Trochoidal Paths Traced Out by a Subvortex Revolving Around a Parent Vortex: A Simulation Study

Novel parametric equations are developed to investigate and elucidate the transient behaviors of tracks traced out by a hypothetical subvortex revolving around a hypothetical parent vortex center.  These equations express a set of quantities as explicit functions of independent variables.  The following variables characterize different types of subvortex tracks including trochoidal/cycloidal patterns: (a) speed at which and (b) direction toward which the parent vortex travels, (c) beginning time at which a subvortex track commences, (d) ending time of the track, (e) rotational speed at which the subvortex rotates around the parent vortex, (f) radial distance from parent vortex center to subvortex center, and (g) linear/non-linear parent vortex and subvortex track lengths.  Simulation results show that complex trochoidal/cycloidal-like tracks traced out by the subvortex rotating cyclonically around the parent vortex are produced when (a) subvortex rotational speeds, (b) distances between the subvortex and parent vortex centers, (c) parent vortex speeds (e.g., accelerate, maintain constant speed and decelerate) and directions (e.g., turn left and right), (d) ratios of the subvortex rotational speed to the parent vortex speed, (e) subvortex track length and (f) parent vortex path length are varied.  The evolutionary characteristics of several parameters are plotted against time to interpret the transient behaviors of simulated trochoidal/cycloidal tracks that bear resemblance to the observed tornado damage tracks.