Investigation of trajectories of inviscid fluid particles in two-dimensional rotating boxes

Abstract

The particle trajectories of inviscid fluid flow within two-dimensional rotating (elliptic, triangular, and square) boxes are numerically investigated. The source panel method is employed to represent the instantaneous potential interior flow field, and the Runge–Kutta method is used to track the fluid particles. The analytic solutions for the fluid trajectories for the elliptic box are used to verify the numerical accuracy of the method. The numerical error can be reduced to the level of the round-off error if the panels are properly configured and an appropriate number of panels is used. The stagnation of the particles at the corners of the triangular box is successfully predicted with this method. The corner of the square box is found to be a singularity. A logarithmic complex potential is proposed to account for the singularity, using which the stagnation of the particles at the corner in the square box is also captured. The natural frequency of the particles in the rotating elliptic box is constant throughout the flow domain, and the fluid trajectories are epitrochoidal curves. In the triangular box and the square box, the natural frequency strongly depends on the particle position, and the particle trajectories are similar to epitrochoidal curves. In general, the trajectory patterns depend only on the box rotating frequency and the natural frequency of the fluid particle motion.