Generalized vortex-model for the inverse cascade of two-dimensional turbulence

TL;DR

This paper introduces a rotor model extending Kirchhoff's vortex model to explain the inverse cascade in 2D turbulence, enabling analysis of energy transfer through dynamical systems theory.

Contribution

The paper presents a novel rotor model with vortex clusters that captures inverse cascade phenomena, bridging vortex dynamics with energy transport analysis.

Findings

Rotor model reproduces inverse cascade behavior

Rotor clustering leads to energy transfer across scales

Model provides a framework for dynamical systems analysis of turbulence

Abstract

We generalize Kirchhoff's point vortex model of two-dimensional fluid motion to a rotor model which exhibits an inverse cascade by the formation of rotor clusters. A rotor is composed of two vortices with like-signed circulations glued together by an overdamped spring. The model is motivated by a treatment of the vorticity equation representing the vorticity field as a superposition of vortices with elliptic Gaussian shapes of variable widths, augmented by a suitable forcing mechanism. The rotor model opens up the way to discuss the energy transport in the inverse cascade on the basis of dynamical systems theory.