Past exam of the mathematics course of the University of Cambridge 2005 iii Paper 75 3 3 Solution Created 2026-10-03 Updated 2026-10-14
In Gaussian units, the ensemble-averaged magnetic energy density isLet , and assume the relevant moment exists and endpoint terms vanish. Twice applying integration by parts to the conservative magnitude equation givesIn particular, the magnetic stretching moment growth for isThis is a kinematic magnetic dynamo result with prescribed velocity statistics and no Ohmic loss. Once the Lorentz force appreciably changes the flow, this indefinitely exponential kinematic approximation is no longer self-consistent.