Ensemble model of turbulence based on states of constant flux in wavenumber space

TL;DR

This paper introduces an ensemble turbulence model based on flow fields with constant flux across wavenumbers, using Monte Carlo sampling to derive energy spectra consistent with theoretical scaling laws.

Contribution

It proposes a novel ensemble model of turbulence based on constant flux states and derives energy spectra matching theoretical predictions.

Findings

Energy spectra follow the $k^{-3}( ext{log}(k/k_b))^{-1/3}$ scaling.

Monte Carlo sampling effectively generates flow fields with desired flux properties.

The model aligns with theoretical turbulence scaling laws.

Abstract

An ensemble model of turbulence is proposed. The ensemble consists of flow fields in which the flux of an inviscid conserved quantity, such as energy (or enstrophy in two-dimensional flow fields), across the wavenumber $k$ is a constant independent of $k$ in an appropriate range. Two-dimensional flow fields of constant enstrophy flux are sampled randomly by a Monte Carlo method. The energy spectra $E_k$ of the flow fields are consistent with the scaling $E_k \propto k^{-3}(\ln(k/k_\mathrm{b}))^{-1/3}$ where $k_\mathrm{b}$ is the bottom wavenumber of the constant-flux range.