1Department of Mechanical Engineering, Indian Institute of Technology, Madras, Chennai-600036, India, Email: shaligt@iitm.ac.in
2Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, Kanpur-208016, India, Email: gtm@iitk.ac.in
3Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, U.S.A. Email: Mihir.Sen.1@nd.edu
The present investigation has been carried out using Lagrangian approach to study the flow field arising due to interaction of two and three inviscid and fixed vortex filaments with their axes mutually perpendicular to each other. The equations governing motion of a fluid particle form a dynamical system which is a set of three nonlinear ordinary differential equations. The dynamical system for intersecting vortex system is found to be integrable and the path of a fluid particle closed. Moreover, the small axial separation of first two vortices acts like a perturbation parameter with respect to the closed path. Presence of third vortex in the flow field of the first two vortices results into an interesting particle kinematics. Also, the translational superposition on the considered boundless velocity field has been investigated. Results are analyzed by considering path of a fluid particle, Poincare maps of its trajectory on a predefined plane, temporal evolution of transverse velocity of the fluid particle and its Fourier spectrum. The sensitivity of fluid particle motion has been examined to changes in the initial position of the particle. The interacting vortex field in presence of translation shows sensitivity to initial conditions.
Lagrangian study, inviscid vortices, orthogonal orientation, dynamical system, fluid mixing, chaotic transition, critical strength
