Transition in inclined internally heated fluid layers

Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

Range of validity of weakly non-linear theory in Rayleigh-Bénard problem

In this paper we examine the equilibrium states of finite amplitude flow in a horizontal fluid layer with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau constants and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infinitesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighborhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable. © 2009 The Physical Society of Japan.

Range of validity of weakly non-linear theory in Rayleigh-Bénard convection

In this paper we examine the equilibrium states of periodic finite amplitude flow in a horizontal channel with differential heating between the two rigid boundaries. The solutions to the Navier-Stokes equations are obtained by means of a perturbation method for evaluating the Landau coefficients and through a Newton-Raphson iterative method that results from the Fourier expansion of the solutions that bifurcate above the linear stability threshold of infini- tesimal disturbances. The results obtained from these two different methods of evaluating the convective flow are compared in the neighbourhood of the critical Rayleigh number. We find that for small Prandtl numbers the discrepancy of the two methods is noticeable.

Pattern formation in volumetrically heated fluids

Finite element simulations have been performed along side normal mode analysis on the linear stability that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.

Bifurcation contrasts between plane Poiseuille flow and plane Magnetohydrodynamic flow

The stability characteristics of an incompressible viscous pressure-driven flow of an electrically conducting fluid between two parallel boundaries in the presence of a transverse magnetic field are compared and contrasted with those of Plane Poiseuille flow (PPF). Assuming that the outer regions adjacent to the fluid layer are perfectly electrically insulating, the appropriate boundary conditions are applied. The eigenvalue problems are then solved numerically to obtain the critical Reynolds number Rec and the critical wave number ac in the limit of small Hartmann number (M) range to produce the curves of marginal stability. The non-linear two-dimensional travelling waves that bifurcate by way of a Hopf bifurcation from the neutral curves are approximated by a truncated Fourier series in the streamwise direction. Two and three dimensional secondary disturbances are applied to both the constant pressure and constant flux equilibrium solutions using Floquet theory as this is believed to be the generic mechanism of instability in shear flows. The change in shape of the undisturbed velocity profile caused by the magnetic field is found to be the dominant factor. Consequently the critical Reynolds number is found to increase rapidly with increasing M so the transverse magnetic field has a powerful stabilising effect on this type of flow.

Asymptotic theory of wall-attached convection in a horizontal fluid layer with a vertical magnetic field

A horizontal fluid layer heated from below in the presence of a vertical magnetic field is considered. A simple asymptotic analysis is presented which demonstrates that a convection mode attached to the side walls of the layer sets in at Rayleigh numbers much below those required for the onset of convection in the bulk of the layer. The analysis complements an earlier analysis by Houchens [J. Fluid Mech. 469, 189 (2002)] which derived expressions for the critical Rayleigh number for the onset of convection in a vertical cylinder with an axial magnetic field in the cases of two aspect ratios. © 2008 American Institute of Physics.

Pattern competition in volumetricaly heated fluids

Finite element simulations have been performed along side Galerkin-type calculations that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.

Linear stability of flow past two circular cylinders in a side-by-side arrangement

The linear stability of flow past two circular cylinders in a side-by-side arrangement is investigated theoretically, numerically and experimentally under the assumption of a two-dimensional flow field, in order to explore the origin of in-phase and antiphase oscillatory flows. Steady symmetric flow is realized at a small Reynolds number, but becomes unstable above a critical Reynolds number though the solution corresponding to the flow still satisfies the basic equations irrespective of the magnitude of the Reynolds number. We obtained the solution numerically and investigated its linear stability. We found that there are two kinds of unstable modes, i.e., antisymmetric and symmetric modes, which lead to in-phase and antiphase oscillatory flows, respectively. We determined the critical Reynolds numbers for the two modes and evaluated the critical distance at which the most unstable disturbance changes from the antisymmetric to the symmetric mode, or vice versa. ©2005 The Physical Society of Japan.

角柱列を過ぎる流れの合流現象と乱流への遷移

Interactions between the wakes in a flow past a row of square bars are investigated by numerical simulations, the linear stability analysis and the bifurcation analysis. It is assumed that the row of square bars is placed across a uniform flow. Two-dimensional and incompressible flow field is also assumed. The flow is steady and symmetric along a streamwise centerline through the center of each square bar at low Reynolds numbers. However, it becomes unsteady and periodic in time at the Reynolds numbers larger than a critical value, and then the wakes behind the square bars become oscillatory. It is found by numerical simulations that vortices are shed synchronously from every couple of adjacent square bars in the same phase or in the anti-phase depending upon the distance between the bars. The synchronous shedding of vortices is clarified to occur due to an instability of the steady symmetric flow by the linear stability analysis. The bifurcation diagram of the flow is obtained and the critical Reynolds number of the instability is evaluated numerically.

Police interviews with women reporting rape: a critical discourse analysis

This study investigates the discursive patterns of interactions between police interviewers and women reporting rape in significant witness interviews. Data in the form of video recorded interviews were obtained from a UK police force for the purposes of this study. The data are analysed using a multi-method approach, incorporating tools from micro-sociology, Conversation Analysis and Discursive Psychology, to reveal patterns of interactional control, negotiation, and interpretation. The study adopts a critical approach, which is to say that as well as describing discursive patterns, it explains them in light of the discourse processes involved in the production and consumption of police interview talk, and comments on the relationship between these discourse processes and the social context in which they occur. A central focus of the study is how interviewers draw on particular interactional resources to shape interviewees? accounts in particular ways, and this is discussed in relation to the institutional role of the significant witness interview. The discussion is also extended to the ways in which mainstream rape ideology is both reflected in, and maintained by, the discursive choices of participants. The findings of this study indicate that there are a number of issues to be addressed in terms of the training currently offered to officers at Level 2 of the Professionalising Investigation Programme (PIP) (NPIA, 2009) who intend to conduct significant witness interviews. Furthermore, a need is identified to bring the linguistic and discursive processes of negotiation and transformation identified by the study to the attention of the justice system as a whole. This is a particularly pressing need in light of judicial reluctance to replace written witness statements, the current „end product? of significant witness interviews, with the video recorded interview in place of direct examination in cases of rape.

The core critical success factors in implementation of enterprise resource planning systems

The Implementation of Enterprise Resource Planning (ERP) systems require huge investments while ineffective implementations of such projects are commonly observed. A considerable number of these projects have been reported to fail or take longer than it was initially planned, while previous studies show that the aim of rapid implementation of such projects has not been successful and the failure of the fundamental goals in these projects have imposed huge amounts of costs on investors. Some of the major consequences are the reduction in demand for such products and the introduction of further skepticism to the managers and investors of ERP systems. In this regard, it is important to understand the factors determining success or failure of ERP implementation. The aim of this paper is to study the critical success factors (CSFs) in implementing ERP systems and to develop a conceptual model which can serve as a basis for ERP project managers. These critical success factors that are called “core critical success factors” are extracted from 62 published papers using the content analysis and the entropy method. The proposed conceptual model has been verified in the context of five multinational companies.

The value of risk reporting:a critical analysis of value-at-risk disclosures in the banking sector

This paper critically reviews the evolution of financial reporting in the banking sector with specific reference to the reporting of market risk and the growing use of the measure known as Value at Risk (VaR). The paper investigates the process by which VaR became 'institutionalised'. The analysis highlights a number of inherent limitations of VaR as a risk measure and questions the usefulness of published VaR disclosures, concluding that risk 'disclosure' might be more apparent than real. It also looks at some of the implications for risk reporting practice and the accounting profession more generally.