Turbulence, cascade and singularity in a generalization of the Constantin-Lax-Majda equation

TL;DR

This paper numerically investigates a generalized one-dimensional fluid turbulence model, revealing turbulent cascade phenomena and their relation to singularities, using tools from turbulence analysis.

Contribution

It introduces a generalized Constantin-Lax-Majda-De Gregorio model and analyzes its turbulent behavior and singularity properties with viscosity and forcing.

Findings

Turbulent cascade of the inviscid invariant occurs in the model.

Properties of the turbulent state relate to singularities in the inviscid case.

Standard turbulence analysis tools are effective in studying this model.

Abstract

We study numerically a Constantin-Lax-Majda-De Gregorio model generalized by Okamoto, Sakajo and Wunsch, which is a model of fluid turbulence in one dimension with an inviscid conservation law. In the presence of the viscosity and two types of the large-scale forcings, we show that turbulent cascade of the inviscid invariant, which is not limited to quadratic quantity, occurs and that properties of this model's turbulent state are related to singularity of the inviscid case by adopting standard tools of analyzing fluid turbulence.