspects [13] and are too hard to introduce. They also ignore the domain-specific focus of the DSLs. The initial results from this project’s outcomes will be presented at the conference as experimentation at the time of writing this paper is still ongoing. Concluding, our plans include the design and development of a custom simulator on top of the presented software. The domain-specific languages technology will be also used for this to provide a customised simulator and enable medical professionals to contribute directly to the software development [14]. Please, note that this research has been the output of work carried out by a multidisciplinary collaboration between model-driven engineering researchers from Bournemouth University and medical researchers from University of Southampton. It has been supported by MDENet [15] (an Engineering and Physical Sciences Research Council (EPSRC) network for Model-Driven Engineering managed by King’s College in London) under the MDENet Seedcorn funding. Specifically, the project involved BU master’s graduates from the Digital Health pathway with backgrounds in both clinical and IT fields, and medical experts from the University of Southampton including primary care clinicians, public health and nephrology. The applicability of the research was preliminary applied and tested in the medical education context of University of Southampton medical school

The predictability of large-scale wind-driven flows

International audienceThe singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving examples of wind-driven, double-gyre circulations in different flow regimes are explored. By changing the Reynolds number in simple quasi-geostrophic models of the wind-driven circulation, steady, weakly aperiodic and chaotic states may be examined. The singular vectors of the steady state reveal some of the physical mechanisms responsible for optimally growing perturbations. In time-dependent cases, the dominant singular values show significant variability in time, indicating strong variations in the predictability of the flow. When the underlying flow is weakly aperiodic, the dominant singular values co-vary with integral measures of the large-scale flow, such as the basin-integrated upper ocean kinetic energy and the transport in the western boundary current extension. Furthermore, in a reduced gravity quasi-geostrophic model of a weakly aperiodic, double-gyre flow, the behaviour of the dominant singular values may be used to predict a change in the large-scale flow, a feature not shared by an analogous two-layer model. When the circulation is in a strongly aperiodic state, the dominant singular values no longer vary coherently with integral measures of the flow. Instead, they fluctuate in a very aperiodic fashion on mesoscale time scales. The dominant singular vectors then depend strongly on the arrangement of mesoscale features in the flow and the evolved forms of the associated singular vectors have relatively short spatial scales. These results have several implications. In weakly aperiodic, periodic, and stationary regimes, the mesoscale energy content is usually relatively low and the predictability of the wind-driven circulation is determined by the large-scale structure of the flow. In the more realistic, strongly chaotic regime, in which energetic mesoscale eddies are produced by the meandering of the separated western boundary current extension, the predictability of the flow locally tends to be a stronger function of the local mesoscale eddy structure than of the larger scale structure of the circulation. This has a broader implication for the effectiveness of different approaches to forecasting the ocean with models which sequentially assimilate new observations