### Citations

332 | Magnetic field generation in electrically conducting fluids, - Moffatt - 1983 |

32 |
Transition from laminar convection to thermal turbulence in a rotating uid layer
- Kuppers, Lorz
- 1969
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Citation Context ...moved by a Galilean transformation. L is kept fixed at a value of 4 and P at 6.8. The Taylor number, measuring the rotation rate, is restricted to values below the critical one for the Küppers-Lortz =-=[31]-=- instability. Here we find the primary convection patterns near onset to be never capable of dynamo action, neither with nor without rotation (for studies of dynamos in rapidly rotating plane layers s... |

29 |
Sur la topologie des ecoulements stationnaires de fluides parfaits
- ARNOL'D
- 1965
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Citation Context ...orticity (∇×v) vectors. The ABC flows satisfy the Beltrami condition, ∇×v = γv, with a constant γ, namely γ = k0, which is a necessary condition for the existence of chaotic domains in Beltrami flows =-=[4]-=-. For this reason, they have received much interest [5,14], notably in the kinematic context as candidates for fast dynamos [6] (for which the growth rate remains bounded from below by a positive cons... |

23 | Thermal Convection with Strongly Temperature-Dependent Viscosity, - Booker - 1976 |

21 | Magnetic structures in a dynamo simulation
- Brandenburg, Jennings, et al.
- 1996
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Citation Context ...y suggestive of Shilnikov-type homoclinic chaos (for details see [7]). 6 3 Dynamo in asymmetric square convection Studies of convection-driven dynamos have concentrated either on turbulent convection =-=[18]-=- or on convection near onset, where simple steady flows can be obtained [19,20]. For Rayleigh-Bénard Boussinesq convection with symmetric top and bottom boundary conditions, i.e. for convection with ... |

13 |
Dynamo action in a family of flows with chaotic streamlines. Geophys. Astrophys. Fluid Dyn
- GALLOWAY, FRISCH
- 1986
(Show Context)
Citation Context ...cessary condition for the existence of chaotic domains in Beltrami flows [4]. For this reason, they have received much interest [5,14], notably in the kinematic context as candidates for fast dynamos =-=[6]-=- (for which the growth rate remains bounded from below by a positive constant as the magnetic diffusivity tends to zero). Imposing an external body force f = −∇2vABC = k20vABC (6) in the NSE and apply... |

12 |
Instabilities of Convection Rolls in a Fluid of Moderate Prandtl
- Busse, Glever
- 1979
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Citation Context ...associated unstable magnetic eigenmode for Pm = 5.5 (b). The values in the horizontal midplane are shown, bright areas indicating positive values. 8 The square pattern appears via the skewed-varicose =-=[34]-=- instability of primary rolls (details are described in [24]). Depending on the initial conditions, cells with rising or descending motion in the center appear. The spectrum of the excited Fourier mod... |

11 |
A note on the stability of a family of space-periodic Beltrami
- Galloway, Frisch
- 1987
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Citation Context ...d structure in real (configuration) space. In kinematic dynamo studies using the ABC flow with A = B = C cigar-like concentrations of the magnetic field about velocity stagnation points were observed =-=[15,17]-=-. The ABC flow with A = B = C has eight stagnation points, which are unstable fixed points of the flow v. The corresponding eigenvalues are real and have signs (+,−,−) or (−,+,+). The intersections of... |

11 | Hexagonal convection cells under conditions of vertical symmetry. - Clever, Busse - 1996 |

10 | Thess. Square cells in surface-tension-driven Benard convection: experiment and theory - Eckert, Bestehorn, et al. - 1998 |

10 |
Convection-driven dynamos in a rotating plane layer
- Jones, Roberts
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Citation Context ...stability. Here we find the primary convection patterns near onset to be never capable of dynamo action, neither with nor without rotation (for studies of dynamos in rapidly rotating plane layers see =-=[32,33]-=-). An example of steady up-square convection in the absence of rotation is shown in Fig. 4(a). (a) (b) Fig. 4. Shadowgraph images of the vertical velocity component vz of an asymmetric square pattern ... |

9 |
The strong field branch of the Childress-Soward dynamo
- Pierre
- 1993
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Citation Context ...stability. Here we find the primary convection patterns near onset to be never capable of dynamo action, neither with nor without rotation (for studies of dynamos in rapidly rotating plane layers see =-=[32,33]-=-). An example of steady up-square convection in the absence of rotation is shown in Fig. 4(a). (a) (b) Fig. 4. Shadowgraph images of the vertical velocity component vz of an asymmetric square pattern ... |

8 |
The growth of a magnetic field in the three-dimensional steady flow of an incompressible fluid. Moskovskii Universitet Vestnik Seriia Matematika Mekhanika
- Arnold, Korkina
- 1983
(Show Context)
Citation Context ...ami condition, ∇×v = γv, with a constant γ, namely γ = k0, which is a necessary condition for the existence of chaotic domains in Beltrami flows [4]. For this reason, they have received much interest =-=[5,14]-=-, notably in the kinematic context as candidates for fast dynamos [6] (for which the growth rate remains bounded from below by a positive constant as the magnetic diffusivity tends to zero). Imposing ... |

8 |
Convection driven hydromagnetic dynamo
- Childress, Soward
- 1972
(Show Context)
Citation Context ...ynamo in asymmetric square convection Studies of convection-driven dynamos have concentrated either on turbulent convection [18] or on convection near onset, where simple steady flows can be obtained =-=[19,20]-=-. For Rayleigh-Bénard Boussinesq convection with symmetric top and bottom boundary conditions, i.e. for convection with up-down reflection symmetry, the preferred convection pattern near onset is rol... |

8 |
Dynamo action in simple convective flows
- Matthews
- 1999
(Show Context)
Citation Context ...ynamo in asymmetric square convection Studies of convection-driven dynamos have concentrated either on turbulent convection [18] or on convection near onset, where simple steady flows can be obtained =-=[19,20]-=-. For Rayleigh-Bénard Boussinesq convection with symmetric top and bottom boundary conditions, i.e. for convection with up-down reflection symmetry, the preferred convection pattern near onset is rol... |

8 |
Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour
- Matthews, Proctor, et al.
- 1995
(Show Context)
Citation Context ...tained in a more general Galerkin ansatz used in [23] to study asymmetric squares in Boussinesq convection. Asymmetric squares were also found numerically in compressible magnetoconvection near onset =-=[35]-=-. Without rotation, the checkerboard pattern solutions are symmetric to reflections in vertical planes parallel to one of the sides of a square (additionally there is a symmetry to up-down reflections... |

7 | Observation of coexisting upflow and downflow hexagons in Boussinesq Rayleigh-Benard convection. - Assenheimer, Steinberg - 1996 |

6 |
Bifurcation to oscillations in three-dimensional Rayleigh-Bénard convection
- Scheel, Seehafer
- 1997
(Show Context)
Citation Context ...he top and bottom planes are assumed to be stress-free, isothermal and impenetrable for matter and electromagnetic energy: ∂vx ∂z = ∂vy ∂z = vz = θ = ∂Bx ∂z = ∂By ∂z = Bz = 0 at z = 0, 1 . (14) As in =-=[29,30]-=- we restrict ourselves to the case of a vanishing mean horizontal flow since such a flow can be removed by a Galilean transformation. L is kept fixed at a value of 4 and P at 6.8. The Taylor number, m... |

5 | Symmetry-breaking bifurcations for the magnetohydrodynamic equations with helical forcing, Phys - Feudel, Seehafer, et al. - 1996 |

5 |
Linear and non-linear dynamos associated with ABC flows
- Galanti, Sulem, et al.
- 1992
(Show Context)
Citation Context ...fusivity tends to zero). Imposing an external body force f = −∇2vABC = k20vABC (6) in the NSE and applying periodic boundary conditions with period 2pi in all three spatial directions, Galanti et al. =-=[15]-=- investigated the system of the MHD equations [Eqs. (1)–(3)]. Numerically simulating the system for different Reynolds numbers and selected initial conditions, they observed that at some critical valu... |

5 | Time-independent square patterns in surface-tension-driven Bénard convection, Phys. Fluids 11 - Schatz, VanHook, et al. - 1999 |

3 | Nonlinear dynamo with ABC forcing, Astron. Astrophys - Seehafer, Feudel, et al. - 1996 |

3 | Nonlinear Galerkin methods for the 3D magnetohydrodynamic equations - Schmidtmann, Feudel, et al. - 1997 |

3 | Nonlinear Galerkin methods based on the concept of determining modes for the magnetohydrodynamic equations - Schmidtmann, Feudel, et al. - 1998 |

3 |
Dynamo bifurcations in an array of driven convectionlike rolls, Phys
- Rüdiger, Feudel, et al.
- 1998
(Show Context)
Citation Context ...ce 2 fABC = −∇2vABC is applied. In the first part of this paper we report bifurcation studies of the MHD equations with the forcing fABC (detailed results are published in Refs. [7–12]; see also Ref. =-=[13]-=- where dynamo bifurcations in an array of driven convection-like rolls similar to the flow in the outer core of the Earth are studied). After that we present results on dynamo action in thermal convec... |

2 | Bifurcation phenomena of the magnetofluid equations - Feudel, Seehafer, et al. - 1996 |

2 |
On the evolution of a magnetic field under the influence of advection and diffusion
- Arnold
- 1984
(Show Context)
Citation Context ...ABC flow [given by Eq. (5)] with a vanishing magnetic field. Its symmetry group is the full equivariance group of the ABC forced MHD equations, the octahedral group O (the rotation group of the cube) =-=[4,14,16]-=-. For varying R, this steady-solution branch was traced and the Jacobian matrix and its eigenvalues were computed in each step. The table in Fig. 1 lists the solution branches detected, along with the... |

2 |
Asymmetric squares as an attracting set in RayleighB\’enard convection
- Busse, \mathrmM
- 1998
(Show Context)
Citation Context ...y or in Bénard-Marangoni convection [25–27], the asymmetric square pattern representing the dominating pattern over a wide range of the control parameters. Details about this pattern can be found in =-=[23,24,28]-=-. In this section we report on the dynamo properties of the asymmetric square pattern. We consider buoyancy-driven rotating convection in an electrically conducting plane fluid layer of thickness d he... |

2 | Heteroclinic behavior in rotating RayleighBénard convection
- Demircan, Scheel, et al.
(Show Context)
Citation Context ...he top and bottom planes are assumed to be stress-free, isothermal and impenetrable for matter and electromagnetic energy: ∂vx ∂z = ∂vy ∂z = vz = θ = ∂Bx ∂z = ∂By ∂z = Bz = 0 at z = 0, 1 . (14) As in =-=[29,30]-=- we restrict ourselves to the case of a vanishing mean horizontal flow since such a flow can be removed by a Galilean transformation. L is kept fixed at a value of 4 and P at 6.8. The Taylor number, m... |

2 |
Linear and nonlinear dynamo action, Phys. Lett. A 249
- Brummell, Cattaneo, et al.
- 1998
(Show Context)
Citation Context ... recent investigations show that the back-reaction of the magnetic field can also extinguish the dynamo. This was observed for flow in triply periodic Cartesian geometry driven by an explicit forcing =-=[36]-=-, spherical dynamo models with rotation and explicit forcing [37] and two-dimensional convection rolls in a plane layer rotating about an oblique axis [20]. Fig. 6(a) shows the time (a) (b) Fig. 6. Ti... |

2 |
On self-killing and self-creating dynamos, Astron
- Fuchs, Rädler, et al.
- 1999
(Show Context)
Citation Context ...c field can also extinguish the dynamo. This was observed for flow in triply periodic Cartesian geometry driven by an explicit forcing [36], spherical dynamo models with rotation and explicit forcing =-=[37]-=- and two-dimensional convection rolls in a plane layer rotating about an oblique axis [20]. Fig. 6(a) shows the time (a) (b) Fig. 6. Time evolutions of kinetic and magnetic energies for (a) T = 0, Ra ... |

1 |
Fluid helicity and dynamo bifurcations, Phys
- Feudel, Seehafer, et al.
- 1995
(Show Context)
Citation Context ...bifurcation parameter R and lose their stability directly to non-magnetic chaotic states. The chaotic attractors found here are strongly suggestive of Shilnikov-type homoclinic chaos (for details see =-=[7]-=-). 6 3 Dynamo in asymmetric square convection Studies of convection-driven dynamos have concentrated either on turbulent convection [18] or on convection near onset, where simple steady flows can be o... |

1 | Nonlinear square patterns in Rayleigh-Bénard convection, Europhys
- Demircan, Seehafer
(Show Context)
Citation Context ...y or in Bénard-Marangoni convection [25–27], the asymmetric square pattern representing the dominating pattern over a wide range of the control parameters. Details about this pattern can be found in =-=[23,24,28]-=-. In this section we report on the dynamo properties of the asymmetric square pattern. We consider buoyancy-driven rotating convection in an electrically conducting plane fluid layer of thickness d he... |