WorldCat Identities

Hall, Philip

Overview
Works: 108 works in 242 publications in 1 language and 4,446 library holdings
Genres: Obituaries  Conference papers and proceedings 
Roles: Author, Editor, Composer, Lyricist, Printer, Other, jt
Classifications: QA171, 512.22
Publication Timeline
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Most widely held works by Philip Hall
Group theory : essays for Philip Hall by F Grunewald( Book )

2 editions published in 1984 in English and held by 296 WorldCat member libraries worldwide

The collected works of Philip Hall by Philip Hall( Book )

6 editions published between 1987 and 1988 in English and held by 234 WorldCat member libraries worldwide

Concerning the interaction of non-stationary cross-flow vortices in a three-dimensional boundary layer by Andrew P Bassom( Book )

5 editions published in 1990 in English and Undetermined and held by 178 WorldCat member libraries worldwide

Recently there has been much work devoted to considering some of the many and varied interaction mechanisms which may be operative in part of three- dimensional boundary layer flows, here are concern resonant triads of crossflow vortices. In contrast to previous work the effects of interactions upon resonant triads are examined with each member of the triad has the property of being linearly neutrally stable; then the importance of the interplay between modes can be relatively easily assessed. Investigating modes within the boundary layer flow above a rotating disc; this choice is motivated by the similarity between this disc flow and many important practical flows and, secondly, our selected flow is an exact solution of the Navier-Stokes equations which makes its theoretical analysis especially attractive. The desired triads of linearly neutrally stable modes can exist within the chosen boundary layer flow and then subsequently obtain evolution equations to describe the development of the amplitudes of these modes once the interaction mechanism is accounted for. The coefficients of the interaction terms within the evolution equations are, the general, given by quite intricate expressions although some elementary numerical work shows that the evaluation of these coefficients is practicable. The basis of this work lends itself to generalization to more complicated boundary layers and effects of detuning or non-parallelism could be provided for within the asymptotic framework
On the instability of hypersonic flow past a flat plate by Nicholas D Blackaby( Book )

4 editions published in 1990 in English and held by 177 WorldCat member libraries worldwide

The instability of hypersonic boundary-layer flows over flat plates is considered. The viscosity of the fluid is taken to be governed by Sutherland's law, which gives a much more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapmans's approximate linear law; although at lower speeds the temperature variation of the mean state is less pronounced so that the Chapman law can be used with some confidence. Attention is focussed on the so-called vorticity mode of instability of the viscous hypersonic boundary layer. The instability of the hypersonic boundary layer is non-interactive. The vorticity mode of instability of this flow operates on a significantly different lengthscale than that obtained if a Chapman viscosity law is assumed. The growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O (M-sq). Next, the development of the vorticity mode as the wavenumber decreases is described, and it is shown that acoustic modes emerge when the wavenumber has decreased from it's O(1) initial value to O (M to the -3/2 power). (jhd)
Nilpotent groups. Notes of lectures given at the Canadian Mathematical Congress summer seminar, University of Alberta, 12-30 August, 1957 by Philip Hall( Book )

17 editions published between 1957 and 1970 in English and held by 130 WorldCat member libraries worldwide

The evolution equations for Taylor vortices in the small gap limit by Philip Hall( Book )

2 editions published in 1983 in English and held by 83 WorldCat member libraries worldwide

On the instability of the flow in an oscillating tank of fluid by Philip Hall( Book )

6 editions published in 1993 in English and held by 83 WorldCat member libraries worldwide

The instability of a viscous fluid inside a rectangular tank oscillating about an axis parallel to the largest face of the tank is investigated in the linear regime. The flow is shown to be unstable to both longitudinal roll and standing wave instabilities. The particular cases of low and high oscillation frequencies are discussed in detail and the results obtained for the standing wave instability at low frequencies shed light on the corresponding steady flow instability problem. The relationship between the roll instability and convective or centrifugal instabilities in unsteady boundary layers is discussed. The eigenvalue problems associated with the roll and standing wave instabilities are solved using Floquet theory and a combination of numerical and asymptotic methods. The results obtained are compared to the recent experimental investigation of Bolton and Maurer (1992) which indeed provided the stimulus for the present investigation. Oscillatory flow, Instability
On the initial stages of vortex wave interactions in highly curved boundary layer flows by Philip Hall( Book )

6 editions published in 1993 in English and held by 82 WorldCat member libraries worldwide

The nonlinear interaction equations describing vortex-Rayleigh wave interactions in highly curved boundary layers are derived. These equations describe a strongly nonlinear interaction between an inviscid wave system and a streamwise vortex. The coupling between the two structures is quite different than that found by Hall and Smith (1991) in the absence of wall curvature. Here the vortex is forced over a finite region of the flow rather than in the critical layer associated with the wave system. When the interaction takes place the wave system remains locally neutral as it moves downstream and it's self interaction drives a vortex field of the same magnitude as that driven by the wall curvature. This modification of the mean state then alters the wave properties and forces the wave amplitude to adjust itself in order that the wave frequency is constant. Solutions of the interaction equations are found for the initial stages of the interaction in the case when the wave amplitude is initially small. Our analysis suggests that finite amplitude disturbances can only exist when the vortex field is finite at the initial position where the interaction is stimulated ... Vortex wave interactions
Crossflow effects on the growth rate of inviscid Görtler vortices in a hypersonic boundary layer by Y. B Fu( Book )

4 editions published in 1992 in English and held by 82 WorldCat member libraries worldwide

The nonlinear evolution of inviscid Gortler vortices in three-dimensional boundary layers by Nicholas D Blackaby( Book )

2 editions published in 1995 in English and held by 82 WorldCat member libraries worldwide

The nonlinear evolution of modes on unstable stratified shear layers by Nicholas D Blackaby( Book )

4 editions published in 1993 in English and held by 81 WorldCat member libraries worldwide

The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical- layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by ail integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear
On the nonlinear development of the most unstable Görtler vortex mode by J. P Denier( Book )

6 editions published in 1991 in English and held by 81 WorldCat member libraries worldwide

The nonlinear development of the most unstable Goertler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Goertlermode is confined to a viscous wall layer of thickness O(G to the 1/5th power) and has spanwise wavelength O(G to the 1/5th power); it is, of course, most relevant to flow situations where the Gortler number G>> 1. The nonlinear equations governing the evolution of this mode over an O(G to the 3/5th power) streamwise lengthscale are derived and are found to be a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Goertler equations valid for O(1) Goertler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flow field as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer
On the spatial evolution of long-wavelength Görtler vortices governed by a viscous inviscid interaction by Meelan Choudhari( Book )

2 editions published in 1992 in English and held by 80 WorldCat member libraries worldwide

On the receptivity problem for Görtler vortices vortex motions induced by wall roughness by J. P Denier( Book )

4 editions published in 1990 in English and held by 79 WorldCat member libraries worldwide

The receptivity problem for Goertler vortices induced by wall roughness is investigated. The roughness is modelled by small amplitude perturbations to the curved wall over which the flow takes place. Linear theory can be used for small perturbations. The roughness will vary in the spanwise direction on the boundary layer length scale, whilst in the flow direction the corresponding variation is on the length scale over which the wall curvature varies. In fact the latter condition can be relaxed to allow for a faster stream wise roughness variation so long as the variation does not become as fast as that in the spanwise direction. The function which describes the roughness is assumed to be such that its spanwise and streamwise dependencies can be separated; this will enable the use of Fourier or Laplace transforms where appropriate. The cases of isolated and distributed roughness elements are investigated and the coupling coefficient which relates the amplitude of the forcing and the induced vortex amplitude is found asymptotically in the small wavelength limit. This coefficient is exponentially small in the latter limit so that it is unlikely that this mode can be stimulated directly by wall roughness. The situation at 0(1) wavelengths is quite different and this is investigated numerically for different forcing functions. An isolated roughness element induces a vortex field which grows within a wedge at a finite distance downstream of the element. Immediately downstream of the obstacle the disturbed flow produced by the element decays in amplitude. The receptivity problem at larger Goertler numbers appropriate to relatively large wall curvature is discussed in detail. (JHD)
On the receptivity problem for 0 (1) wavelength by Andrew P Bassom( Book )

1 edition published in 1993 in English and held by 79 WorldCat member libraries worldwide

Effects of Görtler vortices, wall cooling and gas dissociation on the Rayleigh instability in a hypersonic boundary layer by Y. B Fu( Book )

4 editions published in 1991 in English and held by 79 WorldCat member libraries worldwide

A phase equation approach to boundary layer instability theory Tollmien Schlichting waves by Philip Hall( Book )

3 editions published in 1994 in English and held by 79 WorldCat member libraries worldwide

The inviscid secondary instability of fully nonlinear longitudinal vortex structures in growing boundary layers by Philip Hall( Book )

4 editions published in 1990 in English and held by 78 WorldCat member libraries worldwide

The inviscid instability of a longitudinal vortex structure within a steady boundary layer is investigated. The instability has wavelength comparable with the boundary layer thickness so that a quasi-parallel approach to the instability problem can be justified. The generalization of the Rayleigh equation to such a flow is obtained and solved for the case when the vortex structure is induced by curvature. Two distinct modes of instability are found; these modes correspond with experimental observations on the breakdown process for Goertler vortices. Keywords: Vortex, Inviscid secondary instability
On the instability of boundary layers on heated flat plates by Philip Hall( Book )

4 editions published in 1991 in English and held by 78 WorldCat member libraries worldwide

The stability of a boundary layer on a heated flat plate is investigated in the linear regime. The flow is shown to be unstable to longitudinal vortex structures which in general develop in a nonparallel manner in the streamwise direction. Solutions of the nonparallel equations are obtained numerically at 0(1) values of the appropriate stability parameter, ie the Grashof number. The particular cases investigated relate to the situations when the instability is induced by localized or distributed wall roughness or nonuniform wall heating. The case when the vortices are induced by freestream disturbances is also considered. The fastest growing mode is found to be governed by a quasi-parallel theory at high wavenumbers. The wavenumber and growth rate of the fastest growing mode are found in closed form. At low wavenumbers the vortex instability is shown to be closely related to Tollmein- Schlichting waves, the effect of wall heating or cooling on the latter type of instability is discussed
IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers : proceedings of the IUTAM Symposium held in Manchester, UK, 17-20 July 1995 by Peter W Duck( Book )

5 editions published in 1996 in English and held by 66 WorldCat member libraries worldwide

Most fluid flows of practical importance are fully three-dimensional, so the non-linear instability properties of three-dimensional flows are of particular interest. In some cases the three-dimensionality may have been caused by a finite amplitude disturbance whilst, more usually, the unperturbed state is three-dimensional. Practical applications where transition is thought to be associated with non-linearity in a three- dimensional flow arise, for example, in aerodynamics (swept wings, engine nacelles, etc.), turbines and aortic blood flow. Here inviscid `cross-flow' disturbances as well as Tollmien-Schlichting and Görtler vortices can all occur simultaneously and their mutual non-linear behaviour must be understood if transition is to be predicted. The non-linear interactions are so complex that usually fully numerical or combined asymptotic/numerical methods must be used. Moreover, in view of the complexity of the instability processes, there is also a growing need for detailed and accurate experimental information. Carefully conducted tests allow us to identify those elements of a particular problem which are dominant. This assists in both the formulation of a relevant theoretical problem and the subsequent physical validation of predictions. It should be noted that the demands made upon the skills of the experimentalist are high and that the tests can be extremely sophisticated - often making use of the latest developments in flow diagnostic techniques, automated high speed data gathering, data analysis, fast processing and presentation
 
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IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers : proceedings of the IUTAM Symposium held in Manchester, UK, 17-20 July 1995
Alternative Names
Philip Hall britisk matematikar

Philip Hall britisk matematiker

Philip Hall Brits wiskundige (1904-1982)

Philip Hall brittisk matematiker

Philip Hall englischer Mathematiker

Philip Hall matematico britannico

Philip Hall mathématicien russe

فیلیپ هال ریاضی‌دان بریتانیایی

필립 홀

菲利浦·赫爾

Languages
English (99)

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