One-dimensional model of freely decaying two-dimensional turbulence

TL;DR

This paper introduces a one-dimensional shell-model for 2D turbulence, capturing local and nonlocal interactions, and demonstrates its effectiveness in describing energy spectra in freely decaying turbulence.

Contribution

It presents a novel discrete shell-model linked to the Burgers equation that accurately models key features of 2D turbulence energy spectra.

Findings

The model reproduces the main characteristics of the energy spectrum.

A new approximate scaling solution for the Burgers equation is proposed.

The model effectively captures both local and nonlocal interactions in turbulence.

Abstract

We construct a discrete shell-model for two-dimensional turbulence that takes into account local and nonlocal interactions between velocity modes in Fourier space. In real space, its continuous limit is described by the one-dimensional Burgers equation. We find a novel approximate scaling solution of such an equation and show that it well describes the main characteristics of the energy spectrum in fully developed, freely decaying two-dimensional turbulence.