Objective and widely accepted vortex definition

Establish a widely accepted, objective definition of a vortex that resolves the ambiguity of existing vortex-identification schemes and the difficulty of mathematically describing coherent vortical structures.

Background

The paper notes that vortex identification criteria are commonly derived from velocity-gradient information, pressure-related quantities, streamline geometry, or Lagrangian flow maps. These approaches characterize different local or material aspects of vortical motion, but no single definition is accepted across fluid-mechanics applications.

The unresolved status of the vortex definition motivates the paper’s geometric reinterpretation of existing criteria through pressure-induced curvature. The paper does not resolve the broader problem of constructing a universally accepted objective definition; it only relates established criteria to different geometric quantities.