Three-dimensional vortices generated by cluster explosion in ultrasound

Abstract Vortices are a type of fluid movement characterized by a distinct spiral pattern. This pattern is observed in a variety of environments, from weather patterns to astronomical bodies. The precise geometry of the spiral pattern is essential to our understanding of vortices as it provides valuable insights into their formation and behavior. Logarithmic spirals have been proposed to identify spirals in vortices 1-12 . However, the full geometry of the spiral pattern remains unknown 1-30 . Here we present a quantitative analysis of the geometry of two-dimensional and three-dimensional vortices in water, which were created by exposing micro clusters to ultrasound. Some clusters unexpectedly exploded, creating a previously unknown three-dimensional gyroscope-shaped vortex that ejects a sequence of nodes along the vortex’s central axis. Surprisingly, nodes are spaced with their reciprocal distances arranged in arithmetic progression. Other clusters formed two-dimensional vortices that conformed perfectly to the spiral equation rφ=1. The unique yet interrelated geometries of these three- and two-dimensional vortices suggest that the more commonly seen two-dimensional vortex may only represent a subset of the complete representation of three-dimensional vortices. Our research provides an initial framework for understanding the emergence and dynamics of vortices across diverse scientific disciplines.