Hall, PhilipOverview
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Most widely held works about
Philip Hall
Most widely held works by
Philip Hall
Group theory : essays for Philip Hall
by F Grunewald
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Book
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6 editions published in 1984 in English and Undetermined and held by 300 WorldCat member libraries worldwide
The collected works of Philip Hall
by Philip Hall
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Book
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10 editions published between 1987 and 1988 in English and held by 238 WorldCat member libraries worldwide
The evolution equations for Taylor vortices in the small gap limit
by Philip Hall
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3 editions published in 1983 in English and held by 221 WorldCat member libraries worldwide
The fully nonlinear development of Görtler vortices in growing boundary layers
by Philip Hall
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4 editions published in 1987 in English and held by 185 WorldCat member libraries worldwide
Nilpotent groups. Notes of lectures given at the Canadian Mathematical Congress summer seminar, University of Alberta, 1230 August, 1957
by Philip Hall
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Book
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16 editions published between 1957 and 1979 in English and Undetermined and held by 131 WorldCat member libraries worldwide
On a class of unsteady threedimensional Navier Stokes solutions relevant to rotating disk flows threshold amplitudes and finite time singularities
by Philip Hall
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Book
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2 editions published in 1990 in English and held by 130 WorldCat member libraries worldwide A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the zaxis in a fluid occupying a semiinfinite region which, at large distances from the disc, has velocity field proportional to (x, y,0) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for threedimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to timeperiodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying in time
On the receptivity and nonparallel stability of traveling disturbances in rotating disk flow
by Institute for Computer Applications in Science and Engineering
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Book
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1 edition published in 1990 in English and held by 129 WorldCat member libraries worldwide The generation and evolution of small amplitude long wavelength travelling disturbances in rotating disk flow is the subject of this paper. The steady rotational speed of the disk is perturbed so as to introduce high frequency oscillations in the flow field. Secondly, we introduce surface imperfections on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations which are solved numerically. It is found that, for the class of disturbances considered here (wavelength on the order of Reynolds number), eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are excited the most. The width of these roughness elements in the radial direction is about .1r* sub 0 where r* 0 is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wavenumber than for a positive one. Typical wave angles for these disturbances are about 26 deg
Concerning the interaction of nonstationary crossflow vortices in a threedimensional boundary layer
by Institute for Computer Applications in Science and Engineering
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Book
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2 editions published in 1990 in English and held by 127 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 NavierStokes 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 nonparallelism could be provided for within the asymptotic framework
On the instability of hypersonic flow past a flat plate
by Nicholas D Blackaby
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Book
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2 editions published in 1990 in English and held by 126 WorldCat member libraries worldwide The instability of hypersonic boundarylayer 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 socalled vorticity mode of instability of the viscous hypersonic boundary layer. The instability of the hypersonic boundary layer is noninteractive. 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 (Msq). 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)
Görtler vortices in growing boundary layers the leading edge receptivity problem, linear growth and the nonlinear breakdown stage
by Philip Hall
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Book
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2 editions published in 1989 in English and held by 115 WorldCat member libraries worldwide
On the Görtler instability in hypersonic flows Sutherland law fluids and real gas effects
by Y. B Fu
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Book
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2 editions published in 1990 in English and held by 92 WorldCat member libraries worldwide The Goertler vortex instability mechanism in a hypersonic boundary layer on a curved wall is investigated in this paper. The aim is to clarify the precise roles of the effects of boundary layer growth, wall cooling and gas dissociation in the determination of stability properties. First assume that the fluid is an ideal gas with viscosity given by Sutherland's law. When the free stream Mach number M is large, the boundary layer divides into two sublayers: a wall layer of O(Mexp 3/2) thickness over which the basic state temperature is O(Msq) and a temperature adjustment layer of O(1) thickness over which basic state temperature decreases monotonically to its free stream value. Goertler vortices which have wavelength comparable with the boundary layer thickness (i. e. have local wavenumber of order M exp 3/2) are referred to as wall modes. Their downstream evolution is governed by a set of parabolic partial differential equations and that they have the usual features of Goertler vortices in incompressible boundary layers. As the local wavenumber increases, the neutral Goertler number decreases and the centre of vortex activity moves towards the temperature adjustment layer. Goertler vortices with wavenumber of order one or larger must be necessarily be trapped in the temperature adjustment layer and it is this mode which is most dangerous. For this mode the leading order term in the Goertler number expansion is independent of the wavelength number and is due to the curvature of the basic state. This term is also the asymptotic limit of the neutral Goertler numbers of the wall mode. To determine the higher order correction terms in the Goertler number expansion, one has to distinguish between two wall curvature cases
On the stability of an infinite swept attachment line boundary layer
by Philip Hall
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Book
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1 edition published in 1984 in English and held by 77 WorldCat member libraries worldwide
On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid
by Philip Hall
(
Book
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1 edition published in 1983 in English and held by 76 WorldCat member libraries worldwide
On the instability of the flow in an oscillating tank of fluid
by Philip Hall
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Book
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4 editions published in 1993 in English and held by 72 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
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Book
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4 editions published in 1993 in English and held by 71 WorldCat member libraries worldwide The nonlinear interaction equations describing vortexRayleigh 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
On the receptivity problem for Görtler vortices vortex motions induced by wall roughness
by J. P Denier
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Book
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2 editions published in 1990 in English and held by 71 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
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Book
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2 editions published in 1993 in English and held by 71 WorldCat member libraries worldwide In this paper we make an investigation of the receptivity of boundary layer flows to Gortler vortex modes. A study by Denier, Hall, and Seddougui (1991) of the generation of vortices by wall roughness elements concluded that such elements are extremely poor as mechanisms to stimulate short wavelength modes. That work also examined the equivalent problem pertaining to O(1) wavelength modes but that analysis was in error. We reexamine this problem here and demonstrate how the form of the wall roughness is crucial in determining the vortex stability characteristics downstream of the roughness. In particular we investigate the cases of both isolated and distributed forcing functions and show that in general a distributed function is much more important in generating vortices than are either isolated roughness or freestream disturbances. Receptivity, Vortex
A phase equation approach to boundary layer instability theory Tollmien Schlichting waves
by Philip Hall
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Book
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3 editions published in 1994 in English and held by 71 WorldCat member libraries worldwide Our concern is with the evolution of large amplitude TollmienSchlichting waves in boundary layer flows. In fact the disturbances we consider are of a comparable size to the unperturbed state. We shall describe twodimensional disturbances which are locally periodic in time and space. This is achieved using a phase equation approach of the type discussed by Howard and Kopell (1977) in the context of reactiondiffusion equations. We shall consider both large and 0(1) Reynolds numbers flows though, in order to keep our asymptotics respectable, our finite Reynolds number calculation will be carried out for the asymptotic suction flow. Our large Reynolds number analysis, though carried out for Blasius flow, is valid for any steady twodimensional boundary layer. In both cases the phase equation approach shows that the wavenumber and frequency will develop shocks or other discontinuities as the disturbance evolves. As a special case we consider the evolution of constant frequency/wavenumber disturbances and show that their modulational instability is controlled by Burgers equation at finite Reynolds number and by a new integrodifferential evolution equation at large Reynolds numbers. For the large Reynolds number case the evolution equation points to the development of a spatially localized singularity at a finite time. The threedimensional generalizations of the evolution equations is also given for the case of weak spanwise modulations. Boundary layer, Phase equation
On the spatial evolution of longwavelength Görtler vortices governed by a viscous inviscid interaction
by Meelan Choudhari
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Book
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3 editions published in 1992 in English and held by 70 WorldCat member libraries worldwide The generation of longwavelength, viscousinviscid interactive Gortler vortices is studied in the linear regime by numerically solving the timedependent governing equations. It is found that time dependent surface deformations, which assume a fixed nonzero shape at large times, generate steady Gortler vortices that amplify in the downstream direction. Thus, the Gortler instability in this regime is shown to be convective in nature, contrary to the earlier findings of Ruban and Savenkov. The disturbance pattern created by steady and streamwiseelongated surface obstacles on a concave surface is examined in detail, and also contrasted with the flow pattern due to roughness elements with aspect ratio of order unity on flat surfaces. Finally, tile applicability of the BriggsBers criterion to unstable physical systems of this type is questioned by providing a counterexample in the form of the inviscid limit of interactive Gortler vortices
The nonlinear evolution of inviscid Gortler vortices in threedimensional boundary layers
by Nicholas D Blackaby
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Book
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1 edition published in 1995 in English and held by 70 WorldCat member libraries worldwide more
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Adelaide Symphony Orchestra AirplanesWings, Sweptback Algebra Algebra, Universal Australia Base flow (Aerodynamics) Boundary layer Concert programs Equations, Cubic Fluid dynamics Fluid mechanics Group theory Hall, Philip Hall, Philip, Mathematicians Mathematics Monteverdi, Claudio, Mozart, Wolfgang Amadeus, Nilpotent groups Oscillations Performances Taylor vortices Transition flow Unsteady flow (Aerodynamics) Vortex generators Vortexmotion Wave mechanics

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