Numerical Analysis of Distortion of a Vortex Filament

Motion of a vortex filament with a narrow core in an inviscid and incompressible fluid otherwise at rest is investigated numerically. Two types of initial conditions, a sinusoidal form with a single Fourier component and that of a superposition of the first and the third components, are assumed. In both cases, interaction between different components occurs owing to the nonlinear property of the governing equation, but the filament does not show random behavior and after a certain time it recurs nearly to the initial state. Analytical treatment is made and the numerical results are confirmed. Next, the case where an external flow field with an axisymmetric potential flow exists is examined, and an onset of randomness is observed. This is considered as due to a computational error amplified through the interaction between the filament and the external flow.