Stochastic Perturbations in Vortex Tube Dynamics

TL;DR

This paper develops a vortex tube dynamics model using a dual lattice formulation within a field theoretical framework, incorporating stochastic forces to better understand turbulence behavior.

Contribution

It introduces a novel vortex tube dynamics model based on a dual lattice formulation and stochastic forcing within the Martin-Siggia-Rose approach.

Findings

Vortex tube evolution can be modeled with an additional white-noise velocity background.

The model aligns with wavelet analysis observations of turbulent flows.

The approach generalizes the Navier-Stokes equations for turbulence analysis.

Abstract

A dual lattice vortex formulation of homogeneous turbulence is developed, within the Martin-Siggia-Rose field theoretical approach. It consists of a generalization of the usual dipole version of the Navier-Stokes equations, known to hold in the limit of vanishing external forcing. We investigate, as a straightforward application of our formalism, the dynamics of closed vortex tubes, randomly stirred at large length scales by gaussian stochastic forces. We find that besides the usual self-induced propagation, the vortex tube evolution may be effectively modeled through the introduction of an additional white-noise correlated velocity field background. The resulting phenomenological picture is closely related to observations previously reported from a wavelet decomposition analysis of turbulent flow configurations.