Drift, diffusion and divergence

TL;DR

This paper investigates the behavior of Taylor vortices in high-Reynolds-number Taylor-Couette flow, revealing their Brownian motion and divergence in diffusion constant as vortex count decreases.

Contribution

It provides new insights into vortex dynamics, showing that vortices exhibit Brownian motion and their diffusion constant diverges near a critical vortex number.

Findings

Vortices perform Brownian motion in axial direction.

Diffusion constant diverges as vortex number drops below a critical value.

Long-time simulations reveal vortex behavior at high Reynolds numbers.

Abstract

Turbulent Taylor-Couette flow displays traces of axisymmetric Taylor vortices even at high Reynolds numbers. With this motivation, Feldmann & Avila (2025) carry out long-time numerical simulations of axisymmetric high-Reynolds-number Taylor-Couette flow. They find that the Taylor vortices, using the only degree of freedom that remains available to them, carry out Brownian motion in the axial direction, with a diffusion constant that diverges as the number of rolls is reduced below a critical value.