Inertial range scaling of inhomogeneous turbulence

TL;DR

This paper explores how inhomogeneity affects the classic $k^{-5/3}$ inertial range scaling in turbulence, proposing a perturbation scaling as $k^{-7/3}$ and validating it through numerical simulations.

Contribution

It introduces a theoretical framework for understanding inhomogeneity effects on turbulence spectra and confirms the predicted scaling with direct numerical simulations.

Findings

Inhomogeneity causes a $k^{-7/3}$ perturbation to the energy spectrum.

Theoretical predictions align with numerical simulation results.

Inhomogeneous turbulence exhibits deviations from classical inertial range scaling.

Abstract

We investigate how inhomogeneity influences the $k^{-5/3}$ inertial range scaling of turbulent kinetic energy spectra (with $k$ the wavenumber). For weak statistical inhomogeneity, the energy spectrum can be described as an equilibrium spectrum plus a perturbation. Theoretical arguments suggest that this latter contribution scales as $k^{-7/3}$. This prediction is assessed using direct numerical simulations of three-dimensional Kolmogorov flow.