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Papers by Daniel Segel
In turbulent flows the n'th order structure functions S_n(R) scale like R^ζ_n when R is in th... more In turbulent flows the n'th order structure functions S_n(R) scale like R^ζ_n when R is in the "inertial range". Extended Self-Similarity refers to the substantial increase in the range of power law behaviour of S_n(R) when they are plotted as a function of S_2(R) or S_3(R). In this Letter we demonstrate this phenomenon analytically in the context of the "multiscaling" turbulent advection of a passive scalar. This model gives rise to a series of differential equations for the structure functions S_n(R) which can be solved and shown to exhibit extended self similarity. The phenomenon is understood by comparing the equations for S_n(R) to those for S_n(S_2).
Physical Review E, 1996
ABSTRACT
Physical Review Letters, 1996
In turbulent flows the n'th order structure functions Sn(R) scale like R ζn when R is in the "ine... more In turbulent flows the n'th order structure functions Sn(R) scale like R ζn when R is in the "inertial range". Extended Self-Similarity refers to the substantial increase in the range of power law behaviour of Sn(R) when they are plotted as a function of S2(R) or S3(R). In this Letter we demonstrate this phenomenon analytically in the context of the "multiscaling" turbulent advection of a passive scalar. This model gives rise to a series of differential equations for the structure functions Sn(R) which can be solved and shown to exhibit extended self similarity. The phenomenon is understood by comparing the equations for Sn(R) to those for Sn(S2).
Solar and Planetary Dynamos, 1994
Multifractality, Near-singularities and the Role of Stretching in Turbulence AXEL BRANDENBURG Isa... more Multifractality, Near-singularities and the Role of Stretching in Turbulence AXEL BRANDENBURG Isaac Newton Institute for Mathematical Sciences University of ... dimensions Dq, which differ from each other for different orders q if the field possesses singularities (Halsey et al. ...
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1993
Evolving random cellular structures are observed to reach a universal scaling regime. A mean-fiel... more Evolving random cellular structures are observed to reach a universal scaling regime. A mean-field approach to finding fixed-point distributions in cell-side number is extended to distributions for the average area of cells with a given number of sides. This approach leads to simplified equations that can be analyzed analytically and numerically. The theory's results are compared to experimental results on dynamics and distributions in soap froths and good agreement is achieved.
Physical Review E, 1995
ABSTRACT
Physics of Plasmas, 1995
The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, are investigated with... more The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, are investigated with respect to coherence in the direction of the magnetic field. A length scale, which is interpreted as the diameter of the tubes, is derived from the MHD equations. This scale implies that the tendency towards alignment of flux lines in tubes is a diffusion driven phenomenon. The dynamics of the tubes is also investigated; the major conclusion is that stronger tubes are expected to be straighter. These ideas are tested out on data from numerical simulations of turbulent MHD convection. It is also seen that alignment of flux lines increases with the strength of the tube. Possible reasons for this effect are discussed. 0 1995 American Institlate of Physics.
Physical Review A, 1992
The fractal nature of level sets and the multifractal nature of various scalar and vector fields ... more The fractal nature of level sets and the multifractal nature of various scalar and vector fields in hydromagnetic and hydrodynamic turbulence are investigated using data of direct simulations. It turns out that fields whose evolution is governed by stretching terms (vortex ...
Physics of Plasmas, 1995
The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular,are investigated with ... more The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular,are investigated with respect to coherence in the direction of the magnetic field.A length scale, which is interpreted as the diameter of the tubes, is derived fromthe MHD equations. This scale implies that the tendency towards alignment offlux lines in tubes is a diffusion driven phenomenon. The dynamics of the tubesis
In turbulent flows the n'th order structure functions S_n(R) scale like R^ζ_n when R is in th... more In turbulent flows the n'th order structure functions S_n(R) scale like R^ζ_n when R is in the "inertial range". Extended Self-Similarity refers to the substantial increase in the range of power law behaviour of S_n(R) when they are plotted as a function of S_2(R) or S_3(R). In this Letter we demonstrate this phenomenon analytically in the context of the "multiscaling" turbulent advection of a passive scalar. This model gives rise to a series of differential equations for the structure functions S_n(R) which can be solved and shown to exhibit extended self similarity. The phenomenon is understood by comparing the equations for S_n(R) to those for S_n(S_2).
Physical Review E, 1996
ABSTRACT
Physical Review Letters, 1996
In turbulent flows the n'th order structure functions Sn(R) scale like R ζn when R is in the "ine... more In turbulent flows the n'th order structure functions Sn(R) scale like R ζn when R is in the "inertial range". Extended Self-Similarity refers to the substantial increase in the range of power law behaviour of Sn(R) when they are plotted as a function of S2(R) or S3(R). In this Letter we demonstrate this phenomenon analytically in the context of the "multiscaling" turbulent advection of a passive scalar. This model gives rise to a series of differential equations for the structure functions Sn(R) which can be solved and shown to exhibit extended self similarity. The phenomenon is understood by comparing the equations for Sn(R) to those for Sn(S2).
Solar and Planetary Dynamos, 1994
Multifractality, Near-singularities and the Role of Stretching in Turbulence AXEL BRANDENBURG Isa... more Multifractality, Near-singularities and the Role of Stretching in Turbulence AXEL BRANDENBURG Isaac Newton Institute for Mathematical Sciences University of ... dimensions Dq, which differ from each other for different orders q if the field possesses singularities (Halsey et al. ...
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1993
Evolving random cellular structures are observed to reach a universal scaling regime. A mean-fiel... more Evolving random cellular structures are observed to reach a universal scaling regime. A mean-field approach to finding fixed-point distributions in cell-side number is extended to distributions for the average area of cells with a given number of sides. This approach leads to simplified equations that can be analyzed analytically and numerically. The theory's results are compared to experimental results on dynamics and distributions in soap froths and good agreement is achieved.
Physical Review E, 1995
ABSTRACT
Physics of Plasmas, 1995
The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, are investigated with... more The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, are investigated with respect to coherence in the direction of the magnetic field. A length scale, which is interpreted as the diameter of the tubes, is derived from the MHD equations. This scale implies that the tendency towards alignment of flux lines in tubes is a diffusion driven phenomenon. The dynamics of the tubes is also investigated; the major conclusion is that stronger tubes are expected to be straighter. These ideas are tested out on data from numerical simulations of turbulent MHD convection. It is also seen that alignment of flux lines increases with the strength of the tube. Possible reasons for this effect are discussed. 0 1995 American Institlate of Physics.
Physical Review A, 1992
The fractal nature of level sets and the multifractal nature of various scalar and vector fields ... more The fractal nature of level sets and the multifractal nature of various scalar and vector fields in hydromagnetic and hydrodynamic turbulence are investigated using data of direct simulations. It turns out that fields whose evolution is governed by stretching terms (vortex ...
Physics of Plasmas, 1995
The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular,are investigated with ... more The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular,are investigated with respect to coherence in the direction of the magnetic field.A length scale, which is interpreted as the diameter of the tubes, is derived fromthe MHD equations. This scale implies that the tendency towards alignment offlux lines in tubes is a diffusion driven phenomenon. The dynamics of the tubesis