Saffman, P. G.
Overview
Works:  89 works in 136 publications in 3 languages and 683 library holdings 

Genres:  Academic theses 
Roles:  Author, Thesis advisor 
Classifications:  QA925, 532.0595 
Publication Timeline
.
Most widely held works by
P. G Saffman
Vortex dynamics by
P. G Saffman(
Book
)
36 editions published between 1992 and 2001 in 3 languages and held by 540 WorldCat member libraries worldwide
The discovery of coherent structures in turbulence has fostered the hope that the study of vortices will lead to models and an understanding of turbulent flow, thereby solving or at least making less mysterious one of the great unresolved problems of classical physics. Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. The emphasis in this monograph is on the classical theory of inviscid incompressible fluids containing finite regions of vorticity. The effects of viscosity, compressibility, inhomogeneity, and stratification are enormously important in many fields of application, from hypersonic flight to global environmental fluid mechanics. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary. This book will be of interest to students of fluid mechanics, turbulence, and vortex methods as well as to applied mathematicians and engineers
36 editions published between 1992 and 2001 in 3 languages and held by 540 WorldCat member libraries worldwide
The discovery of coherent structures in turbulence has fostered the hope that the study of vortices will lead to models and an understanding of turbulent flow, thereby solving or at least making less mysterious one of the great unresolved problems of classical physics. Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. The emphasis in this monograph is on the classical theory of inviscid incompressible fluids containing finite regions of vorticity. The effects of viscosity, compressibility, inhomogeneity, and stratification are enormously important in many fields of application, from hypersonic flight to global environmental fluid mechanics. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary. This book will be of interest to students of fluid mechanics, turbulence, and vortex methods as well as to applied mathematicians and engineers
An application of the WienerHermite expansion to the diffusion of a passive scalar in a homogeneous turbulent flow by
P. G Saffman(
Book
)
4 editions published between 1967 and 1968 in English and held by 21 WorldCat member libraries worldwide
The report describes the application of a truncated WienerHermite expansion of the velocity and concentration fields to analyze (1) the diffusion and mixing of a passive scalar from a point source in a turbulent fluid, and (2) the spectrum and intensity decay of a homogeneous distribution in an approximately homogeneous flow. The problem has important practical applications in reentry physics and air and water pollution. The truncated WienerHermite expansion is treated as an approximation to the velocity field that must satisfy the NavierStokes equations; it is truncated at the first stage that gives nontrivial results. The mean concentration from a point source is shown to satisfy an integrodifferential equation with diffusive and wavelike properties. The effective diffusivity is determined in terms of Eulerian velocity coordinates. For the homogeneous case, the concentration spectrum equals the energy spectrum times the meansquare concentration divided by the meansquare velocity component. A modification of Batchelor's theory is combined with this equation to predict the decay rate
4 editions published between 1967 and 1968 in English and held by 21 WorldCat member libraries worldwide
The report describes the application of a truncated WienerHermite expansion of the velocity and concentration fields to analyze (1) the diffusion and mixing of a passive scalar from a point source in a turbulent fluid, and (2) the spectrum and intensity decay of a homogeneous distribution in an approximately homogeneous flow. The problem has important practical applications in reentry physics and air and water pollution. The truncated WienerHermite expansion is treated as an approximation to the velocity field that must satisfy the NavierStokes equations; it is truncated at the first stage that gives nontrivial results. The mean concentration from a point source is shown to satisfy an integrodifferential equation with diffusive and wavelike properties. The effective diffusivity is determined in terms of Eulerian velocity coordinates. For the homogeneous case, the concentration spectrum equals the energy spectrum times the meansquare concentration divided by the meansquare velocity component. A modification of Batchelor's theory is combined with this equation to predict the decay rate
Research in Nonlinear Water Waves(
Book
)
8 editions published between 1989 and 1991 in English and held by 5 WorldCat member libraries worldwide
Work has progressed in two areas. First, the study of finite amplitude waves and wave instabilities in the presence of a thin wind drift layer has continued. With regard to finite amplitude waves, the formulation of the problem in terms of integral equations for the surface shape, which will allow steep (or even overhanging) waves to be calculated, has been completed. The remaining task is to settle the counting issue, i.e. ensure that the number of waves is equal to the number of unknowns, which is proving to be a difficult and tricky problem, and then we should be able to start calculating wave shapes. Keywords: Ocean waves. (cp)
8 editions published between 1989 and 1991 in English and held by 5 WorldCat member libraries worldwide
Work has progressed in two areas. First, the study of finite amplitude waves and wave instabilities in the presence of a thin wind drift layer has continued. With regard to finite amplitude waves, the formulation of the problem in terms of integral equations for the surface shape, which will allow steep (or even overhanging) waves to be calculated, has been completed. The remaining task is to settle the counting issue, i.e. ensure that the number of waves is equal to the number of unknowns, which is proving to be a difficult and tricky problem, and then we should be able to start calculating wave shapes. Keywords: Ocean waves. (cp)
The motion of a vortex filament with axial flow by D. W Moore(
Book
)
2 editions published in 1972 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1972 in English and held by 3 WorldCat member libraries worldwide
Exact solutions for twodimensional Stokes flow by
Darren G Crowdy(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
A spherical vortex model for homogeneous turbulence by Keri A Aivazis(
Book
)
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
SaffmanTaylor fingers in deformed HeleShaw cells /cDonal A. Gallagher ; P.G. Saffman, advisor by Donal A Gallagher(
Book
)
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
Randon advection of a passive scalar by
James P Gleeson(
Book
)
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide
Part I. Vortex dynamics in wake models. : Part II. Wave generation by David J Hill(
Book
)
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1998 in English and held by 2 WorldCat member libraries worldwide
The Stability of Inviscid Vortex Streets of Finite Cored Vortices by
Mathematics Research Center (United States. Army)(
Book
)
2 editions published in 1984 in English and held by 1 WorldCat member library worldwide
The stability of twodimensional infinitesimal disturbances of the inviscid Karman vortex street of finite area vortices is reexamined. Numerical results are obtained for the growth rate and oscillation frequencies of disturbances of arbitrary subharmonic wavenumber and the stability boundaries are calculated. The stabilization of the pairing instability by finite area demonstrated by Staffman and Schatzman (1982) is confirmed and also Kida's (1982) result that this is not the most unstable disturbance when the area is finite. Contrary, however, to Kida's quantitative predictions, it is now found that finite area does not stabilize the street to infinitesimal twodimensional disturbances of arbitrary wavelength and that it is always unstable except for one isolated value of the aspect ratio which depends upon the size of the vortices. (Author)
2 editions published in 1984 in English and held by 1 WorldCat member library worldwide
The stability of twodimensional infinitesimal disturbances of the inviscid Karman vortex street of finite area vortices is reexamined. Numerical results are obtained for the growth rate and oscillation frequencies of disturbances of arbitrary subharmonic wavenumber and the stability boundaries are calculated. The stabilization of the pairing instability by finite area demonstrated by Staffman and Schatzman (1982) is confirmed and also Kida's (1982) result that this is not the most unstable disturbance when the area is finite. Contrary, however, to Kida's quantitative predictions, it is now found that finite area does not stabilize the street to infinitesimal twodimensional disturbances of arbitrary wavelength and that it is always unstable except for one isolated value of the aspect ratio which depends upon the size of the vortices. (Author)
Viscous fingering in HeleShaw cells by
P. G Saffman(
)
1 edition published in 1986 in Undetermined and held by 1 WorldCat member library worldwide
The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (HeleShaw cell) is considered. This flow is currently of interest because of its relation to pattern selection mechanisms and the formation of fractal, structures in a number of physical applications. Attention is concentrated on the fingers that result from the instability when a lessviscous fluid drives a moreviscous one. The status of the problem is reviewed and progress with the thirtyyearold problem of explaining the shape and stability of the fingers is described. The paradoxes and controversies are both mathematical and physical. Theoretical results on the structure and stability of steady shapes are presented for a particular formulation of the boundary conditions at the interface and compared with the experimental phenomenon. Alternative boundary conditions and future approaches are discussed
1 edition published in 1986 in Undetermined and held by 1 WorldCat member library worldwide
The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (HeleShaw cell) is considered. This flow is currently of interest because of its relation to pattern selection mechanisms and the formation of fractal, structures in a number of physical applications. Attention is concentrated on the fingers that result from the instability when a lessviscous fluid drives a moreviscous one. The status of the problem is reviewed and progress with the thirtyyearold problem of explaining the shape and stability of the fingers is described. The paradoxes and controversies are both mathematical and physical. Theoretical results on the structure and stability of steady shapes are presented for a particular formulation of the boundary conditions at the interface and compared with the experimental phenomenon. Alternative boundary conditions and future approaches are discussed
A model of vortex reconnection by
P. G Saffman(
)
1 edition published in 1990 in Undetermined and held by 1 WorldCat member library worldwide
A model is proposed to describe the breaking and rejoining of vortex lines which occurs when vortex filaments of equal and opposite strengths touch. It is based on the idea that viscosity cancels the vorticity where the filaments first touch. The weakening of the centrifugal force in the vortex core then leads to a local increase in the pressure which accelerates the fluid in the cores in the axial direction and convects the vorticity away from the initial contact and produces an apparent rejoining. Hyperbolic equations to describe the process are formulated and numerical solutions are obtained. Estimates of the timescales are made and compared with the experimental data of Schatzle (1987). Reasonable agreement is found
1 edition published in 1990 in Undetermined and held by 1 WorldCat member library worldwide
A model is proposed to describe the breaking and rejoining of vortex lines which occurs when vortex filaments of equal and opposite strengths touch. It is based on the idea that viscosity cancels the vorticity where the filaments first touch. The weakening of the centrifugal force in the vortex core then leads to a local increase in the pressure which accelerates the fluid in the cores in the axial direction and convects the vorticity away from the initial contact and produces an apparent rejoining. Hyperbolic equations to describe the process are formulated and numerical solutions are obtained. Estimates of the timescales are made and compared with the experimental data of Schatzle (1987). Reasonable agreement is found
Part I: Inviscid, swirling flows and vortex breakdown Part II: A numerical investigation of the Lundgren turbulence model
: thesis by James D Buntine(
Book
)
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
1 edition published in 1994 in English and held by 1 WorldCat member library worldwide
Water Wave Instability Induced by a Drift Layer(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
A simple instability mechanism by which water waves can extract energy from a shear flow is isolated. A cubic equation is derived which provides the instability criteria and the growth rate. This mechanism is effective only if the surface drift velocity exceeds the minimum wave speed, which is approximately 23 cm/s in water, and only if the drift layer thickness exceeds a minimum value which is comparable with the unstable wavelength. In the situation of a sufficiently strong wind blowing over a flat calm, this mechanism is triggered early in the development stage, and appears to dominate the initial growth stages of centimeter waves. (JHD)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
A simple instability mechanism by which water waves can extract energy from a shear flow is isolated. A cubic equation is derived which provides the instability criteria and the growth rate. This mechanism is effective only if the surface drift velocity exceeds the minimum wave speed, which is approximately 23 cm/s in water, and only if the drift layer thickness exceeds a minimum value which is comparable with the unstable wavelength. In the situation of a sufficiently strong wind blowing over a flat calm, this mechanism is triggered early in the development stage, and appears to dominate the initial growth stages of centimeter waves. (JHD)
The thermal Rayleigh problem in perfect and ionized gases by Carlos NavarroCantero(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The motion of a sphere in a cylinder filled with a viscous liquid and with a diameter slightly larger than the sphere diameter by Hermanus Snel(
Book
)
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
1 edition published in 1970 in English and held by 1 WorldCat member library worldwide
The rotation of a gravitating sphere in a monatomic gas. The drag of a body moving transversely in a confined stratified fluid by
Michael R Foster(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Dynamics of vorticity by
P. G Saffman(
)
1 edition published in 1981 in Undetermined and held by 1 WorldCat member library worldwide
Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current interest are described
1 edition published in 1981 in Undetermined and held by 1 WorldCat member library worldwide
Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current interest are described
Vortex interactions by
P. G Saffman(
)
1 edition published in 1979 in Undetermined and held by 1 WorldCat member library worldwide
In the past decade, the study of vortices and vortex motions ["the sinews and muscles of fluid motions" (Küchemann 1965)] has received impetus from problems arising in physics, engineering, and mathematics. The theory of line vortices and vortex rings is a part of modern macroscopic treatments of liquid helium II (Donnelly & Roberts 1974) and has stimulated much work on assemblies of line vortices and the properties of vortex rings, particularly in bounded geometries. The persistent trailing vortices behind jumbo jets constitute a hazard to other aircraft, which has led to a study of vortex formation by the rollup of vortex sheets and the decay and interaction of vortex pairs. The attempt to understand turbulence in two dimensions has led to studies (following Onsager 1949) of the statistical mechanics of random arrays of point vortices
1 edition published in 1979 in Undetermined and held by 1 WorldCat member library worldwide
In the past decade, the study of vortices and vortex motions ["the sinews and muscles of fluid motions" (Küchemann 1965)] has received impetus from problems arising in physics, engineering, and mathematics. The theory of line vortices and vortex rings is a part of modern macroscopic treatments of liquid helium II (Donnelly & Roberts 1974) and has stimulated much work on assemblies of line vortices and the properties of vortex rings, particularly in bounded geometries. The persistent trailing vortices behind jumbo jets constitute a hazard to other aircraft, which has led to a study of vortex formation by the rollup of vortex sheets and the decay and interaction of vortex pairs. The attempt to understand turbulence in two dimensions has led to studies (following Onsager 1949) of the statistical mechanics of random arrays of point vortices
Application of the WienerHermite Expansion to the Diffusion of a Passive Scalar in a Homogeneous Turbulent Flow by
P. G Saffman(
)
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
The stochastic expansion of Cameron, Martin, and Wiener is used for the velocity and concentration fields in a homogeneous turbulent flow convecting a passive scalar. The expansion is truncated and analytical solutions are obtained for the concentration field with the velocity distribution given and molecular diffusion neglected. For diffusion from a point source, the effective diffusivity is found in terms of Eulerian velocity correlations. For a statistically homogeneous scalar distribution, the spectrum function is determined in terms of the energy spectrum function. When the Prandtl number is large, the results obtained do not agree with the predictions of the universal equilibrium hypothesis
1 edition published in 1969 in Undetermined and held by 1 WorldCat member library worldwide
The stochastic expansion of Cameron, Martin, and Wiener is used for the velocity and concentration fields in a homogeneous turbulent flow convecting a passive scalar. The expansion is truncated and analytical solutions are obtained for the concentration field with the velocity distribution given and molecular diffusion neglected. For diffusion from a point source, the effective diffusivity is found in terms of Eulerian velocity correlations. For a statistically homogeneous scalar distribution, the spectrum function is determined in terms of the energy spectrum function. When the Prandtl number is large, the results obtained do not agree with the predictions of the universal equilibrium hypothesis
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