Interaction of a skewed Rankine vortex pair

An analytical investigation is carried out to study the kinematics of a fluid particle in an interacting field of a skewed pair of fixed Rankine vortices. A general formulation governing the kinematics of a fluid particle has been presented based on the superposition of the velocity field due to each vortex in the pair. The kinematics of a Lagrangian fluid particle is found to be governed by a nonlinear dynamical system. The fixed or stationary points of the dynamical system have been identified analytically and their existence is confirmed by the nature of particle paths in the neighborhood of fixed points. The nature of the particle path and velocity signal is reported for general as well as special configurations of the vortex pair in the presence and absence of an external uniform flow. As a specific application of the proposed problem, superimposition of the translational velocity on a semi-infinite field of longitudinal vortices generated by vortex generators mounted on fin plates of heat exchangers has also been studied. © 2008 American Institute of Physics.