Kinematic Dynamo — Magnetic Field Generation
Roberts / ABC flow stretching, twisting, and folding magnetic field lines
Field energy: 0.00Growth rate: 0.00Time: 0
The kinematic dynamo problem asks: can a prescribed fluid flow self-sustain a magnetic field against Ohmic dissipation? The field evolves via the induction equation ∂B/∂t = ∇×(u×B) + (1/Rm)∇²B, where Rm = UL/η is the magnetic Reynolds number. At high enough Rm, stretching and folding of field lines can amplify the field exponentially — the fast dynamo conjecture. The Roberts flow (u = (sin y, sin x, cos x + cos y)) and ABC flows are classic examples. This simulation shows the 2D magnetic field (Bx, By) being stretched by the chaotic flow. Colors encode field strength, arrows show orientation. Growth rate λ > 0 signals dynamo action.