A cell by cell anisotropic adaptive mesh ALE scheme for the numerical solution of the Euler equations

In this paper a cell by cell anisotropic adaptive mesh technique is added to an existing staggered mesh Lagrange plus remap finite element ALE code for the solution of the Euler equations. The quadrilateral finite elements may be subdivided isotropically or anisotropically and a hierarchical data structure is employed. An efficient computational method is proposed, which only solves on the finest level of resolution that exists for each part of the domain with disjoint or hanging nodes being used at resolution transitions. The Lagrangian, equipotential mesh relaxation and advection (solution remapping) steps are generalised so that they may be applied on the dynamic mesh. It is shown that for a radial Sod problem and a two-dimensional Riemann problem the anisotropic adaptive mesh method runs over eight times faster.

A cell by cell anisotropic adaptive mesh ALE method

A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian (ALE) method for the solution of the Euler equations is described. An efficient approach to equipotential mesh relaxation on anisotropically refined meshes is developed. Results for two test problems are presented.

On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear

We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. $F\,{>}\,F_\mathrm{critical}\,{\equiv}\, \upi^2/2$), and are therefore consistent with generation by a baroclinic instability. The unbalanced short-wavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia–gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baro-clinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin–Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. $\hbox{\it Ri}\,{<}\,\hbox{\it Ri}_\mathrm{critical}\,{\equiv}\, 1$), and are therefore consistent with generation by a Kelvin–Helmholtz instability. We calculate five indicators of short-wave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of short-wave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia–gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia–gravity waves generated by spontaneous adjustment of the large-scale flow.

Spontaneous generation and impact of inertia-gravity waves in a stratified, two-layer shear flow

Inertia-gravity waves exist ubiquitously throughout the stratified parts of the atmosphere and ocean. They are generated by local velocity shears, interactions with topography, and as geostrophic (or spontaneous) adjustment radiation. Relatively little is known about the details of their interaction with the large-scale flow, however. We report on a joint model/laboratory study of a flow in which inertia-gravity waves are generated as spontaneous adjustment radiation by an evolving large-scale mode. We show that their subsequent impact upon the large-scale dynamics is generally small. However, near a potential transition from one large-scale mode to another, in a flow which is simultaneously baroclinically-unstable to more than one mode, the inertia-gravity waves may strongly influence the selection of the mode which actually occurs.

Voronoi, Delaunay, and Block-Structured Mesh Refinement for Solution of the Shallow-Water Equations on the Sphere

Alternative meshes of the sphere and adaptive mesh refinement could be immensely beneficial for weather and climate forecasts, but it is not clear how mesh refinement should be achieved. A finite-volume model that solves the shallow-water equations on any mesh of the surface of the sphere is presented. The accuracy and cost effectiveness of four quasi-uniform meshes of the sphere are compared: a cubed sphere, reduced latitude–longitude, hexagonal–icosahedral, and triangular–icosahedral. On some standard shallow-water tests, the hexagonal–icosahedral mesh performs best and the reduced latitude–longitude mesh performs well only when the flow is aligned with the mesh. The inclusion of a refined mesh over a disc-shaped region is achieved using either gradual Delaunay, gradual Voronoi, or abrupt 2:1 block-structured refinement. These refined regions can actually degrade global accuracy, presumably because of changes in wave dispersion where the mesh is highly nonuniform. However, using gradual refinement to resolve a mountain in an otherwise coarse mesh can improve accuracy for the same cost. The model prognostic variables are height and momentum collocated at cell centers, and (to remove grid-scale oscillations of the A grid) the mass flux between cells is advanced from the old momentum using the momentum equation. Quadratic and upwind biased cubic differencing methods are used as explicit corrections to a fast implicit solution that uses linear differencing.

Predicting mesh density for adaptive modelling of the global atmosphere

The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1–20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.

Questions of Friendship and Degrees of Transnationality among Second-Generation Return Migrants to Barbados

While the academic literature has demonstrated the importance of social networks in relation to the process of migration, investigations have rarely examined in detail the personal-social adjustment issues that migrants and return migrants face. This study examines the context and types of friendship pattern that young return migrants from Britain cultivate in Barbados. The research centres on a wholly under-researched demographic groupyoung return migrants or second-generation Barbadians who have decided to return to the birthplace of their parents. The investigation is based on 51 in-depth interviews carried out with these young returnees to Barbados. Presenting a taxonomy of friendship types, it is argued that, for the 'Bajan-Brits' under study, the cultivation of new friendships is highly problematic. The research identifies what we refer to as the 'insular transnational', the 'we are different' and the 'all-inclusive transnational' friendship types among the young returnees. Our analysis also shows that problems of friendship are highly gendered, with females reporting the most problems due to what is perceived as sexual and workplace competition. It is stressed that these circumstances exemplify the essentially 'hybrid', 'liminal' and 'in-between' positionality of these second-generation migrants within contemporary Barbadian society.

'Black skins-white masks': Postcolonial reflections on 'race', gender and second generation return migration to the Caribbean

This paper illustrates the opportunities afforded by the adoption of postcolonial discourse in development geography, drawing specifically on issues of transnationalism, hybridity and inbetweeness. The utility of such notions and associated approaches is illustrated by the authors' current research on the migration of young, second generation and foreign-born 'Bajan-Brits' to the small Caribbean island nation of Barbados, the homeland of their parents. Focussing on issues of 'race' and gender, the paper examines the experiences of return migration among this cohort from an interpretative perspective framed within postcolonial discourse. It argues that notwithstanding the considerable sociocultural problems of adjustment encountered, these Bajan-Brit 'returnees' may be seen as occupying positions of relative economic privilege. Theirs is a liminal space derived by virtue of having been born and/or raised in the UK and being of the black 'race'. Accordingly, they are demonstrated to be both advantaged and disadvantaged; both transnational and national; and black but, in some senses, symbolically white.

Quality of Life Issues and Second-Generation Migration: the Case of 'Bajan-Brit Returnees'

This paper forms part of research that is investigating the migration of young Bajan-Brits to Barbados. Specifically, it explores the role of quality of life issues in the decision-making processes of young Bajan-Brits as they negotiate their 'return' to Barbados. The research, based on 51 in-depth qualitative interviews conducted with an under-researched cohort of young Bajan-Brits living in Barbados, argues from a 'lure of home' conceptualisation that the return of young Bajan-Brits to Barbados can best be understood from the context of a search for a better quality of life in the face of social and economic disenfranchisement in the UK context. Subsequently, the paper examines the extent to which the quality of life factors which formed the basis of return to Barbados have in fact been realised on the part of young Bajan-Brits in their adjustment to life in Barbados. The paper ultimately argues that despite problems of adjustment, young Bajan-Brits have generally been successful in actualising a better quality of life in Barbados. Copyright (C) 2009 John Wiley & Sons, Ltd.