Two-fluid model of the truncated Euler Equations

TL;DR

This paper introduces a two-fluid phenomenological model for the spectrally-truncated 3D Euler equation, capturing the thermalized small scales and validating its dynamics against the original system.

Contribution

It proposes a novel two-fluid model incorporating effective viscosity and thermal diffusion, validated through numerical comparisons with the truncated Euler equation.

Findings

Small scales are quasi-normal.

Effective viscosity and thermal diffusion are quantified.

Model accurately reproduces original dynamics.

Abstract

A phenomenological two-fluid model of the (time-reversible) spectrally-truncated 3D Euler equation is proposed. The thermalized small scales are first shown to be quasi-normal. The effective viscosity and thermal diffusion are then determined, using EDQNM closure and Monte-Carlo numerical computations. Finally, the model is validated by comparing its dynamics with that of the original truncated Euler equation.