Nonshielded multipolar vortices at high Reynolds number

Area of Science:

• Fluid Dynamics
• Computational Physics
• Turbulence Research

Background:

• Vortex multipoles, characterized by a central core and surrounding opposite-sign vorticity, are complex structures in fluid dynamics.
• Previous observations of these structures were limited to those emerging from zero-circulation initial conditions.

Purpose of the Study:

• To investigate the formation and characteristics of vortex multipoles.
• To explore the emergence of these structures from non-zero total circulation initial conditions.
• To propose new asymptotic solutions for the Navier-Stokes equations based on observed vortex configurations.

Main Methods:

• Utilized a meshless vortex method for two-dimensional simulations of vorticity evolution.
• Analyzed the resulting vortical structures, including triangular, square, and pentagonal formations.

Main Results:

• Successfully obtained triangular and square vortex multipoles, each with a distinct number of surrounding satellite vortices.
• Observed the formation of a pentagon vortex structure.
• Crucially, achieved the generation of compound vortices exhibiting non-zero total circulation.

Conclusions:

• Demonstrated the possibility of forming vortex multipoles with non-zero total circulation.
• The findings expand the understanding of vortical structure formation in fluid dynamics.
• Suggested a range of multipolar asymptotic solutions relevant to the Navier-Stokes equations.