Lamb–Oseen vortex pair; stationary vortices; nonlinear dynamical system; particle paths; external pulsation.
The effect of external pulsation on a pair of stationary Lamb–Oseen vortices of equal strength has been analyzed to investigate kinematic behavior of a fluid particle. The assumption of vortices being treated stationary or fixed vortex filaments is valid in a reference frame attached to the vortex system with axes along and perpendicular to the line of their centers. Also, it is assumed that change in core shape and size is much small, with least possibility of core merger. In such situations, periodic particle paths are observed and superposition of pulsation becomes beneficial. In the present work, motion of a representative fluid particle is modeled as a non-linear dynamical system by varying both amplitude and frequency of external pulsation. Effect of external pulsation has been brought out with the help of quantification of deviation from periodic paths by using the concept of total average deviation. Results are presented in terms of particle paths, velocity phase plots, velocity signals and their spectra for varying amplitude and frequency of external pulsation.