Interaction of inviscid vortices having orthogonal orientations

The present investigation has been carried out from Lagrangian perspective to study the flow field arising due to two and three inviscid and fixed vortex filaments with their axes mutually perpendicular to each other. The equations governing the motion of a fluid particle are a set of three nonlinear ordinary differential equations. For two vortices, the existence of fixed points has been found only when they have their axes intersecting and no such points exist when their axes are skewed. The dynamical system for vortices having intersecting axes is found to be integrable and the path of a fluid particle is closed. Also, the small axial separation of first two vortices acts like a perturbation parameter with respect to the closed path. Adding a third vortex filament to the flow field of the first two vortices produces an interesting change in the nature of the flow field. There exist critical values for the strength of the third vortex corresponding to which the temporal characteristics show sharp changes. This critical value is found to show weak dependence upon axial separation of the first two skewed vortices considered. Also, the influence of external uniform flow on the considered boundless velocity field has been investigated. Results are presented in the form of path of a fluid particle, transverse velocity of the fluid particle, the Fourier spectrum of the velocity signal and Poincare maps of the time series. PACS code: 47.10.-g; 47.10.Fg; 47.15.ki.