The early stage of the motion along the gradient of a concentrated vortex structure

TL;DR

This paper provides a rigorous mathematical and numerical analysis of how concentrated vortex structures move along the gradient of a vorticity field in 2D and 3D fluids, explaining vortex aggregation.

Contribution

It offers a novel Lagrangian explanation for vortex aggregation in inviscid fluids, supported by both mathematical proof and numerical simulations.

Findings

Vortex blobs move in the direction of the vorticity gradient.

The analysis extends to nearly vertical vortex filaments in 3D domains.

Numerical simulations support the theoretical results.

Abstract

We give a rigorous mathematical result, supported by numerical simulations, of the aggregation of a concentrated vortex blob with an underlying non-constant vorticity field: the blob moves in the direction of the gradient of the field. It is a unique example of a Lagrangian explanation of aggregation of vortex structures of the same sign in 2D inviscid fluids. The result is also extended to almost vertical vortex filaments in a (possibly thin) three-dimensional domain.