Dynamo transition under Taylor-Green forcing
Department of Physics, Indian Institute of Technology - Kanpur 208016, India
2 Department of Mechanical Engineering, Indian Institute of Technology - Kanpur 208016, India
Accepted: 6 September 2010
We perform pseudo-spectral simulations of the Taylor-Green dynamo for magnetic Prandtl number of one and produce a bifurcation diagram near the dynamo transition. We observe that the primary dynamo transition is through a supercritical pitchfork bifurcation. We show that the planar magnetic structures near the dynamo transition are due to the emergence of the B(0, 0, 1) and B(0, 0, 2) magnetic Fourier modes, which are born as a result of triadic interactions. Near the transition, the kinetic energy (Eu) and the magnetic energy (Eb) grow linearly with the forcing amplitude F0 with the same slope. The ratio Eb/Eu for F0=[0, 40] ranges from 0 to 3. Beyond the transition, the numerical simulations reveal complex dynamo states with windows of constant, periodic, quasiperiodic, and chaotic magnetic field configurations.
PACS: 91.25.Cw – Origins and models of the magnetic field; dynamo theories / 52.65.Kj – Magnetohydrodynamic and fluid equation / 47.20.Ky – Nonlinearity, bifurcation, and symmetry breaking
© EPLA, 2010