tsutomu kambe | The University of Tokyo (original) (raw)

Papers by tsutomu kambe

Research paper thumbnail of NEW SCENARIO OF TURBULENCE THEORY AND WALL TURBULENCE

New general scenario of turbulence theory is proposed and applied to wall turbulence. The theory ... more New general scenario of turbulence theory is proposed and applied to wall turbulence. The theory introduces a new wave field supported by a mathematical theorem, and predicts transverse traveling waves. The predictions are consistent with characteristic features of wall turbulence observed in experimental studies. There is a dynamical mechanism in streaky wall flows to excite a wave field, and there exists an energy channel from the flow field to the wave field. Traveling waves predicted by the theory are characterized by two scales of wavelength and damping-length, whose significance is discussed in relation to the two large scales of LSM and VLSM observed in experiments. The waves are accompanied with a new mechanism of energy dissipation, i.e. a new law of internal friction analogous to the Joule effect of electric current. Bulk energy dissipation is expressed in a form analogous to those of eddy-viscosity. WALL TURBULENCE AND NEW FIELD Large scale features is one of the main subjects in the study of wall turbulence such as boundary layer flows or pipe flows. Studies of pipe flows in the past decades have revealed that, at transition to turbulence, the flow supports transverse traveling waves with cross-stream modes. A new scenario of turbulence theory [1] is proposed by introducing a new field into the turbulence field. The theory supports transverse traveling waves. Significance of this formulation rests on a mathematical theorem and formulation by [2 a ,b], stating that a conservation law of current flux implies existence of fields governed by Maxwell-like equations, which supports transverse traveling waves. Along with the fields, a new dissipation mechanism of energy is introduced with the action of an internal friction (Joule-like effect). From numerical studies of pipe-flow and wall-bounded flows [3 a, b, c], it is found that transverse traveling waves are generated by the help of body forces (i.e. introducing external agents), although final results are obtained without such forces. It is not clear why such a complex procedure is required in the study of natural phenomena. A stability analysis of channel turbulence [4] found existence of a disturbance wave-mode observed in the experiments. However, in order to obtain such a wave, a variable turbulent eddy viscosity had to be used instead of the constant molecular viscosity. Turning our attention to the drag coefficient, empirical laws must be used for fully developed pipe turbulence. These may imply that the current theory fails to predict the pipe turbulence adequately. A wind-tunnel experiment of boundary layer flows [5] verified delay of transition to turbulence by a worked-out design on the wall enforcing streaky flow in the wall layer. In wall turbulence, there are ample experimental evidences of streaky large-scale structures: LSM (large-scale motions) and VLSM (very-large-scale motions) [6a, 6b, 7], which are characterized with streamwise streaks and long meandering structures. The LSMs are considered to be created by the vortex packets consisting of hairpin structures, while question of how the scale VLSM is mechanically generated remains open. With a streamwise energy spectrum with respect to a wave number , the pre-multiplied streamwise spectra have two peaks at LSM of 1 and at VLSM of 15 (where is the pipe radius and the streamwise scale), and decays beyond VLSM. The energy spectrum takes a scaling form in the wavenumber section between the two scales, while at higher 's. Here, the newly introduced field is called Transverse-Wave field, TW-field in short. Two dynamical mechanisms are newly found: a mechanism exciting the TW-waves and the other a channel supplying energy to the TW-field. This is studied by a model equation: derived from the present theory described in the next section. The LHS is a wave equation describing a transverse traveling wave of (a fluid-electric field defined below). The second term on RHS is a damping term, while the first is a term exciting the wave and supplying energy to the TW-field by extracting from the flow field. Most importantly, the TW-field accompanies its own mechanism of energy dissipation due to a fluid-Joule effect. This effect is caused by a drift current , newly introduced to the new field, where is a fluid-resistivity. The fluid-Joule loss is given by. The Joule loss can be written in a form analogous to the viscous rate of dissipation. In fact, using and , we have , The Joule viscosity is analogous to the eddy-viscosity. Here, the velocity is the speed of transverse wave in turbulence and the length is the damping distance. NEW SCENARIO OF TURBULENCE THEORY A new scenario of turbulence theory is formulated here without self-contradiction by introducing a new TW-field, which is governed by fluid-Maxwell equations, because conservation of the current is a basic property of fluid turbulence.

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Research paper thumbnail of Recent findings from computational fluid-dynamics - Drag on cylinders, vortex sound and turbulence statistics

30th Fluid Dynamics Conference, 1999

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Research paper thumbnail of Rotational state of BEC-Kambe-FDR-2014

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Research paper thumbnail of Elementary Fluid Mechanics (Translated to Persian Language)

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Research paper thumbnail of 水波のパラメトリック励振 : Nonlinear dynamics and chaos(流れの不安定性と乱流)

数理解析研究所講究録, Jun 1, 1988

... Л~7 ^ Ь V у -p ШШ '■ N on linear dynam fcs and chaos( A uthor(s) К am be, T sutom u ; U ... more ... Л~7 ^ Ь V у -p ШШ '■ N on linear dynam fcs and chaos( A uthor(s) К am be, T sutom u ; U m eki, M akoto ; К aratsu ... Benjamin Ь Ursell (1954) explained the excitation of standing waves of an inviscid liquid which is associated with the instability of solutions of Mathieu equation for ...

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Research paper thumbnail of Preprint-Kambe2013-FDR2013

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Research paper thumbnail of Geometrical Theory of Dynamical Systems and Fluid Flows

Advanced Series in Nonlinear Dynamics, 2009

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Research paper thumbnail of Elementary Fluid Mechanics

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Research paper thumbnail of Vortex sound with special reference to vortex rings: theory, computer simulations, and experiments

International Journal of Aeroacoustics, 2010

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Research paper thumbnail of Direct Numerical Simulation of Transition in Plane Poiseuille Flow

Fluid Mechanics and Its Applications, 2001

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Research paper thumbnail of Statistical Laws Governed by Vortex Structures in Fully Developed Turbulence

Fluid Mechanics and Its Applications, 2001

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Research paper thumbnail of Vorticity in Flow Fields (in Relation to Prandtl s Work and Subsequent Developments)

Solid mechanics and its applications, 2006

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Research paper thumbnail of On the rotational state of a Bose–Einstein condensate

Fluid Dynamics Research, 2014

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Research paper thumbnail of Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systems

An Introduction to the Geometry and Topology of Fluid Flows, 2001

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Research paper thumbnail of On Fluid Maxwell Equations

Springer Proceedings in Physics, 2014

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Research paper thumbnail of Simulation of Invariant Shapes of a Vortex Filament with an Elastic Rod

J Phys Soc Jpn, 1985

The equilibrium form of a thin elastic rod of circular cross section with the bending stiffness A... more The equilibrium form of a thin elastic rod of circular cross section with the bending stiffness A and torsional rigidity C is found to simulate the shape of a motion of thin vortex filament rotating with a constant anglar velocity \mbi{\varOmega} and translating with a constant velocity \mbi{V} and slipping along the filament with a constant speed c, obeying the so-called local induction equation. We have only to satisfy \varOmega0C{=}Ac, \mbi{T}0{=}A\mbi{\varOmega} and \mbi{M}0{=}A\mbi{V}, where the constants \mbi{T}0, \mbi{M}0 and \varOmega0 corresponding respectively to the internal stress, the moment on the cross-section and the torsion angle per unit length are determined by the boundary conditions.

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Research paper thumbnail of Vortex motion; Proceedings of the IUTAM Symposium on Fundamental Aspects of Vortex Motion, Tokyo, Japan, Aug. 31-Sept. 4, 1987

Nasa Sti Recon Technical Report a, Aug 30, 1988

The conference presents papers on two-dimensional vortices, ring and three-dimensional vortices, ... more The conference presents papers on two-dimensional vortices, ring and three-dimensional vortices, reconnection of vortices, vortex breakdown, stability and turbulence, vortex and sound, high-speed flow, and stratified and rotating fluids. Particular attention is given to the elementary aspects of vortex motion, waves on vortex cores, nonlinear analysis for the evolution of vortex sheets, chaos and collapse of a system of point vortices, and the shedding of vorticity from a smooth surface. Other topics include the bifurcation of an elliptic vortex ring, vortex filament motion in terms of Jacobi theta functions, reconnections of vortex filaments, numerical prediction of vortex breakdown, isoenstrophy points and surfaces in turbulent flow and mixing, the vortex pair in a compressible ideal gas, and vortex motions in stratified wake flows.

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Research paper thumbnail of Stability of an Axisymmetric Wake

Journal of the Physical Society of Japan, Mar 1, 1968

The stability of an axisymmetric wake is studied relative to infinitesimal axisymmetric disturban... more The stability of an axisymmetric wake is studied relative to infinitesimal axisymmetric disturbances. The Orr-Sommerfeld equation is solved by an expansion in powers of α R, where α is the non-dimensional wave number and R the Reynolds number with respect to the effective radius and the velocity defect in the center of the wake. The critical Reynolds number is found to be 5.19. The asymptotic behavior of the neutral curve as α→ 0 is such that R→ 1.08α-1 and c→ 0.676.

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Research paper thumbnail of Conditional Averages and Probability Density Functions in the Passive Scalar Field

J Phys Soc Jpn, 1998

Two conditional averages for the increment Δ( x, x+ r) ≡T( x)-T( x+ r) of the scalar field are es... more Two conditional averages for the increment Δ( x, x+ r) ≡T( x)-T( x+ r) of the scalar field are estimated for DNS data:H(Δ)=<∇ x2 Δ( x, x+ r)|Δ( x, x+ r)> andG(Δ)=<|∇ x Δ( x, x+ r)|2| Δ( x, x+ r)>. The probability density function P(Δ) for Δ( x, x+ r) isalso calculated.If Δ, P(Δ), H(Δ), and G(Δ) are expressedas θ, P(θ), h(θ), and g(θ) in a dimensionless form,the data analysis has revealed interesting simple relationships between them:(1) g(θ)P(θ) ˜ \exp(-\int_0θ du h(u)/g(u)) derivedby Ching and Kraichnan was numerically confirmed perfectly, (2) g(θ)P(θ) pass through an almost common point for any scale rangingfrom the dissipative to the inertial, to the energy containing scale,(3) by using fitting parameters A and β as a function of r,h(θ)/g(θ) is satisfactorily fitted by (A/β)tanh(βθ), and then g(θ)P(θ) ˜(cosh βθ)-A/β2.These relations may be helpful to construct a turbulence model.

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Research paper thumbnail of Riemannian Geometrical Analysis of the Motion of a Vortex Filament: A System of C8(S1,SO(3))

Physical Review Letters, Sep 1, 1996

The motion of an isolated vortex filament with small curvature is governed by the local induction... more The motion of an isolated vortex filament with small curvature is governed by the local induction equation. The present work is an attempt to study such an integrable system based on the Riemannian geometry of the solution manifold, by reformulating the governing equation as the geodesic equation on an infinite dimensional Lie group C∞S1,SO(3). The sectional curvatures for the vector fields along the geodesic curves and their perturbations are calculated to show their tendency to be positive for some typical filaments such as a straight vortex, a helical vortex, and a vortex soliton.

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Research paper thumbnail of NEW SCENARIO OF TURBULENCE THEORY AND WALL TURBULENCE

New general scenario of turbulence theory is proposed and applied to wall turbulence. The theory ... more New general scenario of turbulence theory is proposed and applied to wall turbulence. The theory introduces a new wave field supported by a mathematical theorem, and predicts transverse traveling waves. The predictions are consistent with characteristic features of wall turbulence observed in experimental studies. There is a dynamical mechanism in streaky wall flows to excite a wave field, and there exists an energy channel from the flow field to the wave field. Traveling waves predicted by the theory are characterized by two scales of wavelength and damping-length, whose significance is discussed in relation to the two large scales of LSM and VLSM observed in experiments. The waves are accompanied with a new mechanism of energy dissipation, i.e. a new law of internal friction analogous to the Joule effect of electric current. Bulk energy dissipation is expressed in a form analogous to those of eddy-viscosity. WALL TURBULENCE AND NEW FIELD Large scale features is one of the main subjects in the study of wall turbulence such as boundary layer flows or pipe flows. Studies of pipe flows in the past decades have revealed that, at transition to turbulence, the flow supports transverse traveling waves with cross-stream modes. A new scenario of turbulence theory [1] is proposed by introducing a new field into the turbulence field. The theory supports transverse traveling waves. Significance of this formulation rests on a mathematical theorem and formulation by [2 a ,b], stating that a conservation law of current flux implies existence of fields governed by Maxwell-like equations, which supports transverse traveling waves. Along with the fields, a new dissipation mechanism of energy is introduced with the action of an internal friction (Joule-like effect). From numerical studies of pipe-flow and wall-bounded flows [3 a, b, c], it is found that transverse traveling waves are generated by the help of body forces (i.e. introducing external agents), although final results are obtained without such forces. It is not clear why such a complex procedure is required in the study of natural phenomena. A stability analysis of channel turbulence [4] found existence of a disturbance wave-mode observed in the experiments. However, in order to obtain such a wave, a variable turbulent eddy viscosity had to be used instead of the constant molecular viscosity. Turning our attention to the drag coefficient, empirical laws must be used for fully developed pipe turbulence. These may imply that the current theory fails to predict the pipe turbulence adequately. A wind-tunnel experiment of boundary layer flows [5] verified delay of transition to turbulence by a worked-out design on the wall enforcing streaky flow in the wall layer. In wall turbulence, there are ample experimental evidences of streaky large-scale structures: LSM (large-scale motions) and VLSM (very-large-scale motions) [6a, 6b, 7], which are characterized with streamwise streaks and long meandering structures. The LSMs are considered to be created by the vortex packets consisting of hairpin structures, while question of how the scale VLSM is mechanically generated remains open. With a streamwise energy spectrum with respect to a wave number , the pre-multiplied streamwise spectra have two peaks at LSM of 1 and at VLSM of 15 (where is the pipe radius and the streamwise scale), and decays beyond VLSM. The energy spectrum takes a scaling form in the wavenumber section between the two scales, while at higher 's. Here, the newly introduced field is called Transverse-Wave field, TW-field in short. Two dynamical mechanisms are newly found: a mechanism exciting the TW-waves and the other a channel supplying energy to the TW-field. This is studied by a model equation: derived from the present theory described in the next section. The LHS is a wave equation describing a transverse traveling wave of (a fluid-electric field defined below). The second term on RHS is a damping term, while the first is a term exciting the wave and supplying energy to the TW-field by extracting from the flow field. Most importantly, the TW-field accompanies its own mechanism of energy dissipation due to a fluid-Joule effect. This effect is caused by a drift current , newly introduced to the new field, where is a fluid-resistivity. The fluid-Joule loss is given by. The Joule loss can be written in a form analogous to the viscous rate of dissipation. In fact, using and , we have , The Joule viscosity is analogous to the eddy-viscosity. Here, the velocity is the speed of transverse wave in turbulence and the length is the damping distance. NEW SCENARIO OF TURBULENCE THEORY A new scenario of turbulence theory is formulated here without self-contradiction by introducing a new TW-field, which is governed by fluid-Maxwell equations, because conservation of the current is a basic property of fluid turbulence.

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Research paper thumbnail of Recent findings from computational fluid-dynamics - Drag on cylinders, vortex sound and turbulence statistics

30th Fluid Dynamics Conference, 1999

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Research paper thumbnail of Rotational state of BEC-Kambe-FDR-2014

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Research paper thumbnail of Elementary Fluid Mechanics (Translated to Persian Language)

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Research paper thumbnail of 水波のパラメトリック励振 : Nonlinear dynamics and chaos(流れの不安定性と乱流)

数理解析研究所講究録, Jun 1, 1988

... Л~7 ^ Ь V у -p ШШ '■ N on linear dynam fcs and chaos( A uthor(s) К am be, T sutom u ; U ... more ... Л~7 ^ Ь V у -p ШШ '■ N on linear dynam fcs and chaos( A uthor(s) К am be, T sutom u ; U m eki, M akoto ; К aratsu ... Benjamin Ь Ursell (1954) explained the excitation of standing waves of an inviscid liquid which is associated with the instability of solutions of Mathieu equation for ...

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Research paper thumbnail of Preprint-Kambe2013-FDR2013

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Research paper thumbnail of Geometrical Theory of Dynamical Systems and Fluid Flows

Advanced Series in Nonlinear Dynamics, 2009

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Research paper thumbnail of Elementary Fluid Mechanics

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Vortex sound with special reference to vortex rings: theory, computer simulations, and experiments

International Journal of Aeroacoustics, 2010

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Research paper thumbnail of Direct Numerical Simulation of Transition in Plane Poiseuille Flow

Fluid Mechanics and Its Applications, 2001

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Research paper thumbnail of Statistical Laws Governed by Vortex Structures in Fully Developed Turbulence

Fluid Mechanics and Its Applications, 2001

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Research paper thumbnail of Vorticity in Flow Fields (in Relation to Prandtl s Work and Subsequent Developments)

Solid mechanics and its applications, 2006

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Research paper thumbnail of On the rotational state of a Bose–Einstein condensate

Fluid Dynamics Research, 2014

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Research paper thumbnail of Introduction to a Geometrical Theory of Fluid Flows and Dynamical Systems

An Introduction to the Geometry and Topology of Fluid Flows, 2001

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Research paper thumbnail of On Fluid Maxwell Equations

Springer Proceedings in Physics, 2014

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Research paper thumbnail of Simulation of Invariant Shapes of a Vortex Filament with an Elastic Rod

J Phys Soc Jpn, 1985

The equilibrium form of a thin elastic rod of circular cross section with the bending stiffness A... more The equilibrium form of a thin elastic rod of circular cross section with the bending stiffness A and torsional rigidity C is found to simulate the shape of a motion of thin vortex filament rotating with a constant anglar velocity \mbi{\varOmega} and translating with a constant velocity \mbi{V} and slipping along the filament with a constant speed c, obeying the so-called local induction equation. We have only to satisfy \varOmega0C{=}Ac, \mbi{T}0{=}A\mbi{\varOmega} and \mbi{M}0{=}A\mbi{V}, where the constants \mbi{T}0, \mbi{M}0 and \varOmega0 corresponding respectively to the internal stress, the moment on the cross-section and the torsion angle per unit length are determined by the boundary conditions.

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Research paper thumbnail of Vortex motion; Proceedings of the IUTAM Symposium on Fundamental Aspects of Vortex Motion, Tokyo, Japan, Aug. 31-Sept. 4, 1987

Nasa Sti Recon Technical Report a, Aug 30, 1988

The conference presents papers on two-dimensional vortices, ring and three-dimensional vortices, ... more The conference presents papers on two-dimensional vortices, ring and three-dimensional vortices, reconnection of vortices, vortex breakdown, stability and turbulence, vortex and sound, high-speed flow, and stratified and rotating fluids. Particular attention is given to the elementary aspects of vortex motion, waves on vortex cores, nonlinear analysis for the evolution of vortex sheets, chaos and collapse of a system of point vortices, and the shedding of vorticity from a smooth surface. Other topics include the bifurcation of an elliptic vortex ring, vortex filament motion in terms of Jacobi theta functions, reconnections of vortex filaments, numerical prediction of vortex breakdown, isoenstrophy points and surfaces in turbulent flow and mixing, the vortex pair in a compressible ideal gas, and vortex motions in stratified wake flows.

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Research paper thumbnail of Stability of an Axisymmetric Wake

Journal of the Physical Society of Japan, Mar 1, 1968

The stability of an axisymmetric wake is studied relative to infinitesimal axisymmetric disturban... more The stability of an axisymmetric wake is studied relative to infinitesimal axisymmetric disturbances. The Orr-Sommerfeld equation is solved by an expansion in powers of α R, where α is the non-dimensional wave number and R the Reynolds number with respect to the effective radius and the velocity defect in the center of the wake. The critical Reynolds number is found to be 5.19. The asymptotic behavior of the neutral curve as α→ 0 is such that R→ 1.08α-1 and c→ 0.676.

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Research paper thumbnail of Conditional Averages and Probability Density Functions in the Passive Scalar Field

J Phys Soc Jpn, 1998

Two conditional averages for the increment Δ( x, x+ r) ≡T( x)-T( x+ r) of the scalar field are es... more Two conditional averages for the increment Δ( x, x+ r) ≡T( x)-T( x+ r) of the scalar field are estimated for DNS data:H(Δ)=<∇ x2 Δ( x, x+ r)|Δ( x, x+ r)> andG(Δ)=<|∇ x Δ( x, x+ r)|2| Δ( x, x+ r)>. The probability density function P(Δ) for Δ( x, x+ r) isalso calculated.If Δ, P(Δ), H(Δ), and G(Δ) are expressedas θ, P(θ), h(θ), and g(θ) in a dimensionless form,the data analysis has revealed interesting simple relationships between them:(1) g(θ)P(θ) ˜ \exp(-\int_0θ du h(u)/g(u)) derivedby Ching and Kraichnan was numerically confirmed perfectly, (2) g(θ)P(θ) pass through an almost common point for any scale rangingfrom the dissipative to the inertial, to the energy containing scale,(3) by using fitting parameters A and β as a function of r,h(θ)/g(θ) is satisfactorily fitted by (A/β)tanh(βθ), and then g(θ)P(θ) ˜(cosh βθ)-A/β2.These relations may be helpful to construct a turbulence model.

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Research paper thumbnail of Riemannian Geometrical Analysis of the Motion of a Vortex Filament: A System of C8(S1,SO(3))

Physical Review Letters, Sep 1, 1996

The motion of an isolated vortex filament with small curvature is governed by the local induction... more The motion of an isolated vortex filament with small curvature is governed by the local induction equation. The present work is an attempt to study such an integrable system based on the Riemannian geometry of the solution manifold, by reformulating the governing equation as the geodesic equation on an infinite dimensional Lie group C∞S1,SO(3). The sectional curvatures for the vector fields along the geodesic curves and their perturbations are calculated to show their tendency to be positive for some typical filaments such as a straight vortex, a helical vortex, and a vortex soliton.

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