### Citations

11 |
On the theory of hydromagnetic dynamos.
- Ponomarenko
- 1973
(Show Context)
Citation Context ... asymptotic structure of the growing modes is analysed as Rm →∞. This is the first laminar, pressure-driven dynamo to be found. INTRODUCTION A velocity field giving rise to spontaneous magnetic field generation in a conducting fluid is known as a kinematic dynamo. Various simple examples of kinematic dynamos are known, but there are very few dynamically self-consistent examples, in which the initial instability grows to a level where it interacts with the driving mechanism. In this paper we consider configurations with helical symmetry, as originally formulated by [1] and [2]. The Ponomarenko [3] kinematic dynamo can be regarded as a special case of helical flow. Here, a fully nonlinear laminar dynamo driven merely by a steady pressure gradient along a pipe is described. The pipe has a helical shape with a rectangular cross-section, as shown in figure 1. The work has relevance to the construction of laboratory dynamos [4]. Further details can be found in [6]. HELICALLY SYMMETRIC PIPE FLOW Helical symmetry is a natural generalisation of two-dimensionality (ε = 0) and axisymmetry (ε → ∞.) In terms of cylindrical polar coordinates (r, θ, z), a scalar function is helically symmetric if it... |

10 |
A.J.: Steady flow in a helically symmetric pipe.
- Zabielski, Mestel
- 1998
(Show Context)
Citation Context ...eltrami vector field, H, which is related to the unit coordinate vectors eθ and ez by H = (ez − εreθ)/h 2 where h = (1 + ε2r2)1/2 and ∇∧H = − 2ε h2 H. The Navier-Stokes equations and the magnetic induction equation are invariant with respect to this symmetry, and thus helically symmetric solutions to both can be found. The helically symmetric incompressible flow u can be conveniently represented by two scalar functions v(r, φ) and ψ(r, φ) as u = vH + H ∧∇ψ . The governing equations for ψ and v are geometrically linked. Steady, pressure-driven laminar flow down a helical pipe was calculated in [5] as a function of the hydrodynamic Reynolds number,Re. A solution is shown in figure 2 for an intermediate value ofRe. The two left-hand diagrams show the contours of ψ and v, the cross-pipe and down-pipe flow. An important feature of the flow is that the cross-pipe component has a stagnation point structure, with a weaker, counter-rotating portion in the lower right. The associated field stretching influences dynamo action strongly. DYNAMO ACTION Magnetic fields with the same helical symmetry as the flow are sought. For the kinematic problem, the field B can be decomposed as B = (BH + H ∧∇χ)e... |

1 |
Kinematic dynamo action with helical symmetry in an unbounded fluid conductor.
- Benton
- 1979
(Show Context)
Citation Context ...etic Reynolds number, Rm. The asymptotic structure of the growing modes is analysed as Rm →∞. This is the first laminar, pressure-driven dynamo to be found. INTRODUCTION A velocity field giving rise to spontaneous magnetic field generation in a conducting fluid is known as a kinematic dynamo. Various simple examples of kinematic dynamos are known, but there are very few dynamically self-consistent examples, in which the initial instability grows to a level where it interacts with the driving mechanism. In this paper we consider configurations with helical symmetry, as originally formulated by [1] and [2]. The Ponomarenko [3] kinematic dynamo can be regarded as a special case of helical flow. Here, a fully nonlinear laminar dynamo driven merely by a steady pressure gradient along a pipe is described. The pipe has a helical shape with a rectangular cross-section, as shown in figure 1. The work has relevance to the construction of laboratory dynamos [4]. Further details can be found in [6]. HELICALLY SYMMETRIC PIPE FLOW Helical symmetry is a natural generalisation of two-dimensionality (ε = 0) and axisymmetry (ε → ∞.) In terms of cylindrical polar coordinates (r, θ, z), a scalar function... |

1 |
Exact solutions of the hydrodynamic dynamo problem.
- Lortz
- 1968
(Show Context)
Citation Context ...nolds number, Rm. The asymptotic structure of the growing modes is analysed as Rm →∞. This is the first laminar, pressure-driven dynamo to be found. INTRODUCTION A velocity field giving rise to spontaneous magnetic field generation in a conducting fluid is known as a kinematic dynamo. Various simple examples of kinematic dynamos are known, but there are very few dynamically self-consistent examples, in which the initial instability grows to a level where it interacts with the driving mechanism. In this paper we consider configurations with helical symmetry, as originally formulated by [1] and [2]. The Ponomarenko [3] kinematic dynamo can be regarded as a special case of helical flow. Here, a fully nonlinear laminar dynamo driven merely by a steady pressure gradient along a pipe is described. The pipe has a helical shape with a rectangular cross-section, as shown in figure 1. The work has relevance to the construction of laboratory dynamos [4]. Further details can be found in [6]. HELICALLY SYMMETRIC PIPE FLOW Helical symmetry is a natural generalisation of two-dimensionality (ε = 0) and axisymmetry (ε → ∞.) In terms of cylindrical polar coordinates (r, θ, z), a scalar function is heli... |

1 |
The special issue: MHD dynamo experiments.
- Rädler, Cebers
- 2002
(Show Context)
Citation Context ...re very few dynamically self-consistent examples, in which the initial instability grows to a level where it interacts with the driving mechanism. In this paper we consider configurations with helical symmetry, as originally formulated by [1] and [2]. The Ponomarenko [3] kinematic dynamo can be regarded as a special case of helical flow. Here, a fully nonlinear laminar dynamo driven merely by a steady pressure gradient along a pipe is described. The pipe has a helical shape with a rectangular cross-section, as shown in figure 1. The work has relevance to the construction of laboratory dynamos [4]. Further details can be found in [6]. HELICALLY SYMMETRIC PIPE FLOW Helical symmetry is a natural generalisation of two-dimensionality (ε = 0) and axisymmetry (ε → ∞.) In terms of cylindrical polar coordinates (r, θ, z), a scalar function is helically symmetric if it depends only on r and φ = θ + εz, where ε is a constant. The symmetry direction is designated by the Beltrami vector field, H, which is related to the unit coordinate vectors eθ and ez by H = (ez − εreθ)/h 2 where h = (1 + ε2r2)1/2 and ∇∧H = − 2ε h2 H. The Navier-Stokes equations and the magnetic induction equation are invariant ... |

1 |
Dynamo action in helical pipe
- Zabielski, Mestel
- 2003
(Show Context)
Citation Context ...nt examples, in which the initial instability grows to a level where it interacts with the driving mechanism. In this paper we consider configurations with helical symmetry, as originally formulated by [1] and [2]. The Ponomarenko [3] kinematic dynamo can be regarded as a special case of helical flow. Here, a fully nonlinear laminar dynamo driven merely by a steady pressure gradient along a pipe is described. The pipe has a helical shape with a rectangular cross-section, as shown in figure 1. The work has relevance to the construction of laboratory dynamos [4]. Further details can be found in [6]. HELICALLY SYMMETRIC PIPE FLOW Helical symmetry is a natural generalisation of two-dimensionality (ε = 0) and axisymmetry (ε → ∞.) In terms of cylindrical polar coordinates (r, θ, z), a scalar function is helically symmetric if it depends only on r and φ = θ + εz, where ε is a constant. The symmetry direction is designated by the Beltrami vector field, H, which is related to the unit coordinate vectors eθ and ez by H = (ez − εreθ)/h 2 where h = (1 + ε2r2)1/2 and ∇∧H = − 2ε h2 H. The Navier-Stokes equations and the magnetic induction equation are invariant with respect to this symmetry, and th... |