Nonlinear wave analysis on free surface of magnetic fluid without approximations by using the complex magnetic field

摘要

It is known that even normal magnetic fields can form complex shapes on the free surface of magnetic fluid, and the comprehension on this phenomena requires intensive fluid and magnetic analysis. Especially for magnetic analysis, magnetic field must satisfy both harmonicity and interface conditions dose to the free surface. This paper suggests that its analysis can be simplified by the complex magnetic timid, owing to its harmonicity by nature and the conformal mapping. As a result, the analysis on the shape of the free surface reduces to the determination of the inclination angle θ and the contraction rate τ.