2 results
An improved model of near-inertial wave dynamics
- Olivier Asselin, William R. Young
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- Journal:
- Journal of Fluid Mechanics / Volume 876 / 10 October 2019
- Published online by Cambridge University Press:
- 01 August 2019, pp. 428-448
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- Article
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The YBJ equation (Young & Ben Jelloul, J. Marine Res., vol. 55, 1997, pp. 735–766) provides a phase-averaged description of the propagation of near-inertial waves (NIWs) through a geostrophic flow. YBJ is obtained via an asymptotic expansion based on the limit $\mathit{Bu}\rightarrow 0$, where $\mathit{Bu}$ is the Burger number of the NIWs. Here we develop an improved version, the YBJ+ equation. In common with an earlier improvement proposed by Thomas, Smith & Bühler (J. Fluid Mech., vol. 817, 2017, pp. 406–438), YBJ+ has a dispersion relation that is second-order accurate in $\mathit{Bu}$. (YBJ is first-order accurate.) Thus both improvements have the same formal justification. But the dispersion relation of YBJ+ is a Padé approximant to the exact dispersion relation and with $\mathit{Bu}$ of order unity this is significantly more accurate than the power-series approximation of Thomas et al. (2017). Moreover, in the limit of high horizontal wavenumber $k\rightarrow \infty$, the wave frequency of YBJ+ asymptotes to twice the inertial frequency $2f$. This enables solution of YBJ+ with explicit time-stepping schemes using a time step determined by stable integration of oscillations with frequency $2f$. Other phase-averaged equations have dispersion relations with frequency increasing as $k^{2}$ (YBJ) or $k^{4}$ (Thomas et al. 2017): in these cases stable integration with an explicit scheme becomes impractical with increasing horizontal resolution. The YBJ+ equation is tested by comparing its numerical solutions with those of the Boussinesq and YBJ equations. In virtually all cases, YBJ+ is more accurate than YBJ. The error, however, does not go rapidly to zero as the Burger number characterizing the initial condition is reduced: advection and refraction by geostrophic eddies reduces in the initial length scale of NIWs so that $\mathit{Bu}$ increases with time. This increase, if unchecked, would destroy the approximation. We show, however, that dispersion limits the damage by confining most of the wave energy to low $\mathit{Bu}$. In other words, advection and refraction by geostrophic flows does not result in a strong transfer of initially near-inertial energy out of the near-inertial frequency band.
6 - Social Integration of Immigrants with Special Reference to the Local and Spatial Dimension
- Edited by Rinus Penninx, Maria Berger, Karen Kraal
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- Book:
- The Dynamics of Migration and Settlement in Europe
- Published by:
- Amsterdam University Press
- Published online:
- 23 January 2021
- Print publication:
- 28 August 2006, pp 133-170
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Summary
Introduction
This chapter deals with the social dimension of integration processes of immigrants. The organisation of work units within IMISCOE defined the social dimension as distinct from the political, the economic and the cultural/religious dimension which are treated in the two preceding and the following chapter respectively. This field is a vast one covering a significant amount of research in the past decades. In surveying the literature on social integration we will focus specifically on its local and spatial expressions for reasons that we will unfold in the next pages.
In the first section, we discuss some of the conceptual issues related to the term ‘integration’ and its use in the academic and policy fields. We discuss the notion of integration as a general sociological concept and propose to use the social environment, in which individuals and groups form interdependencies, as the special unit of study. Focusing on spaces as the locus of developing interdependencies, we emphasise the spatial dimension of immigrants’ social integration processes.
Section two focuses specifically on the spatial dimensions of integration. It reviews the relationships between the characteristics of the housing market and their implications in terms of socio-ethnic segregation, emphasising the spatial dimension of social integration. Immigrants’ and ethnic minorities’ geographical placement and the extent of their mobility condition their access to urban resources (e.g. housing, education, health, jobs and different kinds of goods and services). We discuss the basic concepts of ethnic segregation as well as its advantages and disadvantages by drawing on contemporary literature. The main determinants of residential segregation and the manner in which they are explained and conveyed in the literature are surveyed. Finally, we discuss the issue of accessibility to urban resources, as a spatial expression of social integration and its measurement.
In the third and final section, we seek to synthesise the key ideas and conclusions of the previous sections and present a number of proposals for future lines of research.
From assimilation to integration and back again
If the current use of the concept of integration in social sciences and policy when dealing with immigrant settlement is relatively recent, the associated notions of assimilation, acculturation and accommodation have a longer history.