Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids

In this paper we investigate the equilibrium properties of magnetic dipolar (ferro-) fluids and discuss finite-size effects originating from the use of different boundary conditions in computer simulations. Both periodic boundary conditions and a finite spherical box are studied. We demonstrate that periodic boundary conditions and subsequent use of Ewald sum to account for the long-range dipolar interactions lead to a much faster convergence (in terms of the number of investigated dipolar particles) of the magnetization curve and the initial susceptibility to their thermodynamic limits. Another unwanted effect of the simulations in a finite spherical box geometry is a considerable sensitivity to the container size. We further investigate the influence of the surface term in the Ewald sum-that is, due to the surrounding continuum with magnetic permeability mu(BC)-on the convergence properties of our observables and on the final results. The two different ways of evaluating the initial susceptibility, i.e., (1) by the magnetization response of the system to an applied field and (2) by the zero-field fluctuation of the mean-square dipole moment of the system, are compared in terms of speed and accuracy.

Observations of urban boundary layer structure during a strong urban heat island event

It has long been known that the urban surface energy balance is different to that of a rural surface, and that heating of the urban surface after sunset gives rise to the Urban Heat Island (UHI). Less well known is how flow and turbulence structure above the urban surface are changed during different phases of the urban boundary layer (UBL). This paper presents new observations above both an urban and rural surface and investigates how much UBL structure deviates from classical behaviour. A 5-day, low wind, cloudless, high pressure period over London, UK, was chosen for analysis, during which there was a strong UHI. Boundary layer evolution for both sites was determined by the diurnal cycle in sensible heat flux, with an extended decay period of approximately 4 h for the convective UBL. This is referred to as the “Urban Convective Island” as the surrounding rural area was already stable at this time. Mixing height magnitude depended on the combination of regional temperature profiles and surface temperature. Given the daytime UHI intensity of 1.5∘C, combined with multiple inversions in the temperature profile, urban and rural mixing heights underwent opposite trends over the period, resulting in a factor of three height difference by the fifth day. Nocturnal jets undergoing inertial oscillations were observed aloft in the urban wind profile as soon as the rural boundary layer became stable: clear jet maxima over the urban surface only emerged once the UBL had become stable. This was due to mixing during the Urban Convective Island reducing shear. Analysis of turbulent moments (variance, skewness and kurtosis) showed “upside-down” boundary layer characteristics on some mornings during initial rapid growth of the convective UBL. During the “Urban Convective Island” phase, turbulence structure still resembled a classical convective boundary layer but with some influence from shear aloft, depending on jet strength. These results demonstrate that appropriate choice of Doppler lidar scan patterns can give detailed profiles of UBL flow. Insights drawn from the observations have implications for accuracy of boundary conditions when simulating urban flow and dispersion, as the UBL is clearly the result of processes driven not only by local surface conditions but also regional atmospheric structure.

Advances in the study of boundary value problems for nonlinear integrable PDEs

In this review I summarise some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the Unified Transform or Fokas Transform, that provides a substantial generalisation of the classical Inverse Scattering Transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the Inverse Scattering Transform follows the "separation of variables" philosophy, albeit in a nonlinear setting, the Unified Transform is a based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalisation to certain nonlinear cases of particular significance.

Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

Climate change projections using the IPSL-CM5 Earth System Model: from CMIP3 to CMIP5

We present the global general circulation model IPSL-CM5 developed to study the long-term response of the climate system to natural and anthropogenic forcings as part of the 5th Phase of the Coupled Model Intercomparison Project (CMIP5). This model includes an interactive carbon cycle, a representation of tropospheric and stratospheric chemistry, and a comprehensive representation of aerosols. As it represents the principal dynamical, physical, and bio-geochemical processes relevant to the climate system, it may be referred to as an Earth System Model. However, the IPSL-CM5 model may be used in a multitude of configurations associated with different boundary conditions and with a range of complexities in terms of processes and interactions. This paper presents an overview of the different model components and explains how they were coupled and used to simulate historical climate changes over the past 150 years and different scenarios of future climate change. A single version of the IPSL-CM5 model (IPSL-CM5A-LR) was used to provide climate projections associated with different socio-economic scenarios, including the different Representative Concentration Pathways considered by CMIP5 and several scenarios from the Special Report on Emission Scenarios considered by CMIP3. Results suggest that the magnitude of global warming projections primarily depends on the socio-economic scenario considered, that there is potential for an aggressive mitigation policy to limit global warming to about two degrees, and that the behavior of some components of the climate system such as the Arctic sea ice and the Atlantic Meridional Overturning Circulation may change drastically by the end of the twenty-first century in the case of a no climate policy scenario. Although the magnitude of regional temperature and precipitation changes depends fairly linearly on the magnitude of the projected global warming (and thus on the scenario considered), the geographical pattern of these changes is strikingly similar for the different scenarios. The representation of atmospheric physical processes in the model is shown to strongly influence the simulated climate variability and both the magnitude and pattern of the projected climate changes.

Storm tracks and climate change

Extratropical and tropical transient storm tracks are investigated from the perspective of feature tracking in the ECHAM5 coupled climate model for the current and a future climate scenario. The atmosphere-only part of the model, forced by observed boundary conditions, produces results that agree well with analyses from the 40-yr ECMWF Re-Analysis (ERA-40), including the distribution of storms as a function of maximum intensity. This provides the authors with confidence in the use of the model for the climate change experiments. The statistical distribution of storm intensities is virtually preserved under climate change using the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emissions Scenarios (SRES) A1B scenario until the end of this century. There are no indications in this study of more intense storms in the future climate, either in the Tropics or extratropics, but rather a minor reduction in the number of weaker storms. However, significant changes occur on a regional basis in the location and intensity of storm tracks. There is a clear poleward shift in the Southern Hemisphere with consequences of reduced precipitation for several areas, including southern Australia. Changes in the Northern Hemisphere are less distinct, but there are also indications of a poleward shift, a weakening of the Mediterranean storm track, and a strengthening of the storm track north of the British Isles. The tropical storm tracks undergo considerable changes including a weakening in the Atlantic sector and a strengthening and equatorward shift in the eastern Pacific. It is suggested that some of the changes, in particular the tropical ones, are due to an SST warming maximum in the eastern Pacific. The shift in the extratropical storm tracks is shown to be associated with changes in the zonal SST gradient in particular for the Southern Hemisphere.

The influence of viscous and latent heating on crystal-rich magma flow in a conduit

The flow dynamics of crystal-rich high-viscosity magma is likely to be strongly influenced by viscous and latent heat release. Viscous heating is observed to play an important role in the dynamics of fluids with temperature-dependent viscosities. The growth of microlite crystals and the accompanying release of latent heat should play a similar role in raising fluid temperatures. Earlier models of viscous heating in magmas have shown the potential for unstable (thermal runaway) flow as described by a Gruntfest number, using an Arrhenius temperature dependence for the viscosity, but have not considered crystal growth or latent heating. We present a theoretical model for magma flow in an axisymmetric conduit and consider both heating effects using Finite Element Method techniques. We consider a constant mass flux in a 1-D infinitesimal conduit segment with isothermal and adiabatic boundary conditions and Newtonian and non-Newtonian magma flow properties. We find that the growth of crystals acts to stabilize the flow field and make the magma less likely to experience a thermal runaway. The additional heating influences crystal growth and can counteract supercooling from degassing-induced crystallization and drive the residual melt composition back towards the liquidus temperature. We illustrate the models with results generated using parameters appropriate for the andesite lava dome-forming eruption at Soufriere Hills Volcano, Montserrat. These results emphasize the radial variability of the magma. Both viscous and latent heating effects are shown to be capable of playing a significant role in the eruption dynamics of Soufriere Hills Volcano. Latent heating is a factor in the top two kilometres of the conduit and may be responsible for relatively short-term (days) transients. Viscous heating is less restricted spatially, but because thermal runaway requires periods of hundreds of days to be achieved, the process is likely to be interrupted. Our models show that thermal evolution of the conduit walls could lead to an increase in the effective diameter of flow and an increase in flux at constant magma pressure.

A combined BIE-FE method for the Stokes equations

A numerical algorithm for the biharmonic equation in domains with piecewise smooth boundaries is presented. It is intended for problems describing the Stokes flow in the situations where one has corners or cusps formed by parts of the domain boundary and, due to the nature of the boundary conditions on these parts of the boundary, these regions have a global effect on the shape of the whole domain and hence have to be resolved with sufficient accuracy. The algorithm combines the boundary integral equation method for the main part of the flow domain and the finite-element method which is used to resolve the corner/cusp regions. Two parts of the solution are matched along a numerical ‘internal interface’ or, as a variant, two interfaces, and they are determined simultaneously by inverting a combined matrix in the course of iterations. The algorithm is illustrated by considering the flow configuration of ‘curtain coating’, a flow where a sheet of liquid impinges onto a moving solid substrate, which is particularly sensitive to what happens in the corner region formed, physically, by the free surface and the solid boundary. The ‘moving contact line problem’ is addressed in the framework of an earlier developed interface formation model which treats the dynamic contact angle as part of the solution, as opposed to it being a prescribed function of the contact line speed, as in the so-called ‘slip models’. Keywords: Dynamic contact angle; finite elements; free surface flows; hybrid numerical technique; Stokes equations.

Magnitude of climate variability during middle Pliocene warmth: a palaeoclimate modelling study

The nature and magnitude of climatic variability during the period of middle Pliocene warmth (ca 3.29–2.97 Ma) is poorly understood. We present a suite of palaeoclimate modelling experiments incorporating an advanced atmospheric general circulation model (GCM), coupled to a Q-flux ocean model for 3.29, 3.12 and 2.97 Ma BP. Astronomical solutions for the periods in question were derived from the Berger and Loutre BL2 astronomical solution. Boundary conditions, excluding sea surface temperatures (SSTs) which were predicted by the slab-ocean model, were provided from the USGS PRISM2 2°×2° digital data set. The model results indicate that little annual variation (0.5°C) in SSTs, relative to a ‘control’ experiment, occurred during the middle Pliocene in response to the altered orbital configurations. Annual surface air temperatures also displayed little variation. Seasonally, surface air temperatures displayed a trend of cooler temperatures during December, January and February, and warmer temperatures during June, July and August. This pattern is consistent with altered seasonality resulting from the prescribed orbital configurations. Precipitation changes follow the seasonal trend observed for surface air temperature. Compared to present-day, surface wind strength and wind stress over the North Atlantic, North Pacific and Southern Ocean remained greater in each of the Pliocene experiments. This suggests that wind-driven gyral circulation may have been consistently greater during the middle Pliocene. The trend of climatic variability predicted by the GCM for the middle Pliocene accords with geological data. However, it is unclear if the model correctly simulates the magnitude of the variation. This uncertainty is derived from, (a) the relative insensitivity of the GCM to perturbation in the imposed boundary conditions, (b) a lack of detailed time series data concerning changes to terrestrial ice cover and greenhouse gas concentrations for the middle Pliocene and (c) difficulties in representing the effects of ‘climatic history’ in snap-shot GCM experiments.

The basic ingredients of the North Atlantic storm track. Part I: land-sea contrast and orography

Understanding and predicting changes in storm tracks over longer time scales is a challenging problem, particularly in the North Atlantic. This is due in part to the complex range of forcings (land–sea contrast, orography, sea surface temperatures, etc.) that combine to produce the structure of the storm track. The impact of land–sea contrast and midlatitude orography on the North Atlantic storm track is investigated through a hierarchy of GCM simulations using idealized and “semirealistic” boundary conditions in a high-resolution version of the Hadley Centre atmosphere model (HadAM3). This framework captures the large-scale essence of features such as the North and South American continents, Eurasia, and the Rocky Mountains, enabling the results to be applied more directly to realistic modeling situations than was possible with previous idealized studies. The physical processes by which the forcing mechanisms impact the large-scale flow and the midlatitude storm tracks are discussed. The characteristics of the North American continent are found to be very important in generating the structure of the North Atlantic storm track. In particular, the southwest–northeast tilt in the upper tropospheric jet produced by southward deflection of the westerly flow incident on the Rocky Mountains leads to enhanced storm development along an axis close to that of the continent’s eastern coastline. The approximately triangular shape of North America also enables a cold pool of air to develop in the northeast, intensifying the surface temperature contrast across the eastern coastline, consistent with further enhancements of baroclinicity and storm growth along the same axis.

Negative correlations between control performance and verbalizable knowledge: indicators for implicit learning in process control tasks?

Negative correlations between task performance in dynamic control tasks and verbalizable knowledge, as assessed by a post-task questionnaire, have been interpreted as dissociations that indicate two antagonistic modes of learning, one being “explicit”, the other “implicit”. This paper views the control tasks as finite-state automata and offers an alternative interpretation of these negative correlations. It is argued that “good controllers” observe fewer different state transitions and, consequently, can answer fewer post-task questions about system transitions than can “bad controllers”. Two experiments demonstrate the validity of the argument by showing the predicted negative relationship between control performance and the number of explored state transitions, and the predicted positive relationship between the number of explored state transitions and questionnaire scores. However, the experiments also elucidate important boundary conditions for the critical effects. We discuss the implications of these findings, and of other problems arising from the process control paradigm, for conclusions about implicit versus explicit learning processes.

High-resolution, unstructured meshes for hydrodynamic models of the Great Barrier Reef, Australia

Accuracy and mesh generation are key issues for the high-resolution hydrodynamic modelling of the whole Great Barrier Reef. Our objective is to generate suitable unstructured grids that can resolve topological and dynamical features like tidal jets and recirculation eddies in the wake of islands. A new strategy is suggested to refine the mesh in areas of interest taking into account the bathymetric field and an approximated distance to islands and reefs. Such a distance is obtained by solving an elliptic differential operator, with specific boundary conditions. Meshes produced illustrate both the validity and the efficiency of the adaptive strategy. Selection of refinement and geometrical parameters is discussed. (c) 2006 Elsevier Ltd. All rights reserved.

The effect of a large freshwater perturbation on the glacial north Atlantic Ocean using a coupled general circulation model

The commonly held view of the conditions in the North Atlantic at the last glacial maximum, based on the interpretation of proxy records, is of large-scale cooling compared to today, limited deep convection, and extensive sea ice, all associated with a southward displaced and weakened overturning thermohaline circulation (THC) in the North Atlantic. Not all studies support that view; in particular, the "strength of the overturning circulation" is contentious and is a quantity that is difficult to determine even for the present day. Quasi-equilibrium simulations with coupled climate models forced by glacial boundary conditions have produced differing results, as have inferences made from proxy records. Most studies suggest the weaker circulation, some suggest little or no change, and a few suggest a stronger circulation. Here results are presented from a three-dimensional climate model, the Hadley Centre Coupled Model version 3 (HadCM3), of the coupled atmosphere - ocean - sea ice system suggesting, in a qualitative sense, that these diverging views could all have occurred at different times during the last glacial period, with different modes existing at different times. One mode might have been characterized by an active THC associated with moderate temperatures in the North Atlantic and a modest expanse of sea ice. The other mode, perhaps forced by large inputs of meltwater from the continental ice sheets into the northern North Atlantic, might have been characterized by a sluggish THC associated with very cold conditions around the North Atlantic and a large areal cover of sea ice. The authors' model simulation of such a mode, forced by a large input of freshwater, bears several of the characteristics of the Climate: Long-range Investigation, Mapping, and Prediction (CLIMAP) Project's reconstruction of glacial sea surface temperature and sea ice extent.

Case study of the use of remotely sensed data for modeling flood inundation on the river Severn, UK.

A methodology for using remotely sensed data to both generate and evaluate a hydraulic model of floodplain inundation is presented for a rural case study in the United Kingdom: Upton-upon-Severn. Remotely sensed data have been processed and assembled to provide an excellent test data set for both model construction and validation. In order to assess the usefulness of the data and the issues encountered in their use, two models for floodplain inundation were constructed: one based on an industry standard one-dimensional approach and the other based on a simple two-dimensional approach. The results and their implications for the future use of remotely sensed data for predicting flood inundation are discussed. Key conclusions for the use of remotely sensed data are that care must be taken to integrate different data sources for both model construction and validation and that improvements in ground height data shift the focus in terms of model uncertainties to other sources such as boundary conditions. The differences between the two models are found to be of minor significance.

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.